From 063523ae5f8da7e6458232f4afb6744ec86dc8bd Mon Sep 17 00:00:00 2001 From: Claudio Sacerdoti Coen Date: Sun, 18 May 2008 17:44:51 +0000 Subject: [PATCH] Dummy dependent types are no longer cleaned in inductive type arities. --- helm/software/matita/library/nat/primes.ma | 30 +++++++++++----------- 1 file changed, 15 insertions(+), 15 deletions(-) diff --git a/helm/software/matita/library/nat/primes.ma b/helm/software/matita/library/nat/primes.ma index dcf7abeea..049801e8a 100644 --- a/helm/software/matita/library/nat/primes.ma +++ b/helm/software/matita/library/nat/primes.ma @@ -81,36 +81,36 @@ qed. theorem divides_plus: \forall n,p,q:nat. n \divides p \to n \divides q \to n \divides p+q. intros. -elim H.elim H1. apply (witness n (p+q) (n2+n1)). +elim H.elim H1. apply (witness n (p+q) (n1+n2)). rewrite > H2.rewrite > H3.apply sym_eq.apply distr_times_plus. qed. theorem divides_minus: \forall n,p,q:nat. divides n p \to divides n q \to divides n (p-q). intros. -elim H.elim H1. apply (witness n (p-q) (n2-n1)). +elim H.elim H1. apply (witness n (p-q) (n1-n2)). rewrite > H2.rewrite > H3.apply sym_eq.apply distr_times_minus. qed. theorem divides_times: \forall n,m,p,q:nat. n \divides p \to m \divides q \to n*m \divides p*q. intros. -elim H.elim H1. apply (witness (n*m) (p*q) (n2*n1)). +elim H.elim H1. apply (witness (n*m) (p*q) (n1*n2)). rewrite > H2.rewrite > H3. -apply (trans_eq nat ? (n*(m*(n2*n1)))). -apply (trans_eq nat ? (n*(n2*(m*n1)))). +apply (trans_eq nat ? (n*(m*(n1*n2)))). +apply (trans_eq nat ? (n*(n1*(m*n2)))). apply assoc_times. apply eq_f. -apply (trans_eq nat ? ((n2*m)*n1)). +apply (trans_eq nat ? ((n1*m)*n2)). apply sym_eq. apply assoc_times. -rewrite > (sym_times n2 m).apply assoc_times. +rewrite > (sym_times n1 m).apply assoc_times. apply sym_eq. apply assoc_times. qed. theorem transitive_divides: transitive ? divides. unfold. intros. -elim H.elim H1. apply (witness x z (n2*n)). +elim H.elim H1. apply (witness x z (n1*n)). rewrite > H3.rewrite > H2. apply assoc_times. qed. @@ -150,7 +150,7 @@ qed. theorem antisymmetric_divides: antisymmetric nat divides. unfold antisymmetric.intros.elim H. elim H1. -apply (nat_case1 n2).intro. +apply (nat_case1 n1).intro. rewrite > H3.rewrite > H2.rewrite > H4. rewrite < times_n_O.reflexivity. intros. @@ -167,11 +167,11 @@ qed. (* divides le *) theorem divides_to_le : \forall n,m. O < m \to n \divides m \to n \le m. -intros. elim H1.rewrite > H2.cut (O < n2). -apply (lt_O_n_elim n2 Hcut).intro.rewrite < sym_times. +intros. elim H1.rewrite > H2.cut (O < n1). +apply (lt_O_n_elim n1 Hcut).intro.rewrite < sym_times. simplify.rewrite < sym_plus. apply le_plus_n. -elim (le_to_or_lt_eq O n2). +elim (le_to_or_lt_eq O n1). assumption. absurd (O H2.rewrite < H3.rewrite < times_n_O. @@ -269,11 +269,11 @@ O \lt b \to c \divides b \to a * (b /c) = (a*b)/c. intros. elim H1. rewrite > H2. -rewrite > (sym_times c n2). +rewrite > (sym_times c n1). cut(O \lt c) -[ rewrite > (lt_O_to_div_times n2 c) +[ rewrite > (lt_O_to_div_times n1 c) [ rewrite < assoc_times. - rewrite > (lt_O_to_div_times (a *n2) c) + rewrite > (lt_O_to_div_times (a *n1) c) [ reflexivity | assumption ] -- 2.39.2