From 41bf87dd6a35255596638f1b1983a0b2d0d071b8 Mon Sep 17 00:00:00 2001 From: herbelin Date: Wed, 14 Feb 2001 15:57:26 +0000 Subject: Renommage des variables dans les schémas d'induction git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@1387 85f007b7-540e-0410-9357-904b9bb8a0f7 --- contrib/omega/Zpower.v | 6 +++--- contrib/ring/Ring_normalize.v | 6 +++--- theories/Logic/Eqdep_dec.v | 4 ++-- theories/Reals/Rbase.v | 12 ++++++------ theories/Reals/Rbasic_fun.v | 4 ++-- theories/Wellfounded/Disjoint_Union.v | 12 ++++++------ theories/Wellfounded/Lexicographic_Exponentiation.v | 4 ++-- theories/Wellfounded/Lexicographic_Product.v | 6 +++--- theories/Zarith/Zmisc.v | 4 ++-- 9 files changed, 29 insertions(+), 29 deletions(-) diff --git a/contrib/omega/Zpower.v b/contrib/omega/Zpower.v index 9e90f63e6a..824012d124 100644 --- a/contrib/omega/Zpower.v +++ b/contrib/omega/Zpower.v @@ -306,7 +306,7 @@ Elim (convert p); Simpl; | Intro n; Rewrite (two_power_nat_S n); Unfold 2 Zdiv_rest_aux; Elim (iter_nat n (Z*Z)*Z Zdiv_rest_aux ((x,`0`),`1`)); - Destruct y; Intros; Apply f_equal with f:=[z:Z]`2*z`; Assumption ]. + Destruct a; Intros; Apply f_equal with f:=[z:Z]`2*z`; Assumption ]. Save. Lemma Zdiv_rest_correct2 : @@ -368,12 +368,12 @@ Lemma Zdiv_rest_correct : Intros x p. Generalize (Zdiv_rest_correct1 x p); Generalize (Zdiv_rest_correct2 x p). Elim (iter_pos p (Z*Z)*Z Zdiv_rest_aux ((x,`0`),`1`)). -Induction y. +Induction a. Intros. Elim H; Intros H1 H2; Clear H. Rewrite -> H0 in H1; Rewrite -> H0 in H2; Elim H2; Intros; -Apply Zdiv_rest_proof with q:=y0 r:=y1; Assumption. +Apply Zdiv_rest_proof with q:=a0 r:=b; Assumption. Save. End power_div_with_rest. diff --git a/contrib/ring/Ring_normalize.v b/contrib/ring/Ring_normalize.v index 34cb485fd6..2590dd72bc 100644 --- a/contrib/ring/Ring_normalize.v +++ b/contrib/ring/Ring_normalize.v @@ -278,7 +278,7 @@ Variable vm : (varmap A). * choice *) Definition interp_var [i:index] := (varmap_find Azero i vm). -Local ivl_aux := Fix ivl_aux {ivl_aux[x:index; t:varlist] : A := +(* Local *) Definition ivl_aux := Fix ivl_aux {ivl_aux[x:index; t:varlist] : A := Cases t of | Nil_var => (interp_var x) | (Cons_var x' t') => (Amult (interp_var x) (ivl_aux x' t')) @@ -290,14 +290,14 @@ Definition interp_vl := [l:varlist] | (Cons_var x t) => (ivl_aux x t) end. -Local interp_m := [c:A][l:varlist] +(* Local *) Definition interp_m := [c:A][l:varlist] Cases l of | Nil_var => c | (Cons_var x t) => (Amult c (ivl_aux x t)) end. -Local ics_aux := Fix ics_aux{ics_aux[a:A; s:canonical_sum] : A := +(* Local *) Definition ics_aux := Fix ics_aux{ics_aux[a:A; s:canonical_sum] : A := Cases s of | Nil_monom => a | (Cons_varlist l