--- a/Integ/Equiv.thy Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,28 +0,0 @@
-(* Title: Equiv.thy
- ID: $Id$
- Authors: Riccardo Mattolini, Dip. Sistemi e Informatica
- Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1994 Universita' di Firenze
- Copyright 1993 University of Cambridge
-
-Equivalence relations in Higher-Order Set Theory
-*)
-
-Equiv = Relation +
-consts
- refl,equiv :: "['a set,('a*'a) set]=>bool"
- sym :: "('a*'a) set=>bool"
- "'/" :: "['a set,('a*'a) set]=>'a set set" (infixl 90)
- (*set of equiv classes*)
- congruent :: "[('a*'a) set,'a=>'b]=>bool"
- congruent2 :: "[('a*'a) set,['a,'a]=>'b]=>bool"
-
-defs
- refl_def "refl(A,r) == r <= Sigma(A,%x.A) & (ALL x: A. <x,x> : r)"
- sym_def "sym(r) == ALL x y. <x,y>: r --> <y,x>: r"
- equiv_def "equiv(A,r) == refl(A,r) & sym(r) & trans(r)"
- quotient_def "A/r == UN x:A. {r^^{x}}"
- congruent_def "congruent(r,b) == ALL y z. <y,z>:r --> b(y)=b(z)"
- congruent2_def "congruent2(r,b) == ALL y1 z1 y2 z2.
- <y1,z1>:r --> <y2,z2>:r --> b(y1,y2) = b(z1,z2)"
-end