diff options
Diffstat (limited to 'theories/Numbers/NatInt/NZBase.v')
| -rw-r--r-- | theories/Numbers/NatInt/NZBase.v | 19 |
1 files changed, 11 insertions, 8 deletions
diff --git a/theories/Numbers/NatInt/NZBase.v b/theories/Numbers/NatInt/NZBase.v index 119f8265..62b14829 100644 --- a/theories/Numbers/NatInt/NZBase.v +++ b/theories/Numbers/NatInt/NZBase.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -8,11 +8,14 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id: NZBase.v 14641 2011-11-06 11:59:10Z herbelin $ i*) - Require Import NZAxioms. -Module Type NZBasePropSig (Import NZ : NZDomainSig'). +Module Type NZBaseProp (Import NZ : NZDomainSig'). + +(** An artificial scope meant to be substituted later *) + +Delimit Scope abstract_scope with abstract. +Bind Scope abstract_scope with t. Include BackportEq NZ NZ. (** eq_refl, eq_sym, eq_trans *) @@ -50,7 +53,7 @@ Theorem succ_inj_wd : forall n1 n2, S n1 == S n2 <-> n1 == n2. Proof. intros; split. apply succ_inj. -apply succ_wd. +intros. now f_equiv. Qed. Theorem succ_inj_wd_neg : forall n m, S n ~= S m <-> n ~= m. @@ -63,7 +66,7 @@ left-inverse to the successor at this point *) Section CentralInduction. -Variable A : predicate t. +Variable A : t -> Prop. Hypothesis A_wd : Proper (eq==>iff) A. Theorem central_induction : @@ -72,7 +75,7 @@ Theorem central_induction : forall n, A n. Proof. intros z Base Step; revert Base; pattern z; apply bi_induction. -solve_predicate_wd. +solve_proper. intro; now apply bi_induction. intro; pose proof (Step n); tauto. Qed. @@ -85,5 +88,5 @@ Tactic Notation "nzinduct" ident(n) := Tactic Notation "nzinduct" ident(n) constr(u) := induction_maker n ltac:(apply central_induction with (z := u)). -End NZBasePropSig. +End NZBaseProp. |