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  1.  
  2. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3. induction n1; intros; eauto.
  4. simpl.
  5. rewrite IHn1.
  6. simpl.
  7. reflexivity.
  8. Qed.
  9.  
  10. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  11. induction n1; intros; eauto.
  12. simpl.
  13. rewrite IHn1.
  14. simpl.
  15. reflexivity.
  16. Qed.
  17.  
  18. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  19. induction n1; intros; eauto.
  20. simpl.
  21. rewrite IHn1.
  22. simpl.
  23. reflexivity.
  24. Qed.
  25.  
  26. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  27. induction n1; intros; eauto.
  28. simpl.
  29. rewrite IHn1.
  30. simpl.
  31. reflexivity.
  32. Qed.
  33.  
  34. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  35. induction n1; intros; eauto.
  36. simpl.
  37. rewrite IHn1.
  38. simpl.
  39. reflexivity.
  40. Qed.
  41.  
  42. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  43. induction n1; intros; eauto.
  44. simpl.
  45. rewrite IHn1.
  46. simpl.
  47. reflexivity.
  48. Qed.
  49.  
  50. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  51. induction n1; intros; eauto.
  52. simpl.
  53. rewrite IHn1.
  54. simpl.
  55. reflexivity.
  56. Qed.
  57.  
  58. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  59. induction n1; intros; eauto.
  60. simpl.
  61. rewrite IHn1.
  62. simpl.
  63. reflexivity.
  64. Qed.
  65.  
  66. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  67. induction n1; intros; eauto.
  68. simpl.
  69. rewrite IHn1.
  70. simpl.
  71. reflexivity.
  72. Qed.
  73.  
  74. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  75. induction n1; intros; eauto.
  76. simpl.
  77. rewrite IHn1.
  78. simpl.
  79. reflexivity.
  80. Qed.
  81.  
  82. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  83. induction n1; intros; eauto.
  84. simpl.
  85. rewrite IHn1.
  86. simpl.
  87. reflexivity.
  88. Qed.
  89.  
  90. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  91. induction n1; intros; eauto.
  92. simpl.
  93. rewrite IHn1.
  94. simpl.
  95. reflexivity.
  96. Qed.
  97.  
  98. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  99. induction n1; intros; eauto.
  100. simpl.
  101. rewrite IHn1.
  102. simpl.
  103. reflexivity.
  104. Qed.
  105.  
  106. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  107. induction n1; intros; eauto.
  108. simpl.
  109. rewrite IHn1.
  110. simpl.
  111. reflexivity.
  112. Qed.
  113.  
  114. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  115. induction n1; intros; eauto.
  116. simpl.
  117. rewrite IHn1.
  118. simpl.
  119. reflexivity.
  120. Qed.
  121.  
  122. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  123. induction n1; intros; eauto.
  124. simpl.
  125. rewrite IHn1.
  126. simpl.
  127. reflexivity.
  128. Qed.
  129.  
  130. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  131. induction n1; intros; eauto.
  132. simpl.
  133. rewrite IHn1.
  134. simpl.
  135. reflexivity.
  136. Qed.
  137.  
  138. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  139. induction n1; intros; eauto.
  140. simpl.
  141. rewrite IHn1.
  142. simpl.
  143. reflexivity.
  144. Qed.
  145.  
  146. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  147. induction n1; intros; eauto.
  148. simpl.
  149. rewrite IHn1.
  150. simpl.
  151. reflexivity.
  152. Qed.
  153.  
  154. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  155. induction n1; intros; eauto.
  156. simpl.
  157. rewrite IHn1.
  158. simpl.
  159. reflexivity.
  160. Qed.
  161.  
  162. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  163. induction n1; intros; eauto.
  164. simpl.
  165. rewrite IHn1.
  166. simpl.
  167. reflexivity.
  168. Qed.
  169.  
  170. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  171. induction n1; intros; eauto.
  172. simpl.
  173. rewrite IHn1.
  174. simpl.
  175. reflexivity.
  176. Qed.
  177.  
  178. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  179. induction n1; intros; eauto.
  180. simpl.
  181. rewrite IHn1.
  182. simpl.
  183. reflexivity.
  184. Qed.
  185.  
  186. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  187. induction n1; intros; eauto.
  188. simpl.
  189. rewrite IHn1.
  190. simpl.
  191. reflexivity.
  192. Qed.
  193.  
  194. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  195. induction n1; intros; eauto.
  196. simpl.
  197. rewrite IHn1.
  198. simpl.
  199. reflexivity.
  200. Qed.
  201.  
  202. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  203. induction n1; intros; eauto.
  204. simpl.
  205. rewrite IHn1.
  206. simpl.
  207. reflexivity.
  208. Qed.
  209.  
  210. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  211. induction n1; intros; eauto.
  212. simpl.
  213. rewrite IHn1.
  214. simpl.
  215. reflexivity.
  216. Qed.
  217.  
  218. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  219. induction n1; intros; eauto.
  220. simpl.
  221. rewrite IHn1.
  222. simpl.
  223. reflexivity.
  224. Qed.
  225.  
  226. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  227. induction n1; intros; eauto.
  228. simpl.
  229. rewrite IHn1.
  230. simpl.
  231. reflexivity.
  232. Qed.
  233.  
  234. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  235. induction n1; intros; eauto.
  236. simpl.
  237. rewrite IHn1.
  238. simpl.
  239. reflexivity.
  240. Qed.
  241.  
  242. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  243. induction n1; intros; eauto.
  244. simpl.
  245. rewrite IHn1.
  246. simpl.
  247. reflexivity.
  248. Qed.
  249.  
  250. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  251. induction n1; intros; eauto.
  252. simpl.
  253. rewrite IHn1.
  254. simpl.
  255. reflexivity.
  256. Qed.
  257.  
  258. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  259. induction n1; intros; eauto.
  260. simpl.
  261. rewrite IHn1.
  262. simpl.
  263. reflexivity.
  264. Qed.
  265.  
  266. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  267. induction n1; intros; eauto.
  268. simpl.
  269. rewrite IHn1.
  270. simpl.
  271. reflexivity.
  272. Qed.
  273.  
  274. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  275. induction n1; intros; eauto.
  276. simpl.
  277. rewrite IHn1.
  278. simpl.
  279. reflexivity.
  280. Qed.
  281.  
  282. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  283. induction n1; intros; eauto.
  284. simpl.
  285. rewrite IHn1.
  286. simpl.
  287. reflexivity.
  288. Qed.
  289.  
  290. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  291. induction n1; intros; eauto.
  292. simpl.
  293. rewrite IHn1.
  294. simpl.
  295. reflexivity.
  296. Qed.
  297.  
  298. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  299. induction n1; intros; eauto.
  300. simpl.
  301. rewrite IHn1.
  302. simpl.
  303. reflexivity.
  304. Qed.
  305.  
  306. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  307. induction n1; intros; eauto.
  308. simpl.
  309. rewrite IHn1.
  310. simpl.
  311. reflexivity.
  312. Qed.
  313.  
  314. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  315. induction n1; intros; eauto.
  316. simpl.
  317. rewrite IHn1.
  318. simpl.
  319. reflexivity.
  320. Qed.
  321.  
  322. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  323. induction n1; intros; eauto.
  324. simpl.
  325. rewrite IHn1.
  326. simpl.
  327. reflexivity.
  328. Qed.
  329.  
  330. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  331. induction n1; intros; eauto.
  332. simpl.
  333. rewrite IHn1.
  334. simpl.
  335. reflexivity.
  336. Qed.
  337.  
  338. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  339. induction n1; intros; eauto.
  340. simpl.
  341. rewrite IHn1.
  342. simpl.
  343. reflexivity.
  344. Qed.
  345.  
  346. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  347. induction n1; intros; eauto.
  348. simpl.
  349. rewrite IHn1.
  350. simpl.
  351. reflexivity.
  352. Qed.
  353.  
  354. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  355. induction n1; intros; eauto.
  356. simpl.
  357. rewrite IHn1.
  358. simpl.
  359. reflexivity.
  360. Qed.
  361.  
  362. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  363. induction n1; intros; eauto.
  364. simpl.
  365. rewrite IHn1.
  366. simpl.
  367. reflexivity.
  368. Qed.
  369.  
  370. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  371. induction n1; intros; eauto.
  372. simpl.
  373. rewrite IHn1.
  374. simpl.
  375. reflexivity.
  376. Qed.
  377.  
  378. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  379. induction n1; intros; eauto.
  380. simpl.
  381. rewrite IHn1.
  382. simpl.
  383. reflexivity.
  384. Qed.
  385.  
  386. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  387. induction n1; intros; eauto.
  388. simpl.
  389. rewrite IHn1.
  390. simpl.
  391. reflexivity.
  392. Qed.
  393.  
  394. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  395. induction n1; intros; eauto.
  396. simpl.
  397. rewrite IHn1.
  398. simpl.
  399. reflexivity.
  400. Qed.
  401.  
  402. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  403. induction n1; intros; eauto.
  404. simpl.
  405. rewrite IHn1.
  406. simpl.
  407. reflexivity.
  408. Qed.
  409.  
  410. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  411. induction n1; intros; eauto.
  412. simpl.
  413. rewrite IHn1.
  414. simpl.
  415. reflexivity.
  416. Qed.
  417.  
  418. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  419. induction n1; intros; eauto.
  420. simpl.
  421. rewrite IHn1.
  422. simpl.
  423. reflexivity.
  424. Qed.
  425.  
  426. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  427. induction n1; intros; eauto.
  428. simpl.
  429. rewrite IHn1.
  430. simpl.
  431. reflexivity.
  432. Qed.
  433.  
  434. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  435. induction n1; intros; eauto.
  436. simpl.
  437. rewrite IHn1.
  438. simpl.
  439. reflexivity.
  440. Qed.
  441.  
  442. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  443. induction n1; intros; eauto.
  444. simpl.
  445. rewrite IHn1.
  446. simpl.
  447. reflexivity.
  448. Qed.
  449.  
  450. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  451. induction n1; intros; eauto.
  452. simpl.
  453. rewrite IHn1.
  454. simpl.
  455. reflexivity.
  456. Qed.
  457.  
  458. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  459. induction n1; intros; eauto.
  460. simpl.
  461. rewrite IHn1.
  462. simpl.
  463. reflexivity.
  464. Qed.
  465.  
  466. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  467. induction n1; intros; eauto.
  468. simpl.
  469. rewrite IHn1.
  470. simpl.
  471. reflexivity.
  472. Qed.
  473.  
  474. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  475. induction n1; intros; eauto.
  476. simpl.
  477. rewrite IHn1.
  478. simpl.
  479. reflexivity.
  480. Qed.
  481.  
  482. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  483. induction n1; intros; eauto.
  484. simpl.
  485. rewrite IHn1.
  486. simpl.
  487. reflexivity.
  488. Qed.
  489.  
  490. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  491. induction n1; intros; eauto.
  492. simpl.
  493. rewrite IHn1.
  494. simpl.
  495. reflexivity.
  496. Qed.
  497.  
  498. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  499. induction n1; intros; eauto.
  500. simpl.
  501. rewrite IHn1.
  502. simpl.
  503. reflexivity.
  504. Qed.
  505.  
  506. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  507. induction n1; intros; eauto.
  508. simpl.
  509. rewrite IHn1.
  510. simpl.
  511. reflexivity.
  512. Qed.
  513.  
  514. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  515. induction n1; intros; eauto.
  516. simpl.
  517. rewrite IHn1.
  518. simpl.
  519. reflexivity.
  520. Qed.
  521.  
  522. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  523. induction n1; intros; eauto.
  524. simpl.
  525. rewrite IHn1.
  526. simpl.
  527. reflexivity.
  528. Qed.
  529.  
  530. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  531. induction n1; intros; eauto.
  532. simpl.
  533. rewrite IHn1.
  534. simpl.
  535. reflexivity.
  536. Qed.
  537.  
