77 |
76 |
78 local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha4_equivp_no}, []), |
77 local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha4_equivp_no}, []), |
79 (build_equivps [@{term alpha_rtrm4}, @{term alpha_rtrm4_list}] @{thms alpha4_reflp} @{thm alpha_rtrm4_alpha_rtrm4_list.induct} @{thms rtrm4.inject list.inject} @{thms alpha4_inj_no} @{thms rtrm4.distinct list.distinct} @{thms alpha_rtrm4_list.cases alpha_rtrm4.cases} @{thms alpha4_eqvt_no} ctxt)) ctxt)) *} |
78 (build_equivps [@{term alpha_rtrm4}, @{term alpha_rtrm4_list}] @{thms alpha4_reflp} @{thm alpha_rtrm4_alpha_rtrm4_list.induct} @{thms rtrm4.inject list.inject} @{thms alpha4_inj_no} @{thms rtrm4.distinct list.distinct} @{thms alpha_rtrm4_list.cases alpha_rtrm4.cases} @{thms alpha4_eqvt_no} ctxt)) ctxt)) *} |
80 lemmas alpha4_equivp = alpha4_equivp_no[simplified fix2] |
79 lemmas alpha4_equivp = alpha4_equivp_no[simplified fix2] |
81 |
80 |
82 (*lemma fv_rtrm4_rsp: |
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83 "xa \<approx>4 ya \<Longrightarrow> fv_rtrm4 xa = fv_rtrm4 ya" |
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84 "x \<approx>4l y \<Longrightarrow> fv_rtrm4_list x = fv_rtrm4_list y" |
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85 apply (induct rule: alpha_rtrm4_alpha_rtrm4_list.inducts) |
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86 apply (simp_all add: alpha_gen) |
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87 done*) |
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88 |
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89 |
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90 quotient_type |
81 quotient_type |
91 trm4 = rtrm4 / alpha_rtrm4 |
82 trm4 = rtrm4 / alpha_rtrm4 |
92 (*and |
83 (*and |
93 trm4list = "rtrm4 list" / alpha_rtrm4_list*) |
84 trm4list = "rtrm4 list" / alpha_rtrm4_list*) |
94 by (simp_all add: alpha4_equivp) |
85 by (simp_all add: alpha4_equivp) |
95 |
86 |
96 local_setup {* |
87 local_setup {* |
97 (fn ctxt => ctxt |
88 (fn ctxt => ctxt |
98 |> snd o (Quotient_Def.quotient_lift_const [] ("Vr4", @{term rVr4})) |
89 |> snd o (Quotient_Def.quotient_lift_const [] ("Vr4", @{term rVr4})) |
99 |> snd o (Quotient_Def.quotient_lift_const [] ("Ap4", @{term rAp4})) |
90 |> snd o (Quotient_Def.quotient_lift_const [@{typ "trm4"}] ("Ap4", @{term rAp4})) |
100 |> snd o (Quotient_Def.quotient_lift_const [] ("Lm4", @{term rLm4}))) |
91 |> snd o (Quotient_Def.quotient_lift_const [] ("Lm4", @{term rLm4})) |
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92 |> snd o (Quotient_Def.quotient_lift_const [] ("fv_trm4", @{term fv_rtrm4}))) |
101 *} |
93 *} |
102 print_theorems |
94 print_theorems |
103 |
95 |
104 local_setup {* snd o prove_const_rsp @{binding fv_rtrm4_rsp} [@{term fv_rtrm4}] |
96 |
105 (fn _ => fvbv_rsp_tac @{thm alpha_rtrm4_alpha_rtrm4_list.inducts(1)} @{thms fv_rtrm4_fv_rtrm4_list.simps} 1) *} |
97 |
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98 lemma fv_rtrm4_rsp: |
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99 "xa \<approx>4 ya \<Longrightarrow> fv_rtrm4 xa = fv_rtrm4 ya" |
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100 "x \<approx>4l y \<Longrightarrow> fv_rtrm4_list x = fv_rtrm4_list y" |
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101 apply (induct rule: alpha_rtrm4_alpha_rtrm4_list.inducts) |
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102 apply (simp_all add: alpha_gen) |
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103 done |
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104 |
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105 local_setup {* snd o prove_const_rsp [] @{binding fv_rtrm4_rsp'} [@{term fv_rtrm4}] |
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106 (fn _ => asm_full_simp_tac (@{simpset} addsimps @{thms fv_rtrm4_rsp}) 1) *} |
106 print_theorems |
107 print_theorems |
107 |
108 |
108 local_setup {* snd o prove_const_rsp @{binding rVr4_rsp} [@{term rVr4}] |
109 ML constr_rsp_tac |
109 (fn _ => constr_rsp_tac @{thms alpha4_inj} @{thms fv_rtrm4_rsp} @{thms alpha4_equivp} 1) *} |
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110 lemma "(alpha_rtrm4 ===> list_rel alpha_rtrm4 ===> alpha_rtrm4) rAp4 rAp4" |
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111 apply simp |
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112 apply clarify |
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113 apply (simp add: alpha4_inj) |
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114 |
110 |
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111 local_setup {* snd o prove_const_rsp [] @{binding rVr4_rsp} [@{term rVr4}] |
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112 (fn _ => constr_rsp_tac @{thms alpha4_inj} @{thms fv_rtrm4_rsp alpha4_equivp} 1) *} |
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113 local_setup {* snd o prove_const_rsp [] @{binding rLm4_rsp} [@{term rLm4}] |
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114 (fn _ => constr_rsp_tac @{thms alpha4_inj} @{thms fv_rtrm4_rsp alpha4_equivp} 1) *} |
115 |
115 |
116 local_setup {* snd o prove_const_rsp @{binding rLm4_rsp} [@{term rLm4}] |
116 lemma [quot_respect]: |
117 (fn _ => constr_rsp_tac @{thms alpha4_inj} @{thms fv_rtrm4_rsp} @{thms alpha4_equivp} 1) *} |
117 "(alpha_rtrm4 ===> list_rel alpha_rtrm4 ===> alpha_rtrm4) rAp4 rAp4" |
118 local_setup {* snd o prove_const_rsp @{binding permute_rtrm4_rsp} |
118 by (simp add: alpha4_inj) |
119 [@{term "permute :: perm \<Rightarrow> rtrm4 \<Rightarrow> rtrm4"}, @{term "permute :: perm \<Rightarrow> rtrm4 list \<Rightarrow> rtrm4 list"}] |
119 |
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120 (* Maybe also need: @{term "permute :: perm \<Rightarrow> rtrm4 list \<Rightarrow> rtrm4 list"} *) |
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121 local_setup {* snd o prove_const_rsp [] @{binding permute_rtrm4_rsp} |
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122 [@{term "permute :: perm \<Rightarrow> rtrm4 \<Rightarrow> rtrm4"}] |
120 (fn _ => asm_simp_tac (HOL_ss addsimps @{thms alpha4_eqvt}) 1) *} |
123 (fn _ => asm_simp_tac (HOL_ss addsimps @{thms alpha4_eqvt}) 1) *} |
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124 print_theorems |
121 |
125 |
122 thm rtrm4.induct |
126 lemma list_rel_rsp: |
123 lemmas trm1_bp_induct = rtrm4.induct[quot_lifted] |
127 "\<lbrakk>\<forall>x y. R x y \<longrightarrow> (\<forall>a b. R a b \<longrightarrow> S x a = T y b); list_rel R x y; list_rel R a b\<rbrakk> |
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128 \<Longrightarrow> list_rel S x a = list_rel T y b" |
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129 sorