2570
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(* $Id$ *)
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open Dagstuhl;
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val YS_def2 = fix_prover2 Dagstuhl.thy YS_def "YS = y && YS";
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val YYS_def2 = fix_prover2 Dagstuhl.thy YYS_def "YYS = y && y && YYS";
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val prems = goal Dagstuhl.thy "YYS << y && YYS";
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by (rtac (YYS_def RS def_fix_ind) 1);
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by (Simp_tac 1);
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by (cont_tacR 1);
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by (stac beta_cfun 1);
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by (cont_tacR 1);
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by (rtac monofun_cfun_arg 1);
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by (rtac monofun_cfun_arg 1);
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by (atac 1);
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val lemma3 = result();
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val prems = goal Dagstuhl.thy "y && YYS << YYS";
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by (stac YYS_def2 1);
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back();
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by (rtac monofun_cfun_arg 1);
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by (rtac lemma3 1);
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val lemma4=result();
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(* val lemma5 = lemma3 RS (lemma4 RS antisym_less) *)
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val prems = goal Dagstuhl.thy "y && YYS = YYS";
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by (rtac antisym_less 1);
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by (rtac lemma4 1);
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by (rtac lemma3 1);
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val lemma5=result();
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val prems = goal Dagstuhl.thy "YS = YYS";
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by (rtac stream.take_lemma 1);
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by (nat_ind_tac "n" 1);
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by (simp_tac (!simpset addsimps stream.rews) 1);
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by (stac YS_def2 1);
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by (stac YYS_def2 1);
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by (asm_simp_tac (!simpset addsimps stream.rews) 1);
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by (rtac (lemma5 RS sym RS subst) 1);
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by (rtac refl 1);
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val wir_moel=result();
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(* ------------------------------------------------------------------------ *)
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(* Zweite L"osung: Bernhard M"oller *)
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(* statt Beweis von wir_moel "uber take_lemma beidseitige Inclusion *)
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(* verwendet lemma5 *)
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(* ------------------------------------------------------------------------ *)
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val prems = goal Dagstuhl.thy "YYS << YS";
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by (rewtac YYS_def);
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by (rtac fix_least 1);
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by (stac beta_cfun 1);
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by (cont_tacR 1);
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by (simp_tac (!simpset addsimps [YS_def2 RS sym]) 1);
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val lemma6=result();
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val prems = goal Dagstuhl.thy "YS << YYS";
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by (rtac (YS_def RS def_fix_ind) 1);
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by (Simp_tac 1);
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by (cont_tacR 1);
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by (stac beta_cfun 1);
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by (cont_tacR 1);
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by (stac (lemma5 RS sym) 1);
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by (etac monofun_cfun_arg 1);
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val lemma7 = result();
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val wir_moel = lemma6 RS (lemma7 RS antisym_less);
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