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- Lemma q5 : forall n : nat, 2 * somme id n = n * (n + 1).
- intros.
- induction n.
- simpl.
- trivial.
- simpl.
- replace (somme id n + id (S n) + (somme id n + id (S n) + 0)) with (2*(somme id n) + 2*(S n)).
- rewrite IHn.
- ring.
- simpl.
- ring_simplify.
- rewrite IHn.
- simpl.
- ring.
- Qed.
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