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(* Title: HOL/BCV/Types0.ML
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ID: $Id$
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Author: Tobias Nipkow
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Copyright 1999 TUM
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*)
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Goalw [le_typ] "(t::typ) <= t";
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by (Blast_tac 1);
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qed "le_typ_refl";
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Goalw [le_typ] "[| (t1::typ) <= t2; t2<=t3 |] ==> t1<=t3";
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by (Blast_tac 1);
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qed "le_typ_trans";
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Goalw [le_typ] "[| (t1::typ) <= t2; t2<=t1 |] ==> t1=t2";
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by (Blast_tac 1);
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qed "le_typ_antisym";
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Goalw [less_typ] "(t1::typ) < t2 = (t1<=t2 & t1 ~= t2)";
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by (rtac refl 1);
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qed "less_le_typ";
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Goal "(UNIV::typ set) = {Atyp,Btyp,Ctyp,Top}";
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by (Auto_tac);
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by (rename_tac "t" 1);
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by (exhaust_tac "t" 1);
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by (Auto_tac);
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qed "UNIV_typ_enum";
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Goal "finite(UNIV::typ set)";
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by (simp_tac (simpset() addsimps [UNIV_typ_enum]) 1);
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qed "finite_UNIV_typ";
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AddIffs [finite_UNIV_typ];
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