Commit 647d63e7 by MARCHE Claude

### preuve de power_sum

parent b50c3f74
 ... @@ -20,9 +20,22 @@ Theorem Power_sum : forall (n:Z) (m:Z), ((0%Z <= n)%Z /\ (0%Z <= m)%Z) -> ... @@ -20,9 +20,22 @@ Theorem Power_sum : forall (n:Z) (m:Z), ((0%Z <= n)%Z /\ (0%Z <= m)%Z) -> ((pow2 (n + m)%Z) = ((pow2 n) * (pow2 m))%Z). ((pow2 (n + m)%Z) = ((pow2 n) * (pow2 m))%Z). (* YOU MAY EDIT THE PROOF BELOW *) (* YOU MAY EDIT THE PROOF BELOW *) intros n m Hmn. intros n m Hmn. cut (0 <= m); auto with zarith. apply Z_lt_induction with (P:= fun m => 0 <= m -> pow2 (n + m) = pow2 n * pow2 m); auto with zarith. intros x Hind Hxpos. assert (h:(x = 0 \/ x > 0)) by omega. destruct h. subst x. rewrite Power_0. (* auto with zarith. elim n. elim n. replace (0+m) with m by omega. replace (0+m) with m by omega. rewrite Power_0. replace (1* pow2 m) with (pow2 m) by omega. replace (1* pow2 m) with (pow2 m) by omega. auto. auto. intro. intro. ... @@ -37,7 +50,7 @@ replace (2 * Zpos p0) with (Zpos p0 * 2) by omega. ... @@ -37,7 +50,7 @@ replace (2 * Zpos p0) with (Zpos p0 * 2) by omega. rewrite<-Zplus_diag_eq_mult_2. rewrite<-Zplus_diag_eq_mult_2. rewrite Power_s. rewrite Power_s. *) Qed. Qed. ... ...
 ... @@ -1036,7 +1036,7 @@ ... @@ -1036,7 +1036,7 @@ expanded="false"> expanded="false"> shape="ainfix =anthafrom_intV0c0aFalseIainfix =amodV0c2c0F"> shape="ainfix =anthafrom_int2cV0c0aFalseIainfix =amodV0c2c0Aainfix >=V0c0F"> shape="ainfix =anthafrom_int2cV0c0aTrueIainfix =amodV0c2c0NAainfix >=V0c0F"> shape="ainfix =anthafrom_int2cV0c0aTrueIainfix =amodV0c2c0Aainfix shape="ainfix =anthafrom_int2cV0c0aFalseIainfix =amodV0c2c0NAainfix ... @@ -2969,14 +2969,14 @@ ... @@ -2969,14 +2969,14 @@ name="x_negative" name="x_negative" sum="75aca8e6393ca908f8163a9722aeb5e8" sum="75aca8e6393ca908f8163a9722aeb5e8" proved="false" proved="false" expanded="true" expanded="false" shape="ainfix =ato_nat_subavarV0c30c0aprefix -V0Iainfix =anthavarV0c31aFalseF"> shape="ainfix =ato_nat_subavarV0c30c0aprefix -V0Iainfix =anthavarV0c31aFalseF"> shape="ainfix =amantissaavarV0ainfix -apow2c31V0Iainfix =anthavarV0c31aFalseF"> shape="ainfix =afrom_intainfix +apow2c31V0ainfix +.afrom_intapow2c31afrom_intV0F">
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