| author | Christian Urban <urbanc@in.tum.de> |
| Sat, 26 Nov 2011 09:48:14 +0000 | |
| changeset 3053 | 324b148fc6b5 |
| parent 2950 | 0911cb7bf696 |
| child 3235 | 5ebd327ffb96 |
| permissions | -rw-r--r-- |
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1 |
theory LetSimple1 |
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imports "../Nominal2" |
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begin |
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atom_decl name |
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6 |
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nominal_datatype trm = |
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Var "name" |
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| App "trm" "trm" |
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| Let x::"name" "trm" t::"trm" binds x in t |
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print_theorems |
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thm trm.fv_defs |
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thm trm.eq_iff |
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thm trm.bn_defs |
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thm trm.bn_inducts |
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thm trm.perm_simps |
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thm trm.induct |
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thm trm.inducts |
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thm trm.distinct |
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thm trm.supp |
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thm trm.fresh |
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thm trm.exhaust |
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thm trm.strong_exhaust |
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thm trm.perm_bn_simps |
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nominal_primrec |
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height_trm :: "trm \<Rightarrow> nat" |
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where |
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"height_trm (Var x) = 1" |
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| "height_trm (App l r) = max (height_trm l) (height_trm r)" |
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| "height_trm (Let x t s) = max (height_trm t) (height_trm s)" |
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apply (simp only: eqvt_def height_trm_graph_def) |
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apply (rule, perm_simp, rule, rule TrueI) |
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apply (case_tac x rule: trm.exhaust(1)) |
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apply (auto)[3] |
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apply(simp_all)[5] |
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apply (subgoal_tac "height_trm_sumC t = height_trm_sumC ta") |
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apply (subgoal_tac "height_trm_sumC s = height_trm_sumC sa") |
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apply simp |
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apply(simp) |
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apply(erule conjE) |
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apply(erule_tac c="()" in Abs_lst1_fcb2) |
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apply(simp_all add: fresh_star_def pure_fresh)[2] |
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apply(simp_all add: eqvt_at_def)[2] |
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apply(simp) |
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done |
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termination |
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by lexicographic_order |
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nominal_primrec (invariant "\<lambda>x (y::atom set). finite y") |
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frees_set :: "trm \<Rightarrow> atom set" |
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where |
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"frees_set (Var x) = {atom x}"
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| "frees_set (App t1 t2) = frees_set t1 \<union> frees_set t2" |
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| "frees_set (Let x t s) = (frees_set s) - {atom x} \<union> (frees_set t)"
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apply(simp add: eqvt_def frees_set_graph_def) |
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apply(rule, perm_simp, rule) |
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apply(erule frees_set_graph.induct) |
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apply(auto)[3] |
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apply(rule_tac y="x" in trm.exhaust) |
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apply(auto)[3] |
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apply(simp_all)[5] |
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apply(simp) |
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apply(erule conjE) |
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apply(subgoal_tac "frees_set_sumC s - {atom x} = frees_set_sumC sa - {atom xa}")
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apply(simp) |
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apply(erule_tac c="()" in Abs_lst1_fcb2) |
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apply(simp add: fresh_minus_atom_set) |
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apply(simp add: fresh_star_def fresh_Unit) |
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apply(simp add: Diff_eqvt eqvt_at_def, perm_simp, rule refl) |
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apply(simp add: Diff_eqvt eqvt_at_def, perm_simp, rule refl) |
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76 |
done |
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termination |
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by lexicographic_order |
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nominal_primrec |
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subst :: "trm \<Rightarrow> name \<Rightarrow> trm \<Rightarrow> trm" ("_ [_ ::= _]" [90, 90, 90] 90)
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84 |
where |
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"(Var x)[y ::= s] = (if x = y then s else (Var x))" |
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86 |
| "(App t1 t2)[y ::= s] = App (t1[y ::= s]) (t2[y ::= s])" |
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87 |
| "atom x \<sharp> (y, s) \<Longrightarrow> (Let x t t')[y ::= s] = Let x (t[y ::= s]) (t'[y ::= s])" |
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apply(simp add: eqvt_def subst_graph_def) |
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89 |
apply (rule, perm_simp, rule) |
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90 |
apply(rule TrueI) |
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91 |
apply(auto)[1] |
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92 |
apply(rule_tac y="a" and c="(aa, b)" in trm.strong_exhaust) |
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93 |
apply(blast)+ |
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94 |
apply(simp_all add: fresh_star_def fresh_Pair_elim)[1] |
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Christian Urban <urbanc@in.tum.de>
parents:
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changeset
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95 |
apply(blast) |
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Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
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96 |
apply(simp_all)[5] |
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parents:
diff
changeset
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97 |
apply(simp (no_asm_use)) |
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parents:
diff
changeset
|
98 |
apply(simp) |
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parents:
diff
changeset
|
99 |
apply(erule conjE)+ |
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parents:
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changeset
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100 |
apply (erule_tac c="(ya,sa)" in Abs_lst1_fcb2) |
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parents:
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101 |
apply(simp add: Abs_fresh_iff) |
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parents:
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changeset
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102 |
apply(simp add: fresh_star_def fresh_Pair) |
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parents:
diff
changeset
|
103 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
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parents:
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changeset
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104 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
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aaef9dec5e1d
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parents:
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|
105 |
done |
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parents:
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|
106 |
|
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parents:
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|
107 |
termination |
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|
108 |
by lexicographic_order |
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parents:
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|
109 |
|
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|
110 |
|
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|
111 |
end |