Commit 20f47637 by MARCHE Claude

### inversion ordre des lemmes

parent 36f2e826
 ... ... @@ -102,9 +102,11 @@ theory Pow2real lemma Power_neg1 : pow2 (-1) = 0.5 lemma Power_non_null_aux: forall n:int.n>=0 -> pow2 n <> 0.0 lemma Power_neg_aux : forall n:int. n>=0 -> pow2 (-n) = 1.0 /. pow2 n lemma Power_non_null: forall n:int. pow2 n <> 0.0 lemma Power_neg_aux : forall n:int. n>=0 ->pow2 (-n) = 1.0 /. pow2 n lemma Power_neg : forall n:int. pow2 (-n) = 1.0 /. pow2 n lemma Power_sum_aux : forall n m: int. m >= 0 -> pow2 (n+m) = pow2 n *. pow2 m ... ...
 ... ... @@ -24,6 +24,8 @@ Axiom Power_1 : ((pow2 1%Z) = 2%R). Axiom Power_neg1 : ((pow2 (-1%Z)%Z) = (05 / 10)%R). Axiom Power_non_null_aux : forall (n:Z), (0%Z <= n)%Z -> ~ ((pow2 n) = 0%R). Axiom Power_non_null : forall (n:Z), ~ ((pow2 n) = 0%R). (* YOU MAY EDIT THE CONTEXT BELOW *) ... ... @@ -53,7 +55,7 @@ unfold Rdiv in |-*. repeat rewrite Rmult_1_l. rewrite<-Rinv_mult_distr;auto. apply Rgt_not_eq;auto with *. apply Power_non_null. apply Power_non_null_aux; omega. (*x = 0*) subst x. replace (-0) with 0 by omega. ... ...
 ... ... @@ -26,6 +26,9 @@ Axiom Power_neg1 : ((pow2 (-1%Z)%Z) = (05 / 10)%R). Axiom Power_non_null_aux : forall (n:Z), (0%Z <= n)%Z -> ~ ((pow2 n) = 0%R). Axiom Power_neg_aux : forall (n:Z), (0%Z <= n)%Z -> ((pow2 (-n)%Z) = (Rdiv 1%R (pow2 n))%R). (* YOU MAY EDIT THE CONTEXT BELOW *) Open Scope Z_scope. (* DO NOT EDIT BELOW *) ... ... @@ -39,43 +42,13 @@ apply Power_non_null_aux;auto with zarith. pose (n':=-n). replace n with (-n') by (subst n';omega). replace (n') with (n'-1+1) by omega. replace (- (n' - 1 + 1)) with (-(n'-1)-1) by omega. rewrite Power_p. apply Rmult_integral_contrapositive. split. rewrite Power_1_2. unfold Rdiv in |-*. rewrite Rmult_1_l. apply Rinv_neq_0_compat. apply Rgt_not_eq;auto with *. cut(n'>0);auto with zarith. apply Z_lt_induction with (P:= fun n' => n' > 0 -> pow2 (- n') <> 0%R);auto with zarith. intros x Hind Hnxpos. replace (x) with (x-1+1) by omega. replace (- (x - 1 + 1)) with (-(x-1)-1) by omega. rewrite Power_p_all;auto with zarith. apply Rmult_integral_contrapositive. split. rewrite Power_1_2. unfold Rdiv in |-*. rewrite Power_neg_aux. unfold Rdiv. rewrite Rmult_1_l. apply Rinv_neq_0_compat. apply Rgt_not_eq;auto with *. apply Hind;auto with zarith. apply Power_non_null_aux. subst n'; auto with zarith. subst n'; auto with zarith. Qed. (* DO NOT EDIT BELOW *) ... ...
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