# HG changeset patch # User nipkow # Date 832342086 -7200 # Node ID 88650ba93c10f08f58bb853e15437c69a0f621f9 # Parent f20c9abe4b50b264c0932f829eeea03dfcd41332 Added if_image_distrib. diff -r f20c9abe4b50 -r 88650ba93c10 src/HOL/equalities.ML --- a/src/HOL/equalities.ML Fri May 17 12:24:47 1996 +0200 +++ b/src/HOL/equalities.ML Fri May 17 16:08:06 1996 +0200 @@ -84,6 +84,15 @@ qed_goal "ball_image" Set.thy "(!y:F``S. P y) = (!x:S. P (F x))" (fn _ => [fast_tac set_cs 1]); +goalw Set.thy [image_def] +"(%x. if P x then f x else g x) `` S \ +\ = (f `` ({x.x:S & P x})) Un (g `` ({x.x:S & ~(P x)}))"; +by(split_tac [expand_if] 1); +by(fast_tac eq_cs 1); +qed "if_image_distrib"; +Addsimps[if_image_distrib]; + + section "range"; qed_goal "ball_range" Set.thy "(!y:range f. P y) = (!x. P (f x))"