(* Title: ZF/EquivClass.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1994 University of Cambridge
Equivalence relations in Zermelo-Fraenkel Set Theory
*)
EquivClass = Rel + Perm +
consts
"'/" :: "[i,i]=>i" (infixl 90) (*set of equiv classes*)
congruent :: "[i,i=>i]=>o"
congruent2 :: "[i,[i,i]=>i]=>o"
rules
quotient_def "A/r == {r``{x} . x:A}"
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