diff options
Diffstat (limited to 'theories/Init/Datatypes.v')
| -rw-r--r-- | theories/Init/Datatypes.v | 38 |
1 files changed, 22 insertions, 16 deletions
diff --git a/theories/Init/Datatypes.v b/theories/Init/Datatypes.v index ddaf08bf..05b741f0 100644 --- a/theories/Init/Datatypes.v +++ b/theories/Init/Datatypes.v @@ -1,9 +1,11 @@ (************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) (* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) (************************************************************************) Set Implicit Arguments. @@ -65,7 +67,7 @@ Infix "&&" := andb : bool_scope. Lemma andb_prop : forall a b:bool, andb a b = true -> a = true /\ b = true. Proof. - destruct a; destruct b; intros; split; try (reflexivity || discriminate). + destruct a, b; repeat split; assumption. Qed. Hint Resolve andb_prop: bool. @@ -262,6 +264,11 @@ Inductive comparison : Set := | Lt : comparison | Gt : comparison. +Lemma comparison_eq_stable : forall c c' : comparison, ~~ c = c' -> c = c'. +Proof. + destruct c, c'; intro H; reflexivity || destruct H; discriminate. +Qed. + Definition CompOpp (r:comparison) := match r with | Eq => Eq @@ -326,13 +333,12 @@ Lemma CompSpec2Type : forall A (eq lt:A->A->Prop) x y c, CompSpec eq lt x y c -> CompSpecT eq lt x y c. Proof. intros. apply CompareSpec2Type; assumption. Defined. - (******************************************************************) (** * Misc Other Datatypes *) (** [identity A a] is the family of datatypes on [A] whose sole non-empty member is the singleton datatype [identity A a a] whose - sole inhabitant is denoted [refl_identity A a] *) + sole inhabitant is denoted [identity_refl A a] *) Inductive identity (A:Type) (a:A) : A -> Type := identity_refl : identity a a. @@ -355,14 +361,14 @@ Definition idProp : IDProp := fun A x => x. (* Compatibility *) -Notation prodT := prod (compat "8.2"). -Notation pairT := pair (compat "8.2"). -Notation prodT_rect := prod_rect (compat "8.2"). -Notation prodT_rec := prod_rec (compat "8.2"). -Notation prodT_ind := prod_ind (compat "8.2"). -Notation fstT := fst (compat "8.2"). -Notation sndT := snd (compat "8.2"). -Notation prodT_uncurry := prod_uncurry (compat "8.2"). -Notation prodT_curry := prod_curry (compat "8.2"). +Notation prodT := prod (only parsing). +Notation pairT := pair (only parsing). +Notation prodT_rect := prod_rect (only parsing). +Notation prodT_rec := prod_rec (only parsing). +Notation prodT_ind := prod_ind (only parsing). +Notation fstT := fst (only parsing). +Notation sndT := snd (only parsing). +Notation prodT_uncurry := prod_uncurry (only parsing). +Notation prodT_curry := prod_curry (only parsing). (* end hide *) |