From 49734f6f824dd310520cbb0cee0e605296e2d975 Mon Sep 17 00:00:00 2001 From: Enrico Tassi Date: Thu, 7 Jul 2005 09:06:48 +0000 Subject: [PATCH] fixed according to the new fresh name generator --- helm/matita/library/Z.ma | 49 +++++++++++++++++++------------------- helm/matita/library/nat.ma | 6 ++--- 2 files changed, 28 insertions(+), 27 deletions(-) diff --git a/helm/matita/library/Z.ma b/helm/matita/library/Z.ma index d0049187a..da6bbadb2 100644 --- a/helm/matita/library/Z.ma +++ b/helm/matita/library/Z.ma @@ -51,13 +51,13 @@ theorem OZ_discr : \forall z. if_then_else (OZ_testb z) (eq Z z OZ) (Not (eq Z z OZ)). intros.elim z.simplify.reflexivity. simplify.intros. -cut match neg e with +cut match neg e1 with [ OZ \Rightarrow True | (pos n) \Rightarrow False | (neg n) \Rightarrow False]. apply Hcut.rewrite > H.simplify.exact I. simplify.intros. -cut match pos e with +cut match pos e2 with [ OZ \Rightarrow True | (pos n) \Rightarrow False | (neg n) \Rightarrow False]. @@ -84,7 +84,7 @@ definition Zpred \def theorem Zpred_succ: \forall z:Z. eq Z (Zpred (Zsucc z)) z. intros.elim z.reflexivity. -elim e.reflexivity. +elim e1.reflexivity. reflexivity. reflexivity. qed. @@ -92,7 +92,7 @@ qed. theorem Zsucc_pred: \forall z:Z. eq Z (Zsucc (Zpred z)) z. intros.elim z.reflexivity. reflexivity. -elim e.reflexivity. +elim e2.reflexivity. reflexivity. qed. @@ -131,30 +131,30 @@ elim y.simplify.reflexivity. simplify. rewrite < (sym_plus e e1).reflexivity. simplify. -rewrite > nat_compare_invert e e1. -simplify.elim nat_compare e1 e.simplify.reflexivity. +rewrite > nat_compare_invert e1 e2. +simplify.elim nat_compare e2 e1.simplify.reflexivity. simplify. reflexivity. simplify. reflexivity. elim y.simplify.reflexivity. -simplify.rewrite > nat_compare_invert e e1. -simplify.elim nat_compare e1 e.simplify.reflexivity. +simplify.rewrite > nat_compare_invert e1 e2. +simplify.elim nat_compare e2 e1.simplify.reflexivity. simplify. reflexivity. simplify. reflexivity. -simplify.elim (sym_plus e1 e).reflexivity. +simplify.elim (sym_plus e2 e).reflexivity. qed. theorem Zpred_neg : \forall z:Z. eq Z (Zpred z) (Zplus (neg O) z). intros.elim z. simplify.reflexivity. simplify.reflexivity. -elim e.simplify.reflexivity. +elim e2.simplify.reflexivity. simplify.reflexivity. qed. theorem Zsucc_pos : \forall z:Z. eq Z (Zsucc z) (Zplus (pos O) z). intros.elim z. simplify.reflexivity. -elim e.simplify.reflexivity. +elim e1.simplify.reflexivity. simplify.reflexivity. simplify.reflexivity. qed. @@ -167,9 +167,9 @@ simplify.reflexivity. simplify.reflexivity. elim m. simplify. -rewrite < plus_n_O e.reflexivity. +rewrite < plus_n_O e1.reflexivity. simplify. -rewrite < plus_n_Sm e e1.reflexivity. +rewrite < plus_n_Sm e1 e.reflexivity. qed. theorem Zplus_succ_pred_pn : @@ -195,11 +195,12 @@ elim n.elim m. simplify.reflexivity. simplify.reflexivity. elim m. -simplify.rewrite < plus_n_Sm e O.reflexivity. -simplify.rewrite > plus_n_Sm e (S