  538. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  539. induction n1; intros; eauto.
  540. simpl.
  541. rewrite IHn1.
  542. simpl.
  543. reflexivity.
  544. Qed.
  545.  
  546. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  547. induction n1; intros; eauto.
  548. simpl.
  549. rewrite IHn1.
  550. simpl.
  551. reflexivity.
  552. Qed.
  553.  
  554. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  555. induction n1; intros; eauto.
  556. simpl.
  557. rewrite IHn1.
  558. simpl.
  559. reflexivity.
  560. Qed.
  561.  
  562. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  563. induction n1; intros; eauto.
  564. simpl.
  565. rewrite IHn1.
  566. simpl.
  567. reflexivity.
  568. Qed.
  569.  
  570. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  571. induction n1; intros; eauto.
  572. simpl.
  573. rewrite IHn1.
  574. simpl.
  575. reflexivity.
  576. Qed.
  577.  
  578. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  579. induction n1; intros; eauto.
  580. simpl.
  581. rewrite IHn1.
  582. simpl.
  583. reflexivity.
  584. Qed.
  585.  
  586. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  587. induction n1; intros; eauto.
  588. simpl.
  589. rewrite IHn1.
  590. simpl.
  591. reflexivity.
  592. Qed.
  593.  
  594. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  595. induction n1; intros; eauto.
  596. simpl.
  597. rewrite IHn1.
  598. simpl.
  599. reflexivity.
  600. Qed.
  601.  
  602. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  603. induction n1; intros; eauto.
  604. simpl.
  605. rewrite IHn1.
  606. simpl.
  607. reflexivity.
  608. Qed.
  609.  
  610. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  611. induction n1; intros; eauto.
  612. simpl.
  613. rewrite IHn1.
  614. simpl.
  615. reflexivity.
  616. Qed.
  617.  
  618. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  619. induction n1; intros; eauto.
  620. simpl.
  621. rewrite IHn1.
  622. simpl.
  623. reflexivity.
  624. Qed.
  625.  
  626. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  627. induction n1; intros; eauto.
  628. simpl.
  629. rewrite IHn1.
  630. simpl.
  631. reflexivity.
  632. Qed.
  633.  
  634. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  635. induction n1; intros; eauto.
  636. simpl.
  637. rewrite IHn1.
  638. simpl.
  639. reflexivity.
  640. Qed.
  641.  
  642. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  643. induction n1; intros; eauto.
  644. simpl.
  645. rewrite IHn1.
  646. simpl.
  647. reflexivity.
  648. Qed.
  649.  
  650. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  651. induction n1; intros; eauto.
  652. simpl.
  653. rewrite IHn1.
  654. simpl.
  655. reflexivity.
  656. Qed.
  657.  
  658. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  659. induction n1; intros; eauto.
  660. simpl.
  661. rewrite IHn1.
  662. simpl.
  663. reflexivity.
  664. Qed.
  665.  
  666. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  667. induction n1; intros; eauto.
  668. simpl.
  669. rewrite IHn1.
  670. simpl.
  671. reflexivity.
  672. Qed.
  673.  
  674. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  675. induction n1; intros; eauto.
  676. simpl.
  677. rewrite IHn1.
  678. simpl.
  679. reflexivity.
  680. Qed.
  681.  
  682. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  683. induction n1; intros; eauto.
  684. simpl.
  685. rewrite IHn1.
  686. simpl.
  687. reflexivity.
  688. Qed.
  689.  
  690. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  691. induction n1; intros; eauto.
  692. simpl.
  693. rewrite IHn1.
  694. simpl.
  695. reflexivity.
  696. Qed.
  697.  
  698. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  699. induction n1; intros; eauto.
  700. simpl.
  701. rewrite IHn1.
  702. simpl.
  703. reflexivity.
  704. Qed.
  705.  
  706. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  707. induction n1; intros; eauto.
  708. simpl.
  709. rewrite IHn1.
  710. simpl.
  711. reflexivity.
  712. Qed.
  713.  
  714. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  715. induction n1; intros; eauto.
  716. simpl.
  717. rewrite IHn1.
  718. simpl.
  719. reflexivity.
  720. Qed.
  721.  
  722. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  723. induction n1; intros; eauto.
  724. simpl.
  725. rewrite IHn1.
  726. simpl.
  727. reflexivity.
  728. Qed.
  729.  
  730. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  731. induction n1; intros; eauto.
  732. simpl.
  733. rewrite IHn1.
  734. simpl.
  735. reflexivity.
  736. Qed.
  737.  
  738. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  739. induction n1; intros; eauto.
  740. simpl.
  741. rewrite IHn1.
  742. simpl.
  743. reflexivity.
  744. Qed.
  745.  
  746. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  747. induction n1; intros; eauto.
  748. simpl.
  749. rewrite IHn1.
  750. simpl.
  751. reflexivity.
  752. Qed.
  753.  
  754. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  755. induction n1; intros; eauto.
  756. simpl.
  757. rewrite IHn1.
  758. simpl.
  759. reflexivity.
  760. Qed.
  761.  
  762. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  763. induction n1; intros; eauto.
  764. simpl.
  765. rewrite IHn1.
  766. simpl.
  767. reflexivity.
  768. Qed.
  769.  
  770. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  771. induction n1; intros; eauto.
  772. simpl.
  773. rewrite IHn1.
  774. simpl.
  775. reflexivity.
  776. Qed.
  777.  
  778. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  779. induction n1; intros; eauto.
  780. simpl.
  781. rewrite IHn1.
  782. simpl.
  783. reflexivity.
  784. Qed.
  785.  
  786. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  787. induction n1; intros; eauto.
  788. simpl.
  789. rewrite IHn1.
  790. simpl.
  791. reflexivity.
  792. Qed.
  793.  
  794. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  795. induction n1; intros; eauto.
  796. simpl.
  797. rewrite IHn1.
  798. simpl.
  799. reflexivity.
  800. Qed.
  801.  
  802. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  803. induction n1; intros; eauto.
  804. simpl.
  805. rewrite IHn1.
  806. simpl.
  807. reflexivity.
  808. Qed.
  809.  
  810. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  811. induction n1; intros; eauto.
  812. simpl.
  813. rewrite IHn1.
  814. simpl.
  815. reflexivity.
  816. Qed.
  817.  
  818. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  819. induction n1; intros; eauto.
  820. simpl.
  821. rewrite IHn1.
  822. simpl.
  823. reflexivity.
  824. Qed.
  825.  
  826. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  827. induction n1; intros; eauto.
  828. simpl.
  829. rewrite IHn1.
  830. simpl.
  831. reflexivity.
  832. Qed.
  833.  
  834. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  835. induction n1; intros; eauto.
  836. simpl.
  837. rewrite IHn1.
  838. simpl.
  839. reflexivity.
  840. Qed.
  841.  
  842. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  843. induction n1; intros; eauto.
  844. simpl.
  845. rewrite IHn1.
  846. simpl.
  847. reflexivity.
  848. Qed.
  849.  
  850. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  851. induction n1; intros; eauto.
  852. simpl.
  853. rewrite IHn1.
  854. simpl.
  855. reflexivity.
  856. Qed.
  857.  
  858. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  859. induction n1; intros; eauto.
  860. simpl.
  861. rewrite IHn1.
  862. simpl.
  863. reflexivity.
  864. Qed.
  865.  
  866. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  867. induction n1; intros; eauto.
  868. simpl.
  869. rewrite IHn1.
  870. simpl.
  871. reflexivity.
  872. Qed.
  873.  
  874. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  875. induction n1; intros; eauto.
  876. simpl.
  877. rewrite IHn1.
  878. simpl.
  879. reflexivity.
  880. Qed.
  881.  
  882. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  883. induction n1; intros; eauto.
  884. simpl.
  885. rewrite IHn1.
  886. simpl.
  887. reflexivity.
  888. Qed.
  889.  
  890. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  891. induction n1; intros; eauto.
  892. simpl.
  893. rewrite IHn1.
  894. simpl.
  895. reflexivity.
  896. Qed.
  897.  
  898. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  899. induction n1; intros; eauto.
  900. simpl.
  901. rewrite IHn1.
  902. simpl.
  903. reflexivity.
  904. Qed.
  905.  
  906. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  907. induction n1; intros; eauto.
  908. simpl.
  909. rewrite IHn1.
  910. simpl.
  911. reflexivity.
  912. Qed.
  913.  
  914. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  915. induction n1; intros; eauto.
  916. simpl.
  917. rewrite IHn1.
  918. simpl.
  919. reflexivity.
  920. Qed.
  921.  
  922. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  923. induction n1; intros; eauto.
  924. simpl.
  925. rewrite IHn1.
  926. simpl.
  927. reflexivity.
  928. Qed.
  929.  
  930. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  931. induction n1; intros; eauto.
  932. simpl.
  933. rewrite IHn1.
  934. simpl.
  935. reflexivity.
  936. Qed.
  937.  
  938. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  939. induction n1; intros; eauto.
  940. simpl.
  941. rewrite IHn1.
  942. simpl.
  943. reflexivity.
  944. Qed.
  945.  
  946. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  947. induction n1; intros; eauto.
  948. simpl.
  949. rewrite IHn1.
  950. simpl.
  951. reflexivity.
  952. Qed.
  953.  
  954. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  955. induction n1; intros; eauto.
  956. simpl.
  957. rewrite IHn1.
  958. simpl.
  959. reflexivity.
  960. Qed.
  961.  
  962. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  963. induction n1; intros; eauto.
  964. simpl.
  965. rewrite IHn1.
  966. simpl.
  967. reflexivity.
  968. Qed.
  969.  
  970. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  971. induction n1; intros; eauto.
  972. simpl.
  973. rewrite IHn1.
  974. simpl.
  975. reflexivity.
  976. Qed.
  977.  
  978. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  979. induction n1; intros; eauto.
  980. simpl.
  981. rewrite IHn1.
  982. simpl.
  983. reflexivity.
  984. Qed.
  985.  
  986. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  987. induction n1; intros; eauto.
  988. simpl.
  989. rewrite IHn1.
  990. simpl.
  991. reflexivity.
  992. Qed.
  993.  
  994. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  995. induction n1; intros; eauto.
  996. simpl.
  997. rewrite IHn1.
  998. simpl.
  999. reflexivity.
  1000. Qed.
  1001.  
  1002. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1003. induction n1; intros; eauto.
  1004. simpl.
  1005. rewrite IHn1.
  1006. simpl.
  1007. reflexivity.
  1008. Qed.
  1009.  
  1010. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1011. induction n1; intros; eauto.
  1012. simpl.
  1013. rewrite IHn1.
  1014. simpl.
  1015. reflexivity.
  1016. Qed.
  1017.  
  1018. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1019. induction n1; intros; eauto.
  1020. simpl.
  1021. rewrite IHn1.
  1022. simpl.
  1023. reflexivity.
  1024. Qed.
  1025.  
  1026. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1027. induction n1; intros; eauto.
  1028. simpl.
  1029. rewrite IHn1.
  1030. simpl.
  1031. reflexivity.
  1032. Qed.
  1033.  
  1034. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1035. induction n1; intros; eauto.
  1036. simpl.
  1037. rewrite IHn1.
  1038. simpl.
  1039. reflexivity.
  1040. Qed.
  1041.  
  1042. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1043. induction n1; intros; eauto.
  1044. simpl.
  1045. rewrite IHn1.
  1046. simpl.
  1047. reflexivity.
  1048. Qed.
  1049.  
  1050. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1051. induction n1; intros; eauto.
  1052. simpl.
  1053. rewrite IHn1.
  1054. simpl.
  1055. reflexivity.
  1056. Qed.
  1057.  
  1058. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1059. induction n1; intros; eauto.
  1060. simpl.
  1061. rewrite IHn1.
  1062. simpl.
  1063. reflexivity.
  1064. Qed.
  1065.  
  1066. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1067. induction n1; intros; eauto.
