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(* Title: HOL/Datatype.ML
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ID: $Id$
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Author: Stefan Berghofer
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Copyright 1999 TU Muenchen
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*)
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(** sum_case -- the selection operator for sums **)
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(*compatibility*)
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val [sum_case_Inl, sum_case_Inr] = sum.cases;
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Goal "sum_case (%x::'a. f(Inl x)) (%y::'b. f(Inr y)) s = f(s)";
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by (EVERY1 [res_inst_tac [("s","s")] sumE,
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etac ssubst, rtac sum_case_Inl,
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etac ssubst, rtac sum_case_Inr]);
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qed "surjective_sum";
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(*Prevents simplification of f and g: much faster*)
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Goal "s=t ==> sum_case f g s = sum_case f g t";
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by (etac arg_cong 1);
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qed "sum_case_weak_cong";
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val [p1,p2] = Goal
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"[| sum_case f1 f2 = sum_case g1 g2; \
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\ [| f1 = g1; f2 = g2 |] ==> P |] \
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\ ==> P";
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by (rtac p2 1);
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by (rtac ext 1);
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by (cut_inst_tac [("x","Inl x")] (p1 RS fun_cong) 1);
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by (Asm_full_simp_tac 1);
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by (rtac ext 1);
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by (cut_inst_tac [("x","Inr x")] (p1 RS fun_cong) 1);
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by (Asm_full_simp_tac 1);
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qed "sum_case_inject";
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