1274
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(*
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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 theory Stream2.thy
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*)
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open Stream2;
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(* ------------------------------------------------------------------------- *)
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(* expand fixed point properties *)
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(* ------------------------------------------------------------------------- *)
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val smap_def2 = fix_prover2 Stream2.thy smap_def
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"smap = (LAM f s. stream_when`(LAM x l.scons`(f`x) `(smap`f`l)) `s)";
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(* ------------------------------------------------------------------------- *)
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(* recursive properties *)
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(* ------------------------------------------------------------------------- *)
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qed_goal "smap1" Stream2.thy "smap`f`UU = UU"
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(fn prems =>
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[
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(rtac (smap_def2 RS ssubst) 1),
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(simp_tac (!simpset addsimps stream_when) 1)
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]);
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qed_goal "smap2" Stream2.thy
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"x~=UU ==> smap`f`(scons`x`xs) = scons `(f`x) `(smap`f`xs)"
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(fn prems =>
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[
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(cut_facts_tac prems 1),
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(rtac trans 1),
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(rtac (smap_def2 RS ssubst) 1),
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(asm_simp_tac (!simpset addsimps stream_rews) 1),
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(rtac refl 1)
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]);
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val stream2_rews = [smap1, smap2];
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