  1068. simpl.
  1069. rewrite IHn1.
  1070. simpl.
  1071. reflexivity.
  1072. Qed.
  1073.  
  1074. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1075. induction n1; intros; eauto.
  1076. simpl.
  1077. rewrite IHn1.
  1078. simpl.
  1079. reflexivity.
  1080. Qed.
  1081.  
  1082. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1083. induction n1; intros; eauto.
  1084. simpl.
  1085. rewrite IHn1.
  1086. simpl.
  1087. reflexivity.
  1088. Qed.
  1089.  
  1090. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1091. induction n1; intros; eauto.
  1092. simpl.
  1093. rewrite IHn1.
  1094. simpl.
  1095. reflexivity.
  1096. Qed.
  1097.  
  1098. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1099. induction n1; intros; eauto.
  1100. simpl.
  1101. rewrite IHn1.
  1102. simpl.
  1103. reflexivity.
  1104. Qed.
  1105.  
  1106. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1107. induction n1; intros; eauto.
  1108. simpl.
  1109. rewrite IHn1.
  1110. simpl.
  1111. reflexivity.
  1112. Qed.
  1113.  
  1114. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1115. induction n1; intros; eauto.
  1116. simpl.
  1117. rewrite IHn1.
  1118. simpl.
  1119. reflexivity.
  1120. Qed.
  1121.  
  1122. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1123. induction n1; intros; eauto.
  1124. simpl.
  1125. rewrite IHn1.
  1126. simpl.
  1127. reflexivity.
  1128. Qed.
  1129.  
  1130. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1131. induction n1; intros; eauto.
  1132. simpl.
  1133. rewrite IHn1.
  1134. simpl.
  1135. reflexivity.
  1136. Qed.
  1137.  
  1138. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1139. induction n1; intros; eauto.
  1140. simpl.
  1141. rewrite IHn1.
  1142. simpl.
  1143. reflexivity.
  1144. Qed.
  1145.  
  1146. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1147. induction n1; intros; eauto.
  1148. simpl.
  1149. rewrite IHn1.
  1150. simpl.
  1151. reflexivity.
  1152. Qed.
  1153.  
  1154. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1155. induction n1; intros; eauto.
  1156. simpl.
  1157. rewrite IHn1.
  1158. simpl.
  1159. reflexivity.
  1160. Qed.
  1161.  
  1162. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1163. induction n1; intros; eauto.
  1164. simpl.
  1165. rewrite IHn1.
  1166. simpl.
  1167. reflexivity.
  1168. Qed.
  1169.  
  1170. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1171. induction n1; intros; eauto.
  1172. simpl.
  1173. rewrite IHn1.
  1174. simpl.
  1175. reflexivity.
  1176. Qed.
  1177.  
  1178. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1179. induction n1; intros; eauto.
  1180. simpl.
  1181. rewrite IHn1.
  1182. simpl.
  1183. reflexivity.
  1184. Qed.
  1185.  
  1186. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1187. induction n1; intros; eauto.
  1188. simpl.
  1189. rewrite IHn1.
  1190. simpl.
  1191. reflexivity.
  1192. Qed.
  1193.  
  1194. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1195. induction n1; intros; eauto.
  1196. simpl.
  1197. rewrite IHn1.
  1198. simpl.
  1199. reflexivity.
  1200. Qed.
  1201.  
  1202. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1203. induction n1; intros; eauto.
  1204. simpl.
  1205. rewrite IHn1.
  1206. simpl.
  1207. reflexivity.
  1208. Qed.
  1209.  
  1210. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1211. induction n1; intros; eauto.
  1212. simpl.
  1213. rewrite IHn1.
  1214. simpl.
  1215. reflexivity.
  1216. Qed.
  1217.  
  1218. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1219. induction n1; intros; eauto.
  1220. simpl.
  1221. rewrite IHn1.
  1222. simpl.
  1223. reflexivity.
  1224. Qed.
  1225.  
  1226. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1227. induction n1; intros; eauto.
  1228. simpl.
  1229. rewrite IHn1.
  1230. simpl.
  1231. reflexivity.
  1232. Qed.
  1233.  
  1234. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1235. induction n1; intros; eauto.
  1236. simpl.
  1237. rewrite IHn1.
  1238. simpl.
  1239. reflexivity.
  1240. Qed.
  1241.  
  1242. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1243. induction n1; intros; eauto.
  1244. simpl.
  1245. rewrite IHn1.
  1246. simpl.
  1247. reflexivity.
  1248. Qed.
  1249.  
  1250. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1251. induction n1; intros; eauto.
  1252. simpl.
  1253. rewrite IHn1.
  1254. simpl.
  1255. reflexivity.
  1256. Qed.
  1257.  
  1258. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1259. induction n1; intros; eauto.
  1260. simpl.
  1261. rewrite IHn1.
  1262. simpl.
  1263. reflexivity.
  1264. Qed.
  1265.  
  1266. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1267. induction n1; intros; eauto.
  1268. simpl.
  1269. rewrite IHn1.
  1270. simpl.
  1271. reflexivity.
  1272. Qed.
  1273.  
  1274. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1275. induction n1; intros; eauto.
  1276. simpl.
  1277. rewrite IHn1.
  1278. simpl.
  1279. reflexivity.
  1280. Qed.
  1281.  
  1282. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1283. induction n1; intros; eauto.
  1284. simpl.
  1285. rewrite IHn1.
  1286. simpl.
  1287. reflexivity.
  1288. Qed.
  1289.  
  1290. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1291. induction n1; intros; eauto.
  1292. simpl.
  1293. rewrite IHn1.
  1294. simpl.
  1295. reflexivity.
  1296. Qed.
  1297.  
  1298. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1299. induction n1; intros; eauto.
  1300. simpl.
  1301. rewrite IHn1.
  1302. simpl.
  1303. reflexivity.
  1304. Qed.
  1305.  
  1306. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1307. induction n1; intros; eauto.
  1308. simpl.
  1309. rewrite IHn1.
  1310. simpl.
  1311. reflexivity.
  1312. Qed.
  1313.  
  1314. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1315. induction n1; intros; eauto.
  1316. simpl.
  1317. rewrite IHn1.
  1318. simpl.
  1319. reflexivity.
  1320. Qed.
  1321.  
  1322. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1323. induction n1; intros; eauto.
  1324. simpl.
  1325. rewrite IHn1.
  1326. simpl.
  1327. reflexivity.
  1328. Qed.
  1329.  
  1330. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1331. induction n1; intros; eauto.
  1332. simpl.
  1333. rewrite IHn1.
  1334. simpl.
  1335. reflexivity.
  1336. Qed.
  1337.  
  1338. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1339. induction n1; intros; eauto.
  1340. simpl.
  1341. rewrite IHn1.
  1342. simpl.
  1343. reflexivity.
  1344. Qed.
  1345.  
  1346. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1347. induction n1; intros; eauto.
  1348. simpl.
  1349. rewrite IHn1.
  1350. simpl.
  1351. reflexivity.
  1352. Qed.
  1353.  
  1354. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1355. induction n1; intros; eauto.
  1356. simpl.
  1357. rewrite IHn1.
  1358. simpl.
  1359. reflexivity.
  1360. Qed.
  1361.  
  1362. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1363. induction n1; intros; eauto.
  1364. simpl.
  1365. rewrite IHn1.
  1366. simpl.
  1367. reflexivity.
  1368. Qed.
  1369.  
  1370. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1371. induction n1; intros; eauto.
  1372. simpl.
  1373. rewrite IHn1.
  1374. simpl.
  1375. reflexivity.
  1376. Qed.
  1377.  
  1378. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1379. induction n1; intros; eauto.
  1380. simpl.
  1381. rewrite IHn1.
  1382. simpl.
  1383. reflexivity.
  1384. Qed.
  1385.  
  1386. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1387. induction n1; intros; eauto.
  1388. simpl.
  1389. rewrite IHn1.
  1390. simpl.
  1391. reflexivity.
  1392. Qed.
  1393.  
  1394. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1395. induction n1; intros; eauto.
  1396. simpl.
  1397. rewrite IHn1.
  1398. simpl.
  1399. reflexivity.
  1400. Qed.
  1401.  
  1402. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1403. induction n1; intros; eauto.
  1404. simpl.
  1405. rewrite IHn1.
  1406. simpl.
  1407. reflexivity.
  1408. Qed.
  1409.  
  1410. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1411. induction n1; intros; eauto.
  1412. simpl.
  1413. rewrite IHn1.
  1414. simpl.
  1415. reflexivity.
  1416. Qed.
  1417.  
  1418. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1419. induction n1; intros; eauto.
  1420. simpl.
  1421. rewrite IHn1.
  1422. simpl.
  1423. reflexivity.
  1424. Qed.
  1425.  
  1426. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1427. induction n1; intros; eauto.
  1428. simpl.
  1429. rewrite IHn1.
  1430. simpl.
  1431. reflexivity.
  1432. Qed.
  1433.  
  1434. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1435. induction n1; intros; eauto.
  1436. simpl.
  1437. rewrite IHn1.
  1438. simpl.
  1439. reflexivity.
  1440. Qed.
  1441.  
  1442. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1443. induction n1; intros; eauto.
  1444. simpl.
  1445. rewrite IHn1.
  1446. simpl.
  1447. reflexivity.
  1448. Qed.
  1449.  
  1450. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1451. induction n1; intros; eauto.
  1452. simpl.
  1453. rewrite IHn1.
  1454. simpl.
  1455. reflexivity.
  1456. Qed.
  1457.  
  1458. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1459. induction n1; intros; eauto.
  1460. simpl.
  1461. rewrite IHn1.
  1462. simpl.
  1463. reflexivity.
  1464. Qed.
  1465.  
  1466. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1467. induction n1; intros; eauto.
  1468. simpl.
  1469. rewrite IHn1.
  1470. simpl.
  1471. reflexivity.
  1472. Qed.
  1473.  
  1474. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1475. induction n1; intros; eauto.
  1476. simpl.
  1477. rewrite IHn1.
  1478. simpl.
  1479. reflexivity.
  1480. Qed.
  1481.  
  1482. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1483. induction n1; intros; eauto.
  1484. simpl.
  1485. rewrite IHn1.
  1486. simpl.
  1487. reflexivity.
  1488. Qed.
  1489.  
  1490. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1491. induction n1; intros; eauto.
  1492. simpl.
  1493. rewrite IHn1.
  1494. simpl.
  1495. reflexivity.
  1496. Qed.
  1497.  
  1498. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1499. induction n1; intros; eauto.
  1500. simpl.
  1501. rewrite IHn1.
  1502. simpl.
  1503. reflexivity.
  1504. Qed.
  1505.  
  1506. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1507. induction n1; intros; eauto.
  1508. simpl.
  1509. rewrite IHn1.
  1510. simpl.
  1511. reflexivity.
  1512. Qed.
  1513.  
  1514. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1515. induction n1; intros; eauto.
  1516. simpl.
  1517. rewrite IHn1.
  1518. simpl.
  1519. reflexivity.
  1520. Qed.
  1521.  
  1522. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1523. induction n1; intros; eauto.
  1524. simpl.
  1525. rewrite IHn1.
  1526. simpl.
  1527. reflexivity.
  1528. Qed.
  1529.  
  1530. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1531. induction n1; intros; eauto.
  1532. simpl.
  1533. rewrite IHn1.
  1534. simpl.
  1535. reflexivity.
  1536. Qed.
  1537.  
  1538. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1539. induction n1; intros; eauto.
  1540. simpl.
  1541. rewrite IHn1.
  1542. simpl.
  1543. reflexivity.
  1544. Qed.
  1545.  
  1546. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1547. induction n1; intros; eauto.
  1548. simpl.
  1549. rewrite IHn1.
  1550. simpl.
  1551. reflexivity.
  1552. Qed.
  1553.  
  1554. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1555. induction n1; intros; eauto.
  1556. simpl.
  1557. rewrite IHn1.