t) => (Aplus a (ics_aux (interp_vl l) t)) diff --git a/theories/Logic/Eqdep_dec.v b/theories/Logic/Eqdep_dec.v index 54845ea07d..6205fc6032 100644 --- a/theories/Logic/Eqdep_dec.v +++ b/theories/Logic/Eqdep_dec.v @@ -71,7 +71,7 @@ Unfold nu. Elim (eq_dec x y) using or_indd; Intros. Reflexivity. -Case y0; Trivial. +Case b; Trivial. Save. @@ -123,7 +123,7 @@ Intro e. Elim e using K_dec; Trivial. Intros. -Case y0; Trivial. +Case b; Trivial. Case H. Reflexivity. diff --git a/theories/Reals/Rbase.v b/theories/Reals/Rbase.v index 1fb31101db..91c3e5409d 100644 --- a/theories/Reals/Rbase.v +++ b/theories/Reals/Rbase.v @@ -64,7 +64,7 @@ Hints Resolve imp_not_Req : real. (**********) Lemma Req_EM:(r1,r2:R)(r1==r2)\/``r1<>r2``. Intros;Elim (total_order_T r1 r2);Intro. -Case y; Auto with real. +Case a; Auto with real. Auto with real. Save. Hints Resolve Req_EM : real. @@ -72,7 +72,7 @@ Hints Resolve Req_EM : real. (**********) Lemma total_order:(r1,r2:R)``r1r2``. Intros;Elim (total_order_T r1 r2);Intro;Auto. -Elim y;Intro;Auto. +Elim a;Intro;Auto. Save. (**********) @@ -199,16 +199,16 @@ Save. (*s Decidability of the order *) Lemma total_order_Rlt:(r1,r2:R)(sumboolT ``r1(well_founded Power Lex_Exp). Proof. Unfold 2 well_founded . - Induction a;Intros. + Induction a;Intros x y. Apply Acc_intro. Induction y0. Unfold 1 lex_exp ;Simpl. @@ -350,7 +350,7 @@ Proof. Apply Acc_intro. Induction y2. Unfold 1 lex_exp . - Simpl;Intros. + Simpl;Intros x4 y3. Intros. Apply (H0 x4 y3);Auto with sets. Intros. diff --git a/theories/Wellfounded/Lexicographic_Product.v b/theories/Wellfounded/Lexicographic_Product.v index 1572650474..a6da918e3c 100644 --- a/theories/Wellfounded/Lexicographic_Product.v +++ b/theories/Wellfounded/Lexicographic_Product.v @@ -29,11 +29,11 @@ Lemma acc_A_B_lexprod : (x:A)(Acc A leA x) ->(y:(B x))(Acc (B x) (leB x) y) ->(Acc (sigS A B) LexProd (existS A B x y)). Proof. - Induction 1. - Induction 4;Intros. + Induction 1; Intros x0 H0 H1 H2 y. + Induction 1;Intros. Apply Acc_intro. Induction y0. - Intros. + Intros x2 y1 H6. Simple Inversion H6;Intros. Cut (leA x2 x0);Intros. Apply H1;Auto with sets. diff --git a/theories/Zarith/Zmisc.v b/theories/Zarith/Zmisc.v index 2aa69092ad..bc90b06123 100644 --- a/theories/Zarith/Zmisc.v +++ b/theories/Zarith/Zmisc.v @@ -303,8 +303,8 @@ Lemma Z_modulo_2 : (x:Z) `x >= 0` -> { y:Z | `x=2*y` }+{ y:Z | `x=2*y+1` }. Proof. Intros x Hx. Elim (Zeven_odd_dec x); Intro. -Left. Split with (Zdiv2 x). Exact (Zeven_div2 x y). -Right. Split with (Zdiv2 x). Exact (Zodd_div2 x Hx y). +Left. Split with (Zdiv2 x). Exact (Zeven_div2 x a). +Right. Split with (Zdiv2 x). Exact (Zodd_div2 x Hx b). Save. (* Very simple *) -- cgit v1.2.3