src/ZF/EquivClass.thy

{HOL,ZF}/indrule/quant_induct: replaced ssubst in eresolve_tac by
separate call to hyp_subst_tac. This avoids substituting in x=f(x)

{HOL,ZF}/indrule/ind_tac: now tries resolve_tac [refl]. This handles
trivial equalities such as x=a.

{HOL,ZF}/intr_elim/intro_tacsf_tac: now calls assume_tac last, to try refl
before any equality assumptions

(*  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