diff options
author | 2009-09-17 15:58:14 +0000 | |
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committer | 2009-09-17 15:58:14 +0000 | |
commit | 61ccbc81a2f3b4662ed4a2bad9d07d2003dda3a2 (patch) | |
tree | 961cc88c714aa91a0276ea9fbf8bc53b2b9d5c28 /theories/Numbers/Natural/SpecViaZ | |
parent | 6d3fbdf36c6a47b49c2a4b16f498972c93c07574 (diff) |
Delete trailing whitespaces in all *.{v,ml*} files
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12337 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Natural/SpecViaZ')
-rw-r--r-- | theories/Numbers/Natural/SpecViaZ/NSig.v | 4 | ||||
-rw-r--r-- | theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v | 4 |
2 files changed, 4 insertions, 4 deletions
diff --git a/theories/Numbers/Natural/SpecViaZ/NSig.v b/theories/Numbers/Natural/SpecViaZ/NSig.v index e53e627ec..5295aaec2 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSig.v +++ b/theories/Numbers/Natural/SpecViaZ/NSig.v @@ -58,7 +58,7 @@ Module Type NType. Parameter spec_eq_bool: forall x y, if eq_bool x y then [x] = [y] else [x] <> [y]. - + Parameter succ : t -> t. Parameter spec_succ: forall n, [succ n] = [n] + 1. @@ -98,7 +98,7 @@ Module Type NType. Parameter spec_div_eucl: forall x y, 0 < [y] -> let (q,r) := div_eucl x y in ([q], [r]) = Zdiv_eucl [x] [y]. - + Parameter div : t -> t -> t. Parameter spec_div: forall x y, 0 < [y] -> [div x y] = [x] / [y]. diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v index 773807120..578cb6256 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v +++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v @@ -97,7 +97,7 @@ Section Induction. Variable A : N.t -> Prop. Hypothesis A_wd : predicate_wd N.eq A. Hypothesis A0 : A 0. -Hypothesis AS : forall n, A n <-> A (N.succ n). +Hypothesis AS : forall n, A n <-> A (N.succ n). Add Morphism A with signature N.eq ==> iff as A_morph. Proof. apply A_wd. Qed. @@ -221,7 +221,7 @@ Proof. Qed. Add Morphism N.compare with signature N.eq ==> N.eq ==> (@eq comparison) as compare_wd. -Proof. +Proof. intros x x' Hx y y' Hy. rewrite 2 spec_compare_alt. unfold N.eq in *. rewrite Hx, Hy; intuition. Qed. |