diff -r ee0a0eb6b738 -r 151b3758f576 src/HOL/Lattices.thy --- a/src/HOL/Lattices.thy Sat Sep 29 08:58:51 2007 +0200 +++ b/src/HOL/Lattices.thy Sat Sep 29 08:58:54 2007 +0200 @@ -401,34 +401,34 @@ "\{a, b} = a \ b" by (simp add: Sup_insert_simp) -end - definition - top :: "'a::complete_lattice" + top :: 'a where "top = Inf {}" definition - bot :: "'a::complete_lattice" + bot :: 'a where "bot = Sup {}" -lemma top_greatest [simp]: "x \ top" +lemma top_greatest [simp]: "x \<^loc>\ top" by (unfold top_def, rule Inf_greatest, simp) -lemma bot_least [simp]: "bot \ x" +lemma bot_least [simp]: "bot \<^loc>\ x" by (unfold bot_def, rule Sup_least, simp) definition - SUPR :: "'a set \ ('a \ 'b::complete_lattice) \ 'b" + SUPR :: "'b set \ ('b \ 'a) \ 'a" where "SUPR A f == Sup (f ` A)" definition - INFI :: "'a set \ ('a \ 'b::complete_lattice) \ 'b" + INFI :: "'b set \ ('b \ 'a) \ 'a" where "INFI A f == Inf (f ` A)" +end + syntax "_SUP1" :: "pttrns => 'b => 'b" ("(3SUP _./ _)" [0, 10] 10) "_SUP" :: "pttrn => 'a set => 'b => 'b" ("(3SUP _:_./ _)" [0, 10] 10)