turned translation for 1::nat into def.
introduced 1' and replaced most occurrences of 1 by 1'.
(* Title: CCL/trancl.thy
ID: $Id$
Author: Martin Coen, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Transitive closure of a relation
*)
Trancl = CCL +
consts
trans :: "i set => o" (*transitivity predicate*)
id :: "i set"
rtrancl :: "i set => i set" ("(_^*)" [100] 100)
trancl :: "i set => i set" ("(_^+)" [100] 100)
O :: "[i set,i set] => i set" (infixr 60)
rules
trans_def "trans(r) == (ALL x y z. <x,y>:r --> <y,z>:r --> <x,z>:r)"
comp_def (*composition of relations*)
"r O s == {xz. EX x y z. xz = <x,z> & <x,y>:s & <y,z>:r}"
id_def (*the identity relation*)
"id == {p. EX x. p = <x,x>}"
rtrancl_def "r^* == lfp(%s. id Un (r O s))"
trancl_def "r^+ == r O rtrancl(r)"
end