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(* Title: HOL/Subst/UTerm.ML
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ID: $Id$
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Author: Martin Coen, Cambridge University Computer Laboratory
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Copyright 1993 University of Cambridge
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Simple term structure for unifiation.
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Binary trees with leaves that are constants or variables.
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*)
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open UTerm;
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(**** vars_of lemmas ****)
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goal UTerm.thy "(v : vars_of(Var(w))) = (w=v)";
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by (Simp_tac 1);
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by (fast_tac HOL_cs 1);
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qed "vars_var_iff";
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goal UTerm.thy "(x : vars_of(t)) = (Var(x) <: t | Var(x) = t)";
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by (uterm.induct_tac "t" 1);
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by (ALLGOALS Simp_tac);
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by (fast_tac HOL_cs 1);
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qed "vars_iff_occseq";
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(* Not used, but perhaps useful in other proofs *)
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goal UTerm.thy "M<:N --> vars_of(M) <= vars_of(N)";
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by (uterm.induct_tac "N" 1);
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by (ALLGOALS Asm_simp_tac);
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by (fast_tac set_cs 1);
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val occs_vars_subset = result();
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goal UTerm.thy
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"vars_of M Un vars_of N <= vars_of(Comb M P) Un vars_of(Comb N Q)";
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by (Simp_tac 1);
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by (fast_tac set_cs 1);
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val monotone_vars_of = result();
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goal UTerm.thy "finite(vars_of M)";
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by (uterm.induct_tac"M" 1);
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by (ALLGOALS Simp_tac);
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by (forward_tac [finite_UnI] 1);
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by (assume_tac 1);
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by (Asm_simp_tac 1);
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val finite_vars_of = result();
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