diff options
Diffstat (limited to 'test-suite/micromega/square.v')
| -rw-r--r-- | test-suite/micromega/square.v | 14 |
1 files changed, 8 insertions, 6 deletions
diff --git a/test-suite/micromega/square.v b/test-suite/micromega/square.v index 30c72e8c..b78bba25 100644 --- a/test-suite/micromega/square.v +++ b/test-suite/micromega/square.v @@ -6,12 +6,12 @@ (* *) (************************************************************************) -Require Import ZArith Zwf Micromegatac QArith. +Require Import ZArith Zwf Psatz QArith. Open Scope Z_scope. Lemma Zabs_square : forall x, (Zabs x)^2 = x^2. Proof. - intros ; case (Zabs_dec x) ; intros ; micromega Z. + intros ; case (Zabs_dec x) ; intros ; psatz Z 2. Qed. Hint Resolve Zabs_pos Zabs_square. @@ -21,11 +21,11 @@ intros [n [p [Heq Hnz]]]; pose (n' := Zabs n); pose (p':=Zabs p). assert (facts : 0 <= Zabs n /\ 0 <= Zabs p /\ Zabs n^2=n^2 /\ Zabs p^2 = p^2) by auto. assert (H : (0 < n' /\ 0 <= p' /\ n' ^2 = 2* p' ^2)) by - (destruct facts as [Hf1 [Hf2 [Hf3 Hf4]]]; unfold n', p' ; micromega Z). + (destruct facts as [Hf1 [Hf2 [Hf3 Hf4]]]; unfold n', p' ; psatz Z 2). generalize p' H; elim n' using (well_founded_ind (Zwf_well_founded 0)); clear. intros n IHn p [Hn [Hp Heq]]. -assert (Hzwf : Zwf 0 (2*p-n) n) by (unfold Zwf; micromega Z). -assert (Hdecr : 0 < 2*p-n /\ 0 <= n-p /\ (2*p-n)^2=2*(n-p)^2) by micromega Z. +assert (Hzwf : Zwf 0 (2*p-n) n) by (unfold Zwf; psatz Z 2). +assert (Hdecr : 0 < 2*p-n /\ 0 <= n-p /\ (2*p-n)^2=2*(n-p)^2) by psatz Z 2. apply (IHn (2*p-n) Hzwf (n-p) Hdecr). Qed. @@ -44,7 +44,9 @@ Lemma QdenZpower : forall x : Q, ' Qden (x ^ 2)%Q = ('(Qden x) ^ 2) %Z. Proof. intros. destruct x. - cbv beta iota zeta delta - [Pmult]. + simpl. + unfold Zpower_pos. + simpl. rewrite Pmult_1_r. reflexivity. Qed. |