  1558. simpl.
  1559. reflexivity.
  1560. Qed.
  1561.  
  1562. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1563. induction n1; intros; eauto.
  1564. simpl.
  1565. rewrite IHn1.
  1566. simpl.
  1567. reflexivity.
  1568. Qed.
  1569.  
  1570. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1571. induction n1; intros; eauto.
  1572. simpl.
  1573. rewrite IHn1.
  1574. simpl.
  1575. reflexivity.
  1576. Qed.
  1577.  
  1578. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1579. induction n1; intros; eauto.
  1580. simpl.
  1581. rewrite IHn1.
  1582. simpl.
  1583. reflexivity.
  1584. Qed.
  1585.  
  1586. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1587. induction n1; intros; eauto.
  1588. simpl.
  1589. rewrite IHn1.
  1590. simpl.
  1591. reflexivity.
  1592. Qed.
  1593.  
  1594. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1595. induction n1; intros; eauto.
  1596. simpl.
  1597. rewrite IHn1.
  1598. simpl.
  1599. reflexivity.
  1600. Qed.
  1601.  
  1602. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1603. induction n1; intros; eauto.
  1604. simpl.
  1605. rewrite IHn1.
  1606. simpl.
  1607. reflexivity.
  1608. Qed.
  1609.  
  1610. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1611. induction n1; intros; eauto.
  1612. simpl.
  1613. rewrite IHn1.
  1614. simpl.
  1615. reflexivity.
  1616. Qed.
  1617.  
  1618. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1619. induction n1; intros; eauto.
  1620. simpl.
  1621. rewrite IHn1.
  1622. simpl.
  1623. reflexivity.
  1624. Qed.
  1625.  
  1626. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1627. induction n1; intros; eauto.
  1628. simpl.
  1629. rewrite IHn1.
  1630. simpl.
  1631. reflexivity.
  1632. Qed.
  1633.  
  1634. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1635. induction n1; intros; eauto.
  1636. simpl.
  1637. rewrite IHn1.
  1638. simpl.
  1639. reflexivity.
  1640. Qed.
  1641.  
  1642. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1643. induction n1; intros; eauto.
  1644. simpl.
  1645. rewrite IHn1.
  1646. simpl.
  1647. reflexivity.
  1648. Qed.
  1649.  
  1650. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1651. induction n1; intros; eauto.
  1652. simpl.
  1653. rewrite IHn1.
  1654. simpl.
  1655. reflexivity.
  1656. Qed.
  1657.  
  1658. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1659. induction n1; intros; eauto.
  1660. simpl.
  1661. rewrite IHn1.
  1662. simpl.
  1663. reflexivity.
  1664. Qed.
  1665.  
  1666. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1667. induction n1; intros; eauto.
  1668. simpl.
  1669. rewrite IHn1.
  1670. simpl.
  1671. reflexivity.
  1672. Qed.
  1673.  
  1674. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1675. induction n1; intros; eauto.
  1676. simpl.
  1677. rewrite IHn1.
  1678. simpl.
  1679. reflexivity.
  1680. Qed.
  1681.  
  1682. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1683. induction n1; intros; eauto.
  1684. simpl.
  1685. rewrite IHn1.
  1686. simpl.
  1687. reflexivity.
  1688. Qed.
  1689.  
  1690. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1691. induction n1; intros; eauto.
  1692. simpl.
  1693. rewrite IHn1.
  1694. simpl.
  1695. reflexivity.
  1696. Qed.
  1697.  
  1698. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1699. induction n1; intros; eauto.
  1700. simpl.
  1701. rewrite IHn1.
  1702. simpl.
  1703. reflexivity.
  1704. Qed.
  1705.  
  1706. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1707. induction n1; intros; eauto.
  1708. simpl.
  1709. rewrite IHn1.
  1710. simpl.
  1711. reflexivity.
  1712. Qed.
  1713.  
  1714. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1715. induction n1; intros; eauto.
  1716. simpl.
  1717. rewrite IHn1.
  1718. simpl.
  1719. reflexivity.
  1720. Qed.
  1721.  
  1722. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1723. induction n1; intros; eauto.
  1724. simpl.
  1725. rewrite IHn1.
  1726. simpl.
  1727. reflexivity.
  1728. Qed.
  1729.  
  1730. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1731. induction n1; intros; eauto.
  1732. simpl.
  1733. rewrite IHn1.
  1734. simpl.
  1735. reflexivity.
  1736. Qed.
  1737.  
  1738. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1739. induction n1; intros; eauto.
  1740. simpl.
  1741. rewrite IHn1.
  1742. simpl.
  1743. reflexivity.
  1744. Qed.
  1745.  
  1746. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1747. induction n1; intros; eauto.
  1748. simpl.
  1749. rewrite IHn1.
  1750. simpl.
  1751. reflexivity.
  1752. Qed.
  1753.  
  1754. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1755. induction n1; intros; eauto.
  1756. simpl.
  1757. rewrite IHn1.
  1758. simpl.
  1759. reflexivity.
  1760. Qed.
  1761.  
  1762. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1763. induction n1; intros; eauto.
  1764. simpl.
  1765. rewrite IHn1.
  1766. simpl.
  1767. reflexivity.
  1768. Qed.
  1769.  
  1770. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1771. induction n1; intros; eauto.
  1772. simpl.
  1773. rewrite IHn1.
  1774. simpl.
  1775. reflexivity.
  1776. Qed.
  1777.  
  1778. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1779. induction n1; intros; eauto.
  1780. simpl.
  1781. rewrite IHn1.
  1782. simpl.
  1783. reflexivity.
  1784. Qed.
  1785.  
  1786. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1787. induction n1; intros; eauto.
  1788. simpl.
  1789. rewrite IHn1.
  1790. simpl.
  1791. reflexivity.
  1792. Qed.
  1793.  
  1794. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1795. induction n1; intros; eauto.
  1796. simpl.
  1797. rewrite IHn1.
  1798. simpl.
  1799. reflexivity.
  1800. Qed.
  1801.  
  1802. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1803. induction n1; intros; eauto.
  1804. simpl.
  1805. rewrite IHn1.
  1806. simpl.
  1807. reflexivity.
  1808. Qed.
  1809.  
  1810. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1811. induction n1; intros; eauto.
  1812. simpl.
  1813. rewrite IHn1.
  1814. simpl.
  1815. reflexivity.
  1816. Qed.
  1817.  
  1818. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1819. induction n1; intros; eauto.
  1820. simpl.
  1821. rewrite IHn1.
  1822. simpl.
  1823. reflexivity.
  1824. Qed.
  1825.  
  1826. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1827. induction n1; intros; eauto.
  1828. simpl.
  1829. rewrite IHn1.
  1830. simpl.
  1831. reflexivity.
  1832. Qed.
  1833.  
  1834. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1835. induction n1; intros; eauto.
  1836. simpl.
  1837. rewrite IHn1.
  1838. simpl.
  1839. reflexivity.
  1840. Qed.
  1841.  
  1842. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1843. induction n1; intros; eauto.
  1844. simpl.
  1845. rewrite IHn1.
  1846. simpl.
  1847. reflexivity.
  1848. Qed.
  1849.  
  1850. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1851. induction n1; intros; eauto.
  1852. simpl.
  1853. rewrite IHn1.
  1854. simpl.
  1855. reflexivity.
  1856. Qed.
  1857.  
  1858. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1859. induction n1; intros; eauto.
  1860. simpl.
  1861. rewrite IHn1.
  1862. simpl.
  1863. reflexivity.
  1864. Qed.
  1865.  
  1866. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1867. induction n1; intros; eauto.
  1868. simpl.
  1869. rewrite IHn1.
  1870. simpl.
  1871. reflexivity.
  1872. Qed.
  1873.  
  1874. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1875. induction n1; intros; eauto.
  1876. simpl.
  1877. rewrite IHn1.
  1878. simpl.
  1879. reflexivity.
  1880. Qed.
  1881.  
  1882. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1883. induction n1; intros; eauto.
  1884. simpl.
  1885. rewrite IHn1.
  1886. simpl.
  1887. reflexivity.
  1888. Qed.
  1889.  
  1890. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1891. induction n1; intros; eauto.
  1892. simpl.
  1893. rewrite IHn1.
  1894. simpl.
  1895. reflexivity.
  1896. Qed.
  1897.  
  1898. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1899. induction n1; intros; eauto.
  1900. simpl.
  1901. rewrite IHn1.
  1902. simpl.
  1903. reflexivity.
  1904. Qed.
  1905.  
  1906. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1907. induction n1; intros; eauto.
  1908. simpl.
  1909. rewrite IHn1.
  1910. simpl.
  1911. reflexivity.
  1912. Qed.
  1913.  
  1914. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1915. induction n1; intros; eauto.
  1916. simpl.
  1917. rewrite IHn1.
  1918. simpl.
  1919. reflexivity.
  1920. Qed.
  1921.  
  1922. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1923. induction n1; intros; eauto.
  1924. simpl.
  1925. rewrite IHn1.
  1926. simpl.
  1927. reflexivity.
  1928. Qed.
  1929.  
  1930. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1931. induction n1; intros; eauto.
  1932. simpl.
  1933. rewrite IHn1.
  1934. simpl.
  1935. reflexivity.
  1936. Qed.
  1937.  
  1938. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1939. induction n1; intros; eauto.
  1940. simpl.
  1941. rewrite IHn1.
  1942. simpl.
  1943. reflexivity.
  1944. Qed.
  1945.  
  1946. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1947. induction n1; intros; eauto.
  1948. simpl.
  1949. rewrite IHn1.
  1950. simpl.
  1951. reflexivity.
  1952. Qed.
  1953.  
  1954. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1955. induction n1; intros; eauto.
  1956. simpl.
  1957. rewrite IHn1.
  1958. simpl.
  1959. reflexivity.
  1960. Qed.
  1961.  
  1962. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1963. induction n1; intros; eauto.
  1964. simpl.
  1965. rewrite IHn1.
  1966. simpl.
  1967. reflexivity.
  1968. Qed.
  1969.  
  1970. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1971. induction n1; intros; eauto.
  1972. simpl.
  1973. rewrite IHn1.
  1974. simpl.
  1975. reflexivity.
  1976. Qed.
  1977.  
  1978. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1979. induction n1; intros; eauto.
  1980. simpl.
  1981. rewrite IHn1.
  1982. simpl.
  1983. reflexivity.
  1984. Qed.
  1985.  
  1986. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1987. induction n1; intros; eauto.
  1988. simpl.
  1989. rewrite IHn1.
  1990. simpl.
  1991. reflexivity.
  1992. Qed.
  1993.  
  1994. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  1995. induction n1; intros; eauto.
  1996. simpl.
  1997. rewrite IHn1.
  1998. simpl.
  1999. reflexivity.
  2000. Qed.
  2001.  
  2002. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2003. induction n1; intros; eauto.
  2004. simpl.
  2005. rewrite IHn1.
  2006. simpl.
  2007. reflexivity.
  2008. Qed.
  2009.  
  2010. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2011. induction n1; intros; eauto.
  2012. simpl.
  2013. rewrite IHn1.
  2014. simpl.
  2015. reflexivity.
  2016. Qed.
  2017.  
  2018. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2019. induction n1; intros; eauto.
  2020. simpl.
  2021. rewrite IHn1.
  2022. simpl.
  2023. reflexivity.
  2024. Qed.
  2025.  
  2026. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2027. induction n1; intros; eauto.
  2028. simpl.
  2029. rewrite IHn1.
  2030. simpl.
  2031. reflexivity.
  2032. Qed.
  2033.  
  2034. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2035. induction n1; intros; eauto.
  2036. simpl.
  2037. rewrite IHn1.
  2038. simpl.
  2039. reflexivity.
  2040. Qed.
  2041.  
  2042. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2043. induction n1; intros; eauto.
  2044. simpl.
  2045. rewrite IHn1.
  2046. simpl.
