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Jan 3rd, 2016
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  1. Lemma optimizer_a_plus_sound : forall a b, aeval (optimizer_a (APlus a b)) = aeval (APlus (optimizer_a a) (optimizer_a b)).
  2. Proof.
  3. intro.
  4. induction a.
  5. intros.
  6. destruct n.
  7. simpl.
  8. reflexivity.
  9. destruct b.
  10. destruct n0.
  11. simpl.
  12. rewrite plus_0_r.
  13. reflexivity.
  14. reflexivity.
  15. reflexivity.
  16. reflexivity.
  17. reflexivity.
  18. intros.
  19. destruct b.
  20. destruct n.
  21. unfold optimizer_a at 3.
  22. unfold aeval.
  23. fold aeval.
  24. rewrite plus_0_r.
  25. reflexivity.
  26. reflexivity.
  27. reflexivity.
  28. reflexivity.
  29. reflexivity.
  30. intros.
  31. destruct b.
  32. destruct n.
  33. unfold optimizer_a at 3.
  34. unfold aeval.
  35. fold aeval.
  36. rewrite plus_0_r.
  37. reflexivity.
  38. reflexivity.
  39. reflexivity.
  40. reflexivity.
  41. reflexivity.
  42. destruct b.
  43. destruct n.
  44. unfold optimizer_a at 3.
  45. unfold aeval.
  46. fold aeval.
  47. rewrite plus_0_r.
  48. reflexivity.
  49. reflexivity.
  50. reflexivity.
  51. reflexivity.
  52. reflexivity.
  53. Qed.
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