diff -r b7866aea0815 -r c4f13ab78f9d src/CCL/Trancl.thy --- a/src/CCL/Trancl.thy Wed Oct 03 19:49:33 2007 +0200 +++ b/src/CCL/Trancl.thy Wed Oct 03 21:29:05 2007 +0200 @@ -15,11 +15,11 @@ 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) + relcomp :: "[i set,i set] => i set" (infixr "O" 60) axioms trans_def: "trans(r) == (ALL x y z. :r --> :r --> :r)" - comp_def: (*composition of relations*) + relcomp_def: (*composition of relations*) "r O s == {xz. EX x y z. xz = & :s & :r}" id_def: (*the identity relation*) "id == {p. EX x. p = }" @@ -57,14 +57,14 @@ subsection {* Composition of two relations *} lemma compI: "[| :s; :r |] ==> : r O s" - unfolding comp_def by blast + unfolding relcomp_def by blast (*proof requires higher-level assumptions or a delaying of hyp_subst_tac*) lemma compE: "[| xz : r O s; !!x y z. [| xz = ; :s; :r |] ==> P |] ==> P" - unfolding comp_def by blast + unfolding relcomp_def by blast lemma compEpair: "[| : r O s;