  2047. reflexivity.
  2048. Qed.
  2049.  
  2050. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2051. induction n1; intros; eauto.
  2052. simpl.
  2053. rewrite IHn1.
  2054. simpl.
  2055. reflexivity.
  2056. Qed.
  2057.  
  2058. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2059. induction n1; intros; eauto.
  2060. simpl.
  2061. rewrite IHn1.
  2062. simpl.
  2063. reflexivity.
  2064. Qed.
  2065.  
  2066. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2067. induction n1; intros; eauto.
  2068. simpl.
  2069. rewrite IHn1.
  2070. simpl.
  2071. reflexivity.
  2072. Qed.
  2073.  
  2074. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2075. induction n1; intros; eauto.
  2076. simpl.
  2077. rewrite IHn1.
  2078. simpl.
  2079. reflexivity.
  2080. Qed.
  2081.  
  2082. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2083. induction n1; intros; eauto.
  2084. simpl.
  2085. rewrite IHn1.
  2086. simpl.
  2087. reflexivity.
  2088. Qed.
  2089.  
  2090. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2091. induction n1; intros; eauto.
  2092. simpl.
  2093. rewrite IHn1.
  2094. simpl.
  2095. reflexivity.
  2096. Qed.
  2097.  
  2098. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2099. induction n1; intros; eauto.
  2100. simpl.
  2101. rewrite IHn1.
  2102. simpl.
  2103. reflexivity.
  2104. Qed.
  2105.  
  2106. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2107. induction n1; intros; eauto.
  2108. simpl.
  2109. rewrite IHn1.
  2110. simpl.
  2111. reflexivity.
  2112. Qed.
  2113.  
  2114. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2115. induction n1; intros; eauto.
  2116. simpl.
  2117. rewrite IHn1.
  2118. simpl.
  2119. reflexivity.
  2120. Qed.
  2121.  
  2122. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2123. induction n1; intros; eauto.
  2124. simpl.
  2125. rewrite IHn1.
  2126. simpl.
  2127. reflexivity.
  2128. Qed.
  2129.  
  2130. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2131. induction n1; intros; eauto.
  2132. simpl.
  2133. rewrite IHn1.
  2134. simpl.
  2135. reflexivity.
  2136. Qed.
  2137.  
  2138. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2139. induction n1; intros; eauto.
  2140. simpl.
  2141. rewrite IHn1.
  2142. simpl.
  2143. reflexivity.
  2144. Qed.
  2145.  
  2146. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2147. induction n1; intros; eauto.
  2148. simpl.
  2149. rewrite IHn1.
  2150. simpl.
  2151. reflexivity.
  2152. Qed.
  2153.  
  2154. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2155. induction n1; intros; eauto.
  2156. simpl.
  2157. rewrite IHn1.
  2158. simpl.
  2159. reflexivity.
  2160. Qed.
  2161.  
  2162. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2163. induction n1; intros; eauto.
  2164. simpl.
  2165. rewrite IHn1.
  2166. simpl.
  2167. reflexivity.
  2168. Qed.
  2169.  
  2170. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2171. induction n1; intros; eauto.
  2172. simpl.
  2173. rewrite IHn1.
  2174. simpl.
  2175. reflexivity.
  2176. Qed.
  2177.  
  2178. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2179. induction n1; intros; eauto.
  2180. simpl.
  2181. rewrite IHn1.
  2182. simpl.
  2183. reflexivity.
  2184. Qed.
  2185.  
  2186. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2187. induction n1; intros; eauto.
  2188. simpl.
  2189. rewrite IHn1.
  2190. simpl.
  2191. reflexivity.
  2192. Qed.
  2193.  
  2194. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2195. induction n1; intros; eauto.
  2196. simpl.
  2197. rewrite IHn1.
  2198. simpl.
  2199. reflexivity.
  2200. Qed.
  2201.  
  2202. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2203. induction n1; intros; eauto.
  2204. simpl.
  2205. rewrite IHn1.
  2206. simpl.
  2207. reflexivity.
  2208. Qed.
  2209.  
  2210. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2211. induction n1; intros; eauto.
  2212. simpl.
  2213. rewrite IHn1.
  2214. simpl.
  2215. reflexivity.
  2216. Qed.
  2217.  
  2218. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2219. induction n1; intros; eauto.
  2220. simpl.
  2221. rewrite IHn1.
  2222. simpl.
  2223. reflexivity.
  2224. Qed.
  2225.  
  2226. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2227. induction n1; intros; eauto.
  2228. simpl.
  2229. rewrite IHn1.
  2230. simpl.
  2231. reflexivity.
  2232. Qed.
  2233.  
  2234. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2235. induction n1; intros; eauto.
  2236. simpl.
  2237. rewrite IHn1.
  2238. simpl.
  2239. reflexivity.
  2240. Qed.
  2241.  
  2242. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2243. induction n1; intros; eauto.
  2244. simpl.
  2245. rewrite IHn1.
  2246. simpl.
  2247. reflexivity.
  2248. Qed.
  2249.  
  2250. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2251. induction n1; intros; eauto.
  2252. simpl.
  2253. rewrite IHn1.
  2254. simpl.
  2255. reflexivity.
  2256. Qed.
  2257.  
  2258. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2259. induction n1; intros; eauto.
  2260. simpl.
  2261. rewrite IHn1.
  2262. simpl.
  2263. reflexivity.
  2264. Qed.
  2265.  
  2266. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2267. induction n1; intros; eauto.
  2268. simpl.
  2269. rewrite IHn1.
  2270. simpl.
  2271. reflexivity.
  2272. Qed.
  2273.  
  2274. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2275. induction n1; intros; eauto.
  2276. simpl.
  2277. rewrite IHn1.
  2278. simpl.
  2279. reflexivity.
  2280. Qed.
  2281.  
  2282. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2283. induction n1; intros; eauto.
  2284. simpl.
  2285. rewrite IHn1.
  2286. simpl.
  2287. reflexivity.
  2288. Qed.
  2289.  
  2290. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2291. induction n1; intros; eauto.
  2292. simpl.
  2293. rewrite IHn1.
  2294. simpl.
  2295. reflexivity.
  2296. Qed.
  2297.  
  2298. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2299. induction n1; intros; eauto.
  2300. simpl.
  2301. rewrite IHn1.
  2302. simpl.
  2303. reflexivity.
  2304. Qed.
  2305.  
  2306. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2307. induction n1; intros; eauto.
  2308. simpl.
  2309. rewrite IHn1.
  2310. simpl.
  2311. reflexivity.
  2312. Qed.
  2313.  
  2314. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2315. induction n1; intros; eauto.
  2316. simpl.
  2317. rewrite IHn1.
  2318. simpl.
  2319. reflexivity.
  2320. Qed.
  2321.  
  2322. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2323. induction n1; intros; eauto.
  2324. simpl.
  2325. rewrite IHn1.
  2326. simpl.
  2327. reflexivity.
  2328. Qed.
  2329.  
  2330. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2331. induction n1; intros; eauto.
  2332. simpl.
  2333. rewrite IHn1.
  2334. simpl.
  2335. reflexivity.
  2336. Qed.
  2337.  
  2338. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2339. induction n1; intros; eauto.
  2340. simpl.
  2341. rewrite IHn1.
  2342. simpl.
  2343. reflexivity.
  2344. Qed.
  2345.  
  2346. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2347. induction n1; intros; eauto.
  2348. simpl.
  2349. rewrite IHn1.
  2350. simpl.
  2351. reflexivity.
  2352. Qed.
  2353.  
  2354. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2355. induction n1; intros; eauto.
  2356. simpl.
  2357. rewrite IHn1.
  2358. simpl.
  2359. reflexivity.
  2360. Qed.
  2361.  
  2362. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2363. induction n1; intros; eauto.
  2364. simpl.
  2365. rewrite IHn1.
  2366. simpl.
  2367. reflexivity.
  2368. Qed.
  2369.  
  2370. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2371. induction n1; intros; eauto.
  2372. simpl.
  2373. rewrite IHn1.
  2374. simpl.
  2375. reflexivity.
  2376. Qed.
  2377.  
  2378. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2379. induction n1; intros; eauto.
  2380. simpl.
  2381. rewrite IHn1.
  2382. simpl.
  2383. reflexivity.
  2384. Qed.
  2385.  
  2386. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2387. induction n1; intros; eauto.
  2388. simpl.
  2389. rewrite IHn1.
  2390. simpl.
  2391. reflexivity.
  2392. Qed.
  2393.  
  2394. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2395. induction n1; intros; eauto.
  2396. simpl.
  2397. rewrite IHn1.
  2398. simpl.
  2399. reflexivity.
  2400. Qed.
  2401.  
  2402. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2403. induction n1; intros; eauto.
  2404. simpl.
  2405. rewrite IHn1.
  2406. simpl.
  2407. reflexivity.
  2408. Qed.
  2409.  
  2410. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2411. induction n1; intros; eauto.
  2412. simpl.
  2413. rewrite IHn1.
  2414. simpl.
  2415. reflexivity.
  2416. Qed.
  2417.  
  2418. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2419. induction n1; intros; eauto.
  2420. simpl.
  2421. rewrite IHn1.
  2422. simpl.
  2423. reflexivity.
  2424. Qed.
  2425.  
  2426. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2427. induction n1; intros; eauto.
  2428. simpl.
  2429. rewrite IHn1.
  2430. simpl.
  2431. reflexivity.
  2432. Qed.
  2433.  
  2434. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2435. induction n1; intros; eauto.
  2436. simpl.
  2437. rewrite IHn1.
  2438. simpl.
  2439. reflexivity.
  2440. Qed.
  2441.  
  2442. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2443. induction n1; intros; eauto.
  2444. simpl.
  2445. rewrite IHn1.
  2446. simpl.
  2447. reflexivity.
  2448. Qed.
  2449.  
  2450. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2451. induction n1; intros; eauto.
  2452. simpl.
  2453. rewrite IHn1.
  2454. simpl.
  2455. reflexivity.
  2456. Qed.
  2457.  
  2458. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2459. induction n1; intros; eauto.
  2460. simpl.
  2461. rewrite IHn1.
  2462. simpl.
  2463. reflexivity.
  2464. Qed.
  2465.  
  2466. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2467. induction n1; intros; eauto.
  2468. simpl.
  2469. rewrite IHn1.
  2470. simpl.
  2471. reflexivity.
  2472. Qed.
  2473.  
  2474. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2475. induction n1; intros; eauto.
  2476. simpl.
  2477. rewrite IHn1.
  2478. simpl.
  2479. reflexivity.
  2480. Qed.
  2481.  
  2482. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2483. induction n1; intros; eauto.
  2484. simpl.
  2485. rewrite IHn1.
  2486. simpl.
  2487. reflexivity.
  2488. Qed.
  2489.  
  2490. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2491. induction n1; intros; eauto.
  2492. simpl.
  2493. rewrite IHn1.
  2494. simpl.
  2495. reflexivity.
  2496. Qed.
  2497.  
  2498. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2499. induction n1; intros; eauto.
  2500. simpl.
  2501. rewrite IHn1.
  2502. simpl.
  2503. reflexivity.
  2504. Qed.
  2505.  
  2506. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2507. induction n1; intros; eauto.
  2508. simpl.
  2509. rewrite IHn1.
  2510. simpl.
  2511. reflexivity.
  2512. Qed.
  2513.  
  2514. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2515. induction n1; intros; eauto.
  2516. simpl.
  2517. rewrite IHn1.
  2518. simpl.
  2519. reflexivity.
  2520. Qed.
  2521.  
  2522. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2523. induction n1; intros; eauto.
  2524. simpl.
  2525. rewrite IHn1.
  2526. simpl.
  2527. reflexivity.
  2528. Qed.
  2529.  
  2530. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2531. induction n1; intros; eauto.
  2532. simpl.
  2533. rewrite IHn1.
  2534. simpl.
  2535. reflexivity.
