diff -r 5eb932e604a2 -r eab6ce8368fa src/HOL/Basic_BNFs.thy --- a/src/HOL/Basic_BNFs.thy Wed Jan 10 15:21:49 2018 +0100 +++ b/src/HOL/Basic_BNFs.thy Wed Jan 10 15:25:09 2018 +0100 @@ -188,22 +188,22 @@ qed auto bnf "'a \ 'b" - map: "op \" + map: "(\)" sets: range bd: "natLeq +c |UNIV :: 'a set|" - rel: "rel_fun op =" + rel: "rel_fun (=)" pred: "pred_fun (\_. True)" proof fix f show "id \ f = id f" by simp next - fix f g show "op \ (g \ f) = op \ g \ op \ f" + fix f g show "(\) (g \ f) = (\) g \ (\) f" unfolding comp_def[abs_def] .. next fix x f g assume "\z. z \ range x \ f z = g z" thus "f \ x = g \ x" by auto next - fix f show "range \ op \ f = op ` f \ range" + fix f show "range \ (\) f = (`) f \ range" by (auto simp add: fun_eq_iff) next show "card_order (natLeq +c |UNIV| )" (is "_ (_ +c ?U)") @@ -222,10 +222,10 @@ finally show "|range f| \o natLeq +c ?U" . next fix R S - show "rel_fun op = R OO rel_fun op = S \ rel_fun op = (R OO S)" by (auto simp: rel_fun_def) + show "rel_fun (=) R OO rel_fun (=) S \ rel_fun (=) (R OO S)" by (auto simp: rel_fun_def) next fix R - show "rel_fun op = R = (\x y. + show "rel_fun (=) R = (\x y. \z. range z \ {(x, y). R x y} \ fst \ z = x \ snd \ z = y)" unfolding rel_fun_def subset_iff by (force simp: fun_eq_iff[symmetric]) qed (auto simp: pred_fun_def)