e1).reflexivity. +simplify.rewrite < plus_n_Sm e1 O.reflexivity. +simplify.rewrite > plus_n_Sm e1 (S e).reflexivity. qed. -(*CSC: da qui in avanti rewrite ancora non utilizzata *) +(* da qui in avanti rewrite ancora non utilizzata *) + theorem Zplus_succ_pred: \forall x,y. eq Z (Zplus x y) (Zplus (Zsucc x) (Zpred y)). intros. @@ -229,7 +230,7 @@ apply nat_double_ind (\lambda n,m. eq Z (Zplus (Zsucc (pos n)) (neg m)) (Zsucc (Zplus (pos n) (neg m)))).intro. intros.elim n1. simplify. reflexivity. -elim e.simplify. reflexivity. +elim e1.simplify. reflexivity. simplify. reflexivity. intros. elim n1. simplify. reflexivity. @@ -246,7 +247,7 @@ apply nat_double_ind (\lambda n,m. eq Z (Zplus (Zsucc (neg n)) (neg m)) (Zsucc (Zplus (neg n) (neg m)))).intro. intros.elim n1. simplify. reflexivity. -elim e.simplify. reflexivity. +elim e1.simplify. reflexivity. simplify. reflexivity. intros. elim n1. simplify. reflexivity. @@ -263,7 +264,7 @@ apply nat_double_ind (\lambda n,m. eq Z (Zplus (Zsucc (neg n)) (pos m)) (Zsucc (Zplus (neg n) (pos m)))). intros.elim n1. simplify. reflexivity. -elim e.simplify. reflexivity. +elim e1.simplify. reflexivity. simplify. reflexivity. intros. elim n1. simplify. reflexivity. @@ -303,15 +304,15 @@ qed. theorem assoc_Zplus : \forall x,y,z:Z. eq Z (Zplus x (Zplus y z)) (Zplus (Zplus x y) z). intros.elim x.simplify.reflexivity. -elim e.elim (Zpred_neg (Zplus y z)). +elim e1.elim (Zpred_neg (Zplus y z)). elim (Zpred_neg y). elim (Zpred_plus ? ?). reflexivity. -elim (sym_eq ? ? ? (Zpred_plus (neg e1) ?)). -elim (sym_eq ? ? ? (Zpred_plus (neg e1) ?)). -elim (sym_eq ? ? ? (Zpred_plus (Zplus (neg e1) y) ?)). +elim (sym_eq ? ? ? (Zpred_plus (neg e) ?)). +elim (sym_eq ? ? ? (Zpred_plus (neg e) ?)). +elim (sym_eq ? ? ? (Zpred_plus (Zplus (neg e) y) ?)). apply f_equal.assumption. -elim e.elim (Zsucc_pos ?). +elim e2.elim (Zsucc_pos ?). elim (Zsucc_pos ?). apply (sym_eq ? ? ? (Zsucc_plus ? ?)) . elim (sym_eq ? ? ? (Zsucc_plus (pos e1) ?)). diff --git a/helm/matita/library/nat.ma b/helm/matita/library/nat.ma index 3ab39d9e4..4ab1feb2b 100644 --- a/helm/matita/library/nat.ma +++ b/helm/matita/library/nat.ma @@ -103,8 +103,8 @@ theorem times_n_Sm : \forall n,m:nat. eq nat (plus n (times n m)) (times n (S m)). intros.elim n.simplify.reflexivity. simplify.apply f_equal.rewrite < H. -transitivity (plus (plus e m) (times e m)).symmetry. -apply assoc_plus.transitivity (plus (plus m e) (times e m)). +transitivity (plus (plus e1 m) (times e1 m)).symmetry. +apply assoc_plus.transitivity (plus (plus m e1) (times e1 m)). apply f_equal2. apply sym_plus.reflexivity.apply assoc_plus. qed. @@ -188,7 +188,7 @@ qed. theorem le_Sn_n : \forall n:nat. Not (le (S n) n). intros.elim n.apply le_Sn_O.simplify.intros. -cut le (S e) e.apply H.assumption.apply le_S_n.assumption. +cut le (S e1) e1.apply H.assumption.apply le_S_n.assumption. qed. theorem le_antisym : \forall n,m:nat. (le n m) \to (le m n) \to (eq nat n m). -- 2.39.2