  2536. Qed.
  2537.  
  2538. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2539. induction n1; intros; eauto.
  2540. simpl.
  2541. rewrite IHn1.
  2542. simpl.
  2543. reflexivity.
  2544. Qed.
  2545.  
  2546. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2547. induction n1; intros; eauto.
  2548. simpl.
  2549. rewrite IHn1.
  2550. simpl.
  2551. reflexivity.
  2552. Qed.
  2553.  
  2554. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2555. induction n1; intros; eauto.
  2556. simpl.
  2557. rewrite IHn1.
  2558. simpl.
  2559. reflexivity.
  2560. Qed.
  2561.  
  2562. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2563. induction n1; intros; eauto.
  2564. simpl.
  2565. rewrite IHn1.
  2566. simpl.
  2567. reflexivity.
  2568. Qed.
  2569.  
  2570. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2571. induction n1; intros; eauto.
  2572. simpl.
  2573. rewrite IHn1.
  2574. simpl.
  2575. reflexivity.
  2576. Qed.
  2577.  
  2578. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2579. induction n1; intros; eauto.
  2580. simpl.
  2581. rewrite IHn1.
  2582. simpl.
  2583. reflexivity.
  2584. Qed.
  2585.  
  2586. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2587. induction n1; intros; eauto.
  2588. simpl.
  2589. rewrite IHn1.
  2590. simpl.
  2591. reflexivity.
  2592. Qed.
  2593.  
  2594. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2595. induction n1; intros; eauto.
  2596. simpl.
  2597. rewrite IHn1.
  2598. simpl.
  2599. reflexivity.
  2600. Qed.
  2601.  
  2602. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2603. induction n1; intros; eauto.
  2604. simpl.
  2605. rewrite IHn1.
  2606. simpl.
  2607. reflexivity.
  2608. Qed.
  2609.  
  2610. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2611. induction n1; intros; eauto.
  2612. simpl.
  2613. rewrite IHn1.
  2614. simpl.
  2615. reflexivity.
  2616. Qed.
  2617.  
  2618. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2619. induction n1; intros; eauto.
  2620. simpl.
  2621. rewrite IHn1.
  2622. simpl.
  2623. reflexivity.
  2624. Qed.
  2625.  
  2626. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2627. induction n1; intros; eauto.
  2628. simpl.
  2629. rewrite IHn1.
  2630. simpl.
  2631. reflexivity.
  2632. Qed.
  2633.  
  2634. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2635. induction n1; intros; eauto.
  2636. simpl.
  2637. rewrite IHn1.
  2638. simpl.
  2639. reflexivity.
  2640. Qed.
  2641.  
  2642. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2643. induction n1; intros; eauto.
  2644. simpl.
  2645. rewrite IHn1.
  2646. simpl.
  2647. reflexivity.
  2648. Qed.
  2649.  
  2650. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2651. induction n1; intros; eauto.
  2652. simpl.
  2653. rewrite IHn1.
  2654. simpl.
  2655. reflexivity.
  2656. Qed.
  2657.  
  2658. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2659. induction n1; intros; eauto.
  2660. simpl.
  2661. rewrite IHn1.
  2662. simpl.
  2663. reflexivity.
  2664. Qed.
  2665.  
  2666. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2667. induction n1; intros; eauto.
  2668. simpl.
  2669. rewrite IHn1.
  2670. simpl.
  2671. reflexivity.
  2672. Qed.
  2673.  
  2674. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2675. induction n1; intros; eauto.
  2676. simpl.
  2677. rewrite IHn1.
  2678. simpl.
  2679. reflexivity.
  2680. Qed.
  2681.  
  2682. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2683. induction n1; intros; eauto.
  2684. simpl.
  2685. rewrite IHn1.
  2686. simpl.
  2687. reflexivity.
  2688. Qed.
  2689.  
  2690. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2691. induction n1; intros; eauto.
  2692. simpl.
  2693. rewrite IHn1.
  2694. simpl.
  2695. reflexivity.
  2696. Qed.
  2697.  
  2698. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2699. induction n1; intros; eauto.
  2700. simpl.
  2701. rewrite IHn1.
  2702. simpl.
  2703. reflexivity.
  2704. Qed.
  2705.  
  2706. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2707. induction n1; intros; eauto.
  2708. simpl.
  2709. rewrite IHn1.
  2710. simpl.
  2711. reflexivity.
  2712. Qed.
  2713.  
  2714. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2715. induction n1; intros; eauto.
  2716. simpl.
  2717. rewrite IHn1.
  2718. simpl.
  2719. reflexivity.
  2720. Qed.
  2721.  
  2722. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2723. induction n1; intros; eauto.
  2724. simpl.
  2725. rewrite IHn1.
  2726. simpl.
  2727. reflexivity.
  2728. Qed.
  2729.  
  2730. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2731. induction n1; intros; eauto.
  2732. simpl.
  2733. rewrite IHn1.
  2734. simpl.
  2735. reflexivity.
  2736. Qed.
  2737.  
  2738. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2739. induction n1; intros; eauto.
  2740. simpl.
  2741. rewrite IHn1.
  2742. simpl.
  2743. reflexivity.
  2744. Qed.
  2745.  
  2746. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2747. induction n1; intros; eauto.
  2748. simpl.
  2749. rewrite IHn1.
  2750. simpl.
  2751. reflexivity.
  2752. Qed.
  2753.  
  2754. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2755. induction n1; intros; eauto.
  2756. simpl.
  2757. rewrite IHn1.
  2758. simpl.
  2759. reflexivity.
  2760. Qed.
  2761.  
  2762. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2763. induction n1; intros; eauto.
  2764. simpl.
  2765. rewrite IHn1.
  2766. simpl.
  2767. reflexivity.
  2768. Qed.
  2769.  
  2770. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2771. induction n1; intros; eauto.
  2772. simpl.
  2773. rewrite IHn1.
  2774. simpl.
  2775. reflexivity.
  2776. Qed.
  2777.  
  2778. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2779. induction n1; intros; eauto.
  2780. simpl.
  2781. rewrite IHn1.
  2782. simpl.
  2783. reflexivity.
  2784. Qed.
  2785.  
  2786. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2787. induction n1; intros; eauto.
  2788. simpl.
  2789. rewrite IHn1.
  2790. simpl.
  2791. reflexivity.
  2792. Qed.
  2793.  
  2794. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2795. induction n1; intros; eauto.
  2796. simpl.
  2797. rewrite IHn1.
  2798. simpl.
  2799. reflexivity.
  2800. Qed.
  2801.  
  2802. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2803. induction n1; intros; eauto.
  2804. simpl.
  2805. rewrite IHn1.
  2806. simpl.
  2807. reflexivity.
  2808. Qed.
  2809.  
  2810. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2811. induction n1; intros; eauto.
  2812. simpl.
  2813. rewrite IHn1.
  2814. simpl.
  2815. reflexivity.
  2816. Qed.
  2817.  
  2818. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2819. induction n1; intros; eauto.
  2820. simpl.
  2821. rewrite IHn1.
  2822. simpl.
  2823. reflexivity.
  2824. Qed.
  2825.  
  2826. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2827. induction n1; intros; eauto.
  2828. simpl.
  2829. rewrite IHn1.
  2830. simpl.
  2831. reflexivity.
  2832. Qed.
  2833.  
  2834. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2835. induction n1; intros; eauto.
  2836. simpl.
  2837. rewrite IHn1.
  2838. simpl.
  2839. reflexivity.
  2840. Qed.
  2841.  
  2842. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2843. induction n1; intros; eauto.
  2844. simpl.
  2845. rewrite IHn1.
  2846. simpl.
  2847. reflexivity.
  2848. Qed.
  2849.  
  2850. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2851. induction n1; intros; eauto.
  2852. simpl.
  2853. rewrite IHn1.
  2854. simpl.
  2855. reflexivity.
  2856. Qed.
  2857.  
  2858. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2859. induction n1; intros; eauto.
  2860. simpl.
  2861. rewrite IHn1.
  2862. simpl.
  2863. reflexivity.
  2864. Qed.
  2865.  
  2866. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2867. induction n1; intros; eauto.
  2868. simpl.
  2869. rewrite IHn1.
  2870. simpl.
  2871. reflexivity.
  2872. Qed.
  2873.  
  2874. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2875. induction n1; intros; eauto.
  2876. simpl.
  2877. rewrite IHn1.
  2878. simpl.
  2879. reflexivity.
  2880. Qed.
  2881.  
  2882. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2883. induction n1; intros; eauto.
  2884. simpl.
  2885. rewrite IHn1.
  2886. simpl.
  2887. reflexivity.
  2888. Qed.
  2889.  
  2890. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2891. induction n1; intros; eauto.
  2892. simpl.
  2893. rewrite IHn1.
  2894. simpl.
  2895. reflexivity.
  2896. Qed.
  2897.  
  2898. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2899. induction n1; intros; eauto.
  2900. simpl.
  2901. rewrite IHn1.
  2902. simpl.
  2903. reflexivity.
  2904. Qed.
  2905.  
  2906. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2907. induction n1; intros; eauto.
  2908. simpl.
  2909. rewrite IHn1.
  2910. simpl.
  2911. reflexivity.
  2912. Qed.
  2913.  
  2914. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2915. induction n1; intros; eauto.
  2916. simpl.
  2917. rewrite IHn1.
  2918. simpl.
  2919. reflexivity.
  2920. Qed.
  2921.  
  2922. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2923. induction n1; intros; eauto.
  2924. simpl.
  2925. rewrite IHn1.
  2926. simpl.
  2927. reflexivity.
  2928. Qed.
  2929.  
  2930. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2931. induction n1; intros; eauto.
  2932. simpl.
  2933. rewrite IHn1.
  2934. simpl.
  2935. reflexivity.
  2936. Qed.
  2937.  
  2938. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2939. induction n1; intros; eauto.
  2940. simpl.
  2941. rewrite IHn1.
  2942. simpl.
  2943. reflexivity.
  2944. Qed.
  2945.  
  2946. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2947. induction n1; intros; eauto.
  2948. simpl.
  2949. rewrite IHn1.
  2950. simpl.
  2951. reflexivity.
  2952. Qed.
  2953.  
  2954. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2955. induction n1; intros; eauto.
  2956. simpl.
  2957. rewrite IHn1.
  2958. simpl.
  2959. reflexivity.
  2960. Qed.
  2961.  
  2962. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2963. induction n1; intros; eauto.
  2964. simpl.
  2965. rewrite IHn1.
  2966. simpl.
  2967. reflexivity.
  2968. Qed.
  2969.  
  2970. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2971. induction n1; intros; eauto.
  2972. simpl.
  2973. rewrite IHn1.
  2974. simpl.
  2975. reflexivity.
  2976. Qed.
  2977.  
  2978. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2979. induction n1; intros; eauto.
  2980. simpl.
  2981. rewrite IHn1.
  2982. simpl.
  2983. reflexivity.
  2984. Qed.
  2985.  
  2986. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2987. induction n1; intros; eauto.
  2988. simpl.
  2989. rewrite IHn1.
  2990. simpl.
  2991. reflexivity.
  2992. Qed.
  2993.  
  2994. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  2995. induction n1; intros; eauto.
  2996. simpl.
  2997. rewrite IHn1.
  2998. simpl.
  2999. reflexivity.
  3000. Qed.
  3001.  
  3002. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3003. induction n1; intros; eauto.
  3004. simpl.
  3005. rewrite IHn1.
  3006. simpl.
  3007. reflexivity.
  3008. Qed.
  3009.  
  3010. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3011. induction n1; intros; eauto.
  3012. simpl.
  3013. rewrite IHn1.
  3014. simpl.
  3015. reflexivity.
  3016. Qed.
  3017.  
  3018. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3019. induction n1; intros; eauto.
  3020. simpl.
  3021. rewrite IHn1.
  3022. simpl.
  3023. reflexivity.
  3024. Qed.
  3025.  
