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(* Title: HOL/Lex/RegSet.ML
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ID: $Id$
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Author: Tobias Nipkow
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Copyright 1998 TUM
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*)
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AddIffs [star.NilI];
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Addsimps [star.ConsI];
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AddIs [star.ConsI];
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Goal "(!xs: set xss. xs:S) --> concat xss : star S";
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by (induct_tac "xss" 1);
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by (ALLGOALS Asm_full_simp_tac);
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qed_spec_mp "concat_in_star";
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Goal
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"w : star U = (? us. (!u : set(us). u : U) & (w = concat us))";
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by (rtac iffI 1);
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be star.induct 1;
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by (res_inst_tac [("x","[]")] exI 1);
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by (Simp_tac 1);
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by (Clarify_tac 1);
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by (res_inst_tac [("x","a#us")] exI 1);
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by (Asm_simp_tac 1);
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by (Clarify_tac 1);
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by (asm_simp_tac (simpset() addsimps [concat_in_star]) 1);
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qed "in_star";
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