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| author |  Stephane Glondu <steph@glondu.net> | 2010-07-21 09:46:51 +0200 |
|---|---|---|
| committer | Stephane Glondu <steph@glondu.net> | 2010-07-21 09:46:51 +0200 |
| commit | 5b7eafd0f00a16d78f99a27f5c7d5a0de77dc7e6 (patch) | |
| tree | 631ad791a7685edafeb1fb2e8faeedc8379318ae /theories/ZArith/Zsqrt.v | |
| parent | da178a880e3ace820b41d38b191d3785b82991f5 (diff) | |
Imported Upstream snapshot 8.3~beta0+13298
Diffstat (limited to 'theories/ZArith/Zsqrt.v')
| -rw-r--r-- | theories/ZArith/Zsqrt.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/ZArith/Zsqrt.v b/theories/ZArith/Zsqrt.v index 6ea952e6..b845cf47 100644 --- a/theories/ZArith/Zsqrt.v +++ b/theories/ZArith/Zsqrt.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(* $Id: Zsqrt.v 10295 2007-11-06 22:46:21Z letouzey $ *) +(* $Id$ *) Require Import ZArithRing. Require Import Omega. @@ -119,7 +119,7 @@ Definition Zsqrt : | Zneg p => fun h => False_rec - {s : Z & + {s : Z & {r : Z | Zneg p = s * s + r /\ s * s <= Zneg p < (s + 1) * (s + 1)}} (h (refl_equal Datatypes.Gt)) @@ -199,7 +199,7 @@ Qed. Theorem Zsqrt_le: forall p q, 0 <= p <= q -> Zsqrt_plain p <= Zsqrt_plain q. Proof. - intros p q [H1 H2]; case Zle_lt_or_eq with (1:=H2); clear H2; intros H2; + intros p q [H1 H2]; case Zle_lt_or_eq with (1:=H2); clear H2; intros H2; [ | subst q; auto with zarith]. case (Zle_or_lt (Zsqrt_plain p) (Zsqrt_plain q)); auto; intros H3. assert (Hp: (0 <= Zsqrt_plain q)). |