diff -r f04b33ce250f -r a4dc62a46ee4 Integ/Equiv.thy --- 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. : r)" - sym_def "sym(r) == ALL x y. : r --> : 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. :r --> b(y)=b(z)" - congruent2_def "congruent2(r,b) == ALL y1 z1 y2 z2. - :r --> :r --> b(y1,y2) = b(z1,z2)" -end