author | paulson |
Thu, 21 Mar 1996 13:02:26 +0100 | |
changeset 1601 | 0ef6ea27ab15 |
parent 1461 | 6bcb44e4d6e5 |
child 2033 | 639de962ded4 |
permissions | -rw-r--r-- |
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(* Title: HOLCF/cfun1.ML |
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ID: $Id$ |
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Author: Franz Regensburger |
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Copyright 1993 Technische Universitaet Muenchen |
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Lemmas for cfun1.thy |
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*) |
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open Cfun1; |
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(* ------------------------------------------------------------------------ *) |
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(* A non-emptyness result for Cfun *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "CfunI" Cfun1.thy [Cfun_def] "(% x.x):Cfun" |
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(fn prems => |
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[ |
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(rtac (mem_Collect_eq RS ssubst) 1), |
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(rtac cont_id 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* less_cfun is a partial order on type 'a -> 'b *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "refl_less_cfun" Cfun1.thy [less_cfun_def] "less_cfun f f" |
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(fn prems => |
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(rtac refl_less 1) |
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]); |
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qed_goalw "antisym_less_cfun" Cfun1.thy [less_cfun_def] |
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"[|less_cfun f1 f2; less_cfun f2 f1|] ==> f1 = f2" |
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(fn prems => |
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(cut_facts_tac prems 1), |
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(rtac injD 1), |
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(rtac antisym_less 2), |
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(atac 3), |
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(atac 2), |
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(rtac inj_inverseI 1), |
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(rtac Rep_Cfun_inverse 1) |
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]); |
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qed_goalw "trans_less_cfun" Cfun1.thy [less_cfun_def] |
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"[|less_cfun f1 f2; less_cfun f2 f3|] ==> less_cfun f1 f3" |
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(fn prems => |
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(cut_facts_tac prems 1), |
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(etac trans_less 1), |
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(atac 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* lemmas about application of continuous functions *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "cfun_cong" Cfun1.thy |
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"[| f=g; x=y |] ==> f`x = g`y" |
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(fn prems => |
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(cut_facts_tac prems 1), |
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(fast_tac HOL_cs 1) |
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]); |
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qed_goal "cfun_fun_cong" Cfun1.thy "f=g ==> f`x = g`x" |
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(fn prems => |
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(cut_facts_tac prems 1), |
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(etac cfun_cong 1), |
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(rtac refl 1) |
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]); |
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qed_goal "cfun_arg_cong" Cfun1.thy "x=y ==> f`x = f`y" |
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(fn prems => |
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(cut_facts_tac prems 1), |
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(rtac cfun_cong 1), |
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(rtac refl 1), |
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(atac 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* additional lemma about the isomorphism between -> and Cfun *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "Abs_Cfun_inverse2" Cfun1.thy "cont(f) ==> fapp(fabs(f)) = f" |
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(fn prems => |
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(cut_facts_tac prems 1), |
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(rtac Abs_Cfun_inverse 1), |
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(rewtac Cfun_def), |
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(etac (mem_Collect_eq RS ssubst) 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* simplification of application *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "Cfunapp2" Cfun1.thy |
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"cont(f) ==> (fabs f)`x = f x" |
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(fn prems => |
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(cut_facts_tac prems 1), |
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(etac (Abs_Cfun_inverse2 RS fun_cong) 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* beta - equality for continuous functions *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "beta_cfun" Cfun1.thy |
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"cont(c1) ==> (LAM x .c1 x)`u = c1 u" |
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(fn prems => |
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(cut_facts_tac prems 1), |
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(rtac Cfunapp2 1), |
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(atac 1) |
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]); |
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