diff -r 268b6bed0cc8 -r 9c9fdf4c2949 src/HOL/FixedPoint.thy --- a/src/HOL/FixedPoint.thy Mon Nov 27 13:42:33 2006 +0100 +++ b/src/HOL/FixedPoint.thy Mon Nov 27 13:42:39 2006 +0100 @@ -120,30 +120,6 @@ subsubsection {* Booleans *} -instance bool :: ord .. - -defs - le_bool_def: "P <= Q == P \ Q" - less_bool_def: "P < Q == (P::bool) <= Q \ P \ Q" - -theorem le_boolI: "(P \ Q) \ P <= Q" - by (simp add: le_bool_def) - -theorem le_boolI': "P \ Q \ P <= Q" - by (simp add: le_bool_def) - -theorem le_boolE: "P <= Q \ P \ (Q \ R) \ R" - by (simp add: le_bool_def) - -theorem le_boolD: "P <= Q \ P \ Q" - by (simp add: le_bool_def) - -instance bool :: order - apply intro_classes - apply (unfold le_bool_def less_bool_def) - apply iprover+ - done - defs Meet_bool_def: "Meet A == ALL x:A. x" instance bool :: comp_lat @@ -201,21 +177,6 @@ subsubsection {* Functions *} -instance "fun" :: (type, ord) ord .. - -defs - le_fun_def: "f <= g == \x. f x <= g x" - less_fun_def: "f < g == (f::'a\'b::ord) <= g \ f \ g" - -theorem le_funI: "(\x. f x <= g x) \ f <= g" - by (simp add: le_fun_def) - -theorem le_funE: "f <= g \ (f x <= g x \ P) \ P" - by (simp add: le_fun_def) - -theorem le_funD: "f <= g \ f x <= g x" - by (simp add: le_fun_def) - text {* Handy introduction and elimination rules for @{text "\"} on unary and binary predicates @@ -251,21 +212,6 @@ apply assumption+ done -instance "fun" :: (type, order) order - apply intro_classes - apply (rule le_funI) - apply (rule order_refl) - apply (rule le_funI) - apply (erule le_funE)+ - apply (erule order_trans) - apply assumption - apply (rule ext) - apply (erule le_funE)+ - apply (erule order_antisym) - apply assumption - apply (simp add: less_fun_def) - done - defs Meet_fun_def: "Meet A == (\x. Meet {y. EX f:A. y = f x})" instance "fun" :: (type, comp_lat) comp_lat