Commit aee107f3 by Jean-Christophe Filliatre

### updated proofs on moloch

parent 94179377
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 ... ... @@ -17,6 +17,9 @@ theory Power lemma Power_mult : forall x n m : int. 0 <= n -> 0 <= m -> power x (n * m) = power (power x n) m lemma Power_mult2 : forall x y n : int. 0 <= n -> power (x * y) n = power x n * power y n end module M ... ...
 (* This file is generated by Why3's Coq driver *) (* Beware! Only edit allowed sections below *) Require Import ZArith. Require Import Rbase. Definition unit := unit. Parameter ignore: forall (a:Type), a -> unit. Implicit Arguments ignore. Parameter label_ : Type. Parameter at1: forall (a:Type), a -> label_ -> a. Implicit Arguments at1. Parameter old: forall (a:Type), a -> a. Implicit Arguments old. Parameter power: Z -> Z -> Z. Axiom Power_0 : forall (x:Z), ((power x 0%Z) = 1%Z). Axiom Power_s : forall (x:Z) (n:Z), (0%Z < n)%Z -> ((power x n) = (x * (power x (n - 1%Z)%Z))%Z). Axiom Power_1 : forall (x:Z), ((power x 1%Z) = x). Axiom Power_sum : forall (x:Z) (n:Z) (m:Z), (0%Z <= n)%Z -> ((0%Z <= m)%Z -> ((power x (n + m)%Z) = ((power x n) * (power x m))%Z)). Axiom Power_mult : forall (x:Z) (n:Z) (m:Z), (0%Z <= n)%Z -> ((0%Z <= m)%Z -> ((power x (n * m)%Z) = (power (power x n) m))). Theorem Power_mult2 : forall (x:Z) (y:Z) (n:Z), (0%Z <= n)%Z -> ((power (x * y)%Z n) = ((power x n) * (power y n))%Z). (* YOU MAY EDIT THE PROOF BELOW *) intros x y n Hn. generalize Hn. pattern n. apply natlike_ind; auto. intros; do 3 rewrite Power_0. omega. intros. rewrite Power_s. 2:omega. rewrite (Power_s x (Zsucc x0)). rewrite (Power_s y (Zsucc x0)). replace (Zsucc x0 - 1)%Z with x0 by omega. rewrite H0. ring. omega. omega. omega. Qed. (* DO NOT EDIT BELOW *)
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