  3026. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3027. induction n1; intros; eauto.
  3028. simpl.
  3029. rewrite IHn1.
  3030. simpl.
  3031. reflexivity.
  3032. Qed.
  3033.  
  3034. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3035. induction n1; intros; eauto.
  3036. simpl.
  3037. rewrite IHn1.
  3038. simpl.
  3039. reflexivity.
  3040. Qed.
  3041.  
  3042. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3043. induction n1; intros; eauto.
  3044. simpl.
  3045. rewrite IHn1.
  3046. simpl.
  3047. reflexivity.
  3048. Qed.
  3049.  
  3050. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3051. induction n1; intros; eauto.
  3052. simpl.
  3053. rewrite IHn1.
  3054. simpl.
  3055. reflexivity.
  3056. Qed.
  3057.  
  3058. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3059. induction n1; intros; eauto.
  3060. simpl.
  3061. rewrite IHn1.
  3062. simpl.
  3063. reflexivity.
  3064. Qed.
  3065.  
  3066. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3067. induction n1; intros; eauto.
  3068. simpl.
  3069. rewrite IHn1.
  3070. simpl.
  3071. reflexivity.
  3072. Qed.
  3073.  
  3074. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3075. induction n1; intros; eauto.
  3076. simpl.
  3077. rewrite IHn1.
  3078. simpl.
  3079. reflexivity.
  3080. Qed.
  3081.  
  3082. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3083. induction n1; intros; eauto.
  3084. simpl.
  3085. rewrite IHn1.
  3086. simpl.
  3087. reflexivity.
  3088. Qed.
  3089.  
  3090. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3091. induction n1; intros; eauto.
  3092. simpl.
  3093. rewrite IHn1.
  3094. simpl.
  3095. reflexivity.
  3096. Qed.
  3097.  
  3098. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3099. induction n1; intros; eauto.
  3100. simpl.
  3101. rewrite IHn1.
  3102. simpl.
  3103. reflexivity.
  3104. Qed.
  3105.  
  3106. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3107. induction n1; intros; eauto.
  3108. simpl.
  3109. rewrite IHn1.
  3110. simpl.
  3111. reflexivity.
  3112. Qed.
  3113.  
  3114. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3115. induction n1; intros; eauto.
  3116. simpl.
  3117. rewrite IHn1.
  3118. simpl.
  3119. reflexivity.
  3120. Qed.
  3121.  
  3122. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3123. induction n1; intros; eauto.
  3124. simpl.
  3125. rewrite IHn1.
  3126. simpl.
  3127. reflexivity.
  3128. Qed.
  3129.  
  3130. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3131. induction n1; intros; eauto.
  3132. simpl.
  3133. rewrite IHn1.
  3134. simpl.
  3135. reflexivity.
  3136. Qed.
  3137.  
  3138. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3139. induction n1; intros; eauto.
  3140. simpl.
  3141. rewrite IHn1.
  3142. simpl.
  3143. reflexivity.
  3144. Qed.
  3145.  
  3146. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3147. induction n1; intros; eauto.
  3148. simpl.
  3149. rewrite IHn1.
  3150. simpl.
  3151. reflexivity.
  3152. Qed.
  3153.  
  3154. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3155. induction n1; intros; eauto.
  3156. simpl.
  3157. rewrite IHn1.
  3158. simpl.
  3159. reflexivity.
  3160. Qed.
  3161.  
  3162. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3163. induction n1; intros; eauto.
  3164. simpl.
  3165. rewrite IHn1.
  3166. simpl.
  3167. reflexivity.
  3168. Qed.
  3169.  
  3170. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3171. induction n1; intros; eauto.
  3172. simpl.
  3173. rewrite IHn1.
  3174. simpl.
  3175. reflexivity.
  3176. Qed.
  3177.  
  3178. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3179. induction n1; intros; eauto.
  3180. simpl.
  3181. rewrite IHn1.
  3182. simpl.
  3183. reflexivity.
  3184. Qed.
  3185.  
  3186. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3187. induction n1; intros; eauto.
  3188. simpl.
  3189. rewrite IHn1.
  3190. simpl.
  3191. reflexivity.
  3192. Qed.
  3193.  
  3194. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3195. induction n1; intros; eauto.
  3196. simpl.
  3197. rewrite IHn1.
  3198. simpl.
  3199. reflexivity.
  3200. Qed.
  3201.  
  3202. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3203. induction n1; intros; eauto.
  3204. simpl.
  3205. rewrite IHn1.
  3206. simpl.
  3207. reflexivity.
  3208. Qed.
  3209.  
  3210. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3211. induction n1; intros; eauto.
  3212. simpl.
  3213. rewrite IHn1.
  3214. simpl.
  3215. reflexivity.
  3216. Qed.
  3217.  
  3218. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3219. induction n1; intros; eauto.
  3220. simpl.
  3221. rewrite IHn1.
  3222. simpl.
  3223. reflexivity.
  3224. Qed.
  3225.  
  3226. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3227. induction n1; intros; eauto.
  3228. simpl.
  3229. rewrite IHn1.
  3230. simpl.
  3231. reflexivity.
  3232. Qed.
  3233.  
  3234. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3235. induction n1; intros; eauto.
  3236. simpl.
  3237. rewrite IHn1.
  3238. simpl.
  3239. reflexivity.
  3240. Qed.
  3241.  
  3242. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3243. induction n1; intros; eauto.
  3244. simpl.
  3245. rewrite IHn1.
  3246. simpl.
  3247. reflexivity.
  3248. Qed.
  3249.  
  3250. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3251. induction n1; intros; eauto.
  3252. simpl.
  3253. rewrite IHn1.
  3254. simpl.
  3255. reflexivity.
  3256. Qed.
  3257.  
  3258. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3259. induction n1; intros; eauto.
  3260. simpl.
  3261. rewrite IHn1.
  3262. simpl.
  3263. reflexivity.
  3264. Qed.
  3265.  
  3266. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3267. induction n1; intros; eauto.
  3268. simpl.
  3269. rewrite IHn1.
  3270. simpl.
  3271. reflexivity.
  3272. Qed.
  3273.  
  3274. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3275. induction n1; intros; eauto.
  3276. simpl.
  3277. rewrite IHn1.
  3278. simpl.
  3279. reflexivity.
  3280. Qed.
  3281.  
  3282. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3283. induction n1; intros; eauto.
  3284. simpl.
  3285. rewrite IHn1.
  3286. simpl.
  3287. reflexivity.
  3288. Qed.
  3289.  
  3290. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3291. induction n1; intros; eauto.
  3292. simpl.
  3293. rewrite IHn1.
  3294. simpl.
  3295. reflexivity.
  3296. Qed.
  3297.  
  3298. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3299. induction n1; intros; eauto.
  3300. simpl.
  3301. rewrite IHn1.
  3302. simpl.
  3303. reflexivity.
  3304. Qed.
  3305.  
  3306. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3307. induction n1; intros; eauto.
  3308. simpl.
  3309. rewrite IHn1.
  3310. simpl.
  3311. reflexivity.
  3312. Qed.
  3313.  
  3314. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3315. induction n1; intros; eauto.
  3316. simpl.
  3317. rewrite IHn1.
  3318. simpl.
  3319. reflexivity.
  3320. Qed.
  3321.  
  3322. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3323. induction n1; intros; eauto.
  3324. simpl.
  3325. rewrite IHn1.
  3326. simpl.
  3327. reflexivity.
  3328. Qed.
  3329.  
  3330. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3331. induction n1; intros; eauto.
  3332. simpl.
  3333. rewrite IHn1.
  3334. simpl.
  3335. reflexivity.
  3336. Qed.
  3337.  
  3338. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3339. induction n1; intros; eauto.
  3340. simpl.
  3341. rewrite IHn1.
  3342. simpl.
  3343. reflexivity.
  3344. Qed.
  3345.  
  3346. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3347. induction n1; intros; eauto.
  3348. simpl.
  3349. rewrite IHn1.
  3350. simpl.
  3351. reflexivity.
  3352. Qed.
  3353.  
  3354. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3355. induction n1; intros; eauto.
  3356. simpl.
  3357. rewrite IHn1.
  3358. simpl.
  3359. reflexivity.
  3360. Qed.
  3361.  
  3362. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3363. induction n1; intros; eauto.
  3364. simpl.
  3365. rewrite IHn1.
  3366. simpl.
  3367. reflexivity.
  3368. Qed.
  3369.  
  3370. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3371. induction n1; intros; eauto.
  3372. simpl.
  3373. rewrite IHn1.
  3374. simpl.
  3375. reflexivity.
  3376. Qed.
  3377.  
  3378. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3379. induction n1; intros; eauto.
  3380. simpl.
  3381. rewrite IHn1.
  3382. simpl.
  3383. reflexivity.
  3384. Qed.
  3385.  
  3386. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3387. induction n1; intros; eauto.
  3388. simpl.
  3389. rewrite IHn1.
  3390. simpl.
  3391. reflexivity.
  3392. Qed.
  3393.  
  3394. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3395. induction n1; intros; eauto.
  3396. simpl.
  3397. rewrite IHn1.
  3398. simpl.
  3399. reflexivity.
  3400. Qed.
  3401.  
  3402. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3403. induction n1; intros; eauto.
  3404. simpl.
  3405. rewrite IHn1.
  3406. simpl.
  3407. reflexivity.
  3408. Qed.
  3409.  
  3410. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3411. induction n1; intros; eauto.
  3412. simpl.
  3413. rewrite IHn1.
  3414. simpl.
  3415. reflexivity.
  3416. Qed.
  3417.  
  3418. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3419. induction n1; intros; eauto.
  3420. simpl.
  3421. rewrite IHn1.
  3422. simpl.
  3423. reflexivity.
  3424. Qed.
  3425.  
  3426. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3427. induction n1; intros; eauto.
  3428. simpl.
  3429. rewrite IHn1.
  3430. simpl.
  3431. reflexivity.
  3432. Qed.
  3433.  
  3434. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3435. induction n1; intros; eauto.
  3436. simpl.
  3437. rewrite IHn1.
  3438. simpl.
  3439. reflexivity.
  3440. Qed.
  3441.  
  3442. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3443. induction n1; intros; eauto.
  3444. simpl.
  3445. rewrite IHn1.
  3446. simpl.
  3447. reflexivity.
  3448. Qed.
  3449.  
  3450. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3451. induction n1; intros; eauto.
  3452. simpl.
  3453. rewrite IHn1.
  3454. simpl.
  3455. reflexivity.
  3456. Qed.
  3457.  
  3458. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3459. induction n1; intros; eauto.
  3460. simpl.
  3461. rewrite IHn1.
  3462. simpl.
  3463. reflexivity.
  3464. Qed.
  3465.  
  3466. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3467. induction n1; intros; eauto.
  3468. simpl.
  3469. rewrite IHn1.
  3470. simpl.
  3471. reflexivity.
  3472. Qed.
  3473.  
  3474. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3475. induction n1; intros; eauto.
  3476. simpl.
  3477. rewrite IHn1.
  3478. simpl.
  3479. reflexivity.
  3480. Qed.
  3481.  
  3482. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3483. induction n1; intros; eauto.
  3484. simpl.
  3485. rewrite IHn1.
  3486. simpl.
  3487. reflexivity.
  3488. Qed.
  3489.  
  3490. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3491. induction n1; intros; eauto.
  3492. simpl.
  3493. rewrite IHn1.
  3494. simpl.
  3495. reflexivity.
  3496. Qed.
  3497.  
  3498. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3499. induction n1; intros; eauto.
  3500. simpl.
  3501. rewrite IHn1.
  3502. simpl.
  3503. reflexivity.
  3504. Qed.
  3505.  
  3506. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3507. induction n1; intros; eauto.
  3508. simpl.
  3509. rewrite IHn1.
  3510. simpl.
  3511. reflexivity.
  3512. Qed.
  3513.  
  3514. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3515. induction n1; intros; eauto.
  3516. simpl.
  3517. rewrite IHn1.
  3518. simpl.
  3519. reflexivity.
  3520. Qed.
  3521.  
  3522. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3523. induction n1; intros; eauto.
  3524. simpl.
  3525. rewrite IHn1.
  3526. simpl.
  3527. reflexivity.
  3528. Qed.
  3529.  
  3530. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3531. induction n1; intros; eauto.
  3532. simpl.
  3533. rewrite IHn1.
  3534. simpl.
  3535. reflexivity.
  3536. Qed.
  3537.  
  3538. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3539. induction n1; intros; eauto.
  3540. simpl.
  3541. rewrite IHn1.
  3542. simpl.
  3543. reflexivity.
  3544. Qed.
  3545.  
  3546. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3547. induction n1; intros; eauto.
  3548. simpl.
  3549. rewrite IHn1.
  3550. simpl.
  3551. reflexivity.
  3552. Qed.
  3553.  
  3554. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3555. induction n1; intros; eauto.
  3556. simpl.
  3557. rewrite IHn1.
  3558. simpl.
  3559. reflexivity.
  3560. Qed.
  3561.  
  3562. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3563. induction n1; intros; eauto.
  3564. simpl.
  3565. rewrite IHn1.
  3566. simpl.
  3567. reflexivity.
  3568. Qed.
  3569.  
  3570. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3571. induction n1; intros; eauto.
  3572. simpl.
  3573. rewrite IHn1.
  3574. simpl.
  3575. reflexivity.
  3576. Qed.
  3577.  
  3578. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3579. induction n1; intros; eauto.
  3580. simpl.
  3581. rewrite IHn1.
  3582. simpl.
  3583. reflexivity.
  3584. Qed.
  3585.  
  3586. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3587. induction n1; intros; eauto.
  3588. simpl.
  3589. rewrite IHn1.
  3590. simpl.
  3591. reflexivity.
  3592. Qed.
  3593.  
  3594. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3595. induction n1; intros; eauto.
  3596. simpl.
  3597. rewrite IHn1.
  3598. simpl.
  3599. reflexivity.
  3600. Qed.
  3601.  
  3602. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3603. induction n1; intros; eauto.
  3604. simpl.
  3605. rewrite IHn1.
  3606. simpl.
  3607. reflexivity.
  3608. Qed.
  3609.  
  3610. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3611. induction n1; intros; eauto.
  3612. simpl.
  3613. rewrite IHn1.
  3614. simpl.
  3615. reflexivity.
  3616. Qed.
  3617.  
  3618. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3619. induction n1; intros; eauto.
  3620. simpl.
  3621. rewrite IHn1.
  3622. simpl.
  3623. reflexivity.
  3624. Qed.
  3625.  
  3626. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3627. induction n1; intros; eauto.
  3628. simpl.
  3629. rewrite IHn1.
  3630. simpl.
  3631. reflexivity.
  3632. Qed.
  3633.  
  3634. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3635. induction n1; intros; eauto.
  3636. simpl.
  3637. rewrite IHn1.
  3638. simpl.
  3639. reflexivity.
  3640. Qed.
  3641.  
  3642. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3643. induction n1; intros; eauto.
  3644. simpl.
  3645. rewrite IHn1.
  3646. simpl.
  3647. reflexivity.
  3648. Qed.
  3649.  
  3650. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3651. induction n1; intros; eauto.
  3652. simpl.
  3653. rewrite IHn1.
  3654. simpl.
  3655. reflexivity.
  3656. Qed.
  3657.  
  3658. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3659. induction n1; intros; eauto.
  3660. simpl.
  3661. rewrite IHn1.
  3662. simpl.
  3663. reflexivity.
  3664. Qed.
  3665.  
  3666. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3667. induction n1; intros; eauto.
  3668. simpl.
  3669. rewrite IHn1.
  3670. simpl.
  3671. reflexivity.
  3672. Qed.
  3673.  
  3674. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3675. induction n1; intros; eauto.
  3676. simpl.
  3677. rewrite IHn1.
  3678. simpl.
  3679. reflexivity.
  3680. Qed.
  3681.  
  3682. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3683. induction n1; intros; eauto.
  3684. simpl.
  3685. rewrite IHn1.
  3686. simpl.
  3687. reflexivity.
  3688. Qed.
  3689.  
  3690. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3691. induction n1; intros; eauto.
  3692. simpl.
  3693. rewrite IHn1.
  3694. simpl.
  3695. reflexivity.
  3696. Qed.
  3697.  
  3698. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3699. induction n1; intros; eauto.
  3700. simpl.
  3701. rewrite IHn1.
  3702. simpl.
  3703. reflexivity.
  3704. Qed.
  3705.  
  3706. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3707. induction n1; intros; eauto.
  3708. simpl.
  3709. rewrite IHn1.
  3710. simpl.
  3711. reflexivity.
  3712. Qed.
  3713.  
  3714. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3715. induction n1; intros; eauto.
  3716. simpl.
  3717. rewrite IHn1.
  3718. simpl.
  3719. reflexivity.
  3720. Qed.
  3721.  
  3722. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3723. induction n1; intros; eauto.
  3724. simpl.
  3725. rewrite IHn1.
  3726. simpl.
  3727. reflexivity.
  3728. Qed.
  3729.  
  3730. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3731. induction n1; intros; eauto.
  3732. simpl.
  3733. rewrite IHn1.
  3734. simpl.
  3735. reflexivity.
  3736. Qed.
  3737.  
  3738. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3739. induction n1; intros; eauto.
  3740. simpl.
  3741. rewrite IHn1.
  3742. simpl.
  3743. reflexivity.
  3744. Qed.
  3745.  
  3746. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3747. induction n1; intros; eauto.
  3748. simpl.
  3749. rewrite IHn1.
  3750. simpl.
  3751. reflexivity.
  3752. Qed.
  3753.  
  3754. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3755. induction n1; intros; eauto.
  3756. simpl.
  3757. rewrite IHn1.
  3758. simpl.
  3759. reflexivity.
  3760. Qed.
  3761.  
  3762. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3763. induction n1; intros; eauto.
  3764. simpl.
  3765. rewrite IHn1.
  3766. simpl.
  3767. reflexivity.
  3768. Qed.
  3769.  
  3770. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3771. induction n1; intros; eauto.
  3772. simpl.
  3773. rewrite IHn1.
  3774. simpl.
  3775. reflexivity.
  3776. Qed.
  3777.  
  3778. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3779. induction n1; intros; eauto.
  3780. simpl.
  3781. rewrite IHn1.
  3782. simpl.
  3783. reflexivity.
  3784. Qed.
  3785.  
  3786. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3787. induction n1; intros; eauto.
  3788. simpl.
  3789. rewrite IHn1.
  3790. simpl.
  3791. reflexivity.
  3792. Qed.
  3793.  
  3794. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3795. induction n1; intros; eauto.
  3796. simpl.
  3797. rewrite IHn1.
  3798. simpl.
  3799. reflexivity.
  3800. Qed.
  3801.  
  3802. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3803. induction n1; intros; eauto.
  3804. simpl.
  3805. rewrite IHn1.
  3806. simpl.
  3807. reflexivity.
  3808. Qed.
  3809.  
  3810. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3811. induction n1; intros; eauto.
  3812. simpl.
  3813. rewrite IHn1.
  3814. simpl.
  3815. reflexivity.
  3816. Qed.
  3817.  
  3818. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3819. induction n1; intros; eauto.
  3820. simpl.
  3821. rewrite IHn1.
  3822. simpl.
  3823. reflexivity.
  3824. Qed.
  3825.  
  3826. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3827. induction n1; intros; eauto.
  3828. simpl.
  3829. rewrite IHn1.
  3830. simpl.
  3831. reflexivity.
  3832. Qed.
  3833.  
  3834. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3835. induction n1; intros; eauto.
  3836. simpl.
  3837. rewrite IHn1.
  3838. simpl.
  3839. reflexivity.
  3840. Qed.
  3841.  
  3842. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3843. induction n1; intros; eauto.
  3844. simpl.
  3845. rewrite IHn1.
  3846. simpl.
  3847. reflexivity.
  3848. Qed.
  3849.  
  3850. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3851. induction n1; intros; eauto.
  3852. simpl.
  3853. rewrite IHn1.
  3854. simpl.
  3855. reflexivity.
  3856. Qed.
  3857.  
  3858. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3859. induction n1; intros; eauto.
  3860. simpl.
  3861. rewrite IHn1.
  3862. simpl.
  3863. reflexivity.
  3864. Qed.
  3865.  
  3866. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3867. induction n1; intros; eauto.
  3868. simpl.
  3869. rewrite IHn1.
  3870. simpl.
  3871. reflexivity.
  3872. Qed.
  3873.  
  3874. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3875. induction n1; intros; eauto.
  3876. simpl.
  3877. rewrite IHn1.
  3878. simpl.
  3879. reflexivity.
  3880. Qed.
  3881.  
  3882. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3883. induction n1; intros; eauto.
  3884. simpl.
  3885. rewrite IHn1.
  3886. simpl.
  3887. reflexivity.
  3888. Qed.
  3889.  
  3890. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3891. induction n1; intros; eauto.
  3892. simpl.
  3893. rewrite IHn1.
  3894. simpl.
  3895. reflexivity.
  3896. Qed.
  3897.  
  3898. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3899. induction n1; intros; eauto.
  3900. simpl.
  3901. rewrite IHn1.
  3902. simpl.
  3903. reflexivity.
  3904. Qed.
  3905.  
  3906. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3907. induction n1; intros; eauto.
  3908. simpl.
  3909. rewrite IHn1.
  3910. simpl.
  3911. reflexivity.
  3912. Qed.
  3913.  
  3914. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3915. induction n1; intros; eauto.
  3916. simpl.
  3917. rewrite IHn1.
  3918. simpl.
  3919. reflexivity.
  3920. Qed.
  3921.  
  3922. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3923. induction n1; intros; eauto.
  3924. simpl.
  3925. rewrite IHn1.
  3926. simpl.
  3927. reflexivity.
  3928. Qed.
  3929.  
  3930. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3931. induction n1; intros; eauto.
  3932. simpl.
  3933. rewrite IHn1.
  3934. simpl.
  3935. reflexivity.
  3936. Qed.
  3937.  
  3938. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3939. induction n1; intros; eauto.
  3940. simpl.
  3941. rewrite IHn1.
  3942. simpl.
  3943. reflexivity.
  3944. Qed.
  3945.  
  3946. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3947. induction n1; intros; eauto.
  3948. simpl.
  3949. rewrite IHn1.
  3950. simpl.
  3951. reflexivity.
  3952. Qed.
  3953.  
  3954. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3955. induction n1; intros; eauto.
  3956. simpl.
  3957. rewrite IHn1.
  3958. simpl.
  3959. reflexivity.
  3960. Qed.
  3961.  
  3962. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3963. induction n1; intros; eauto.
  3964. simpl.
  3965. rewrite IHn1.
  3966. simpl.
  3967. reflexivity.
  3968. Qed.
  3969.  
  3970. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3971. induction n1; intros; eauto.
  3972. simpl.
  3973. rewrite IHn1.
  3974. simpl.
  3975. reflexivity.
  3976. Qed.
  3977.  
  3978. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3979. induction n1; intros; eauto.
  3980. simpl.
  3981. rewrite IHn1.
  3982. simpl.
  3983. reflexivity.
  3984. Qed.
  3985.  
  3986. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3987. induction n1; intros; eauto.
  3988. simpl.
  3989. rewrite IHn1.
  3990. simpl.
  3991. reflexivity.
  3992. Qed.
  3993.  
  3994. Goal forall n1 n2, n1 + S n2 = S n1 + n2.
  3995. induction n1; intros; eauto.
  3996. simpl.
  3997. rewrite IHn1.
  3998. simpl.
  3999. reflexivity.
  4000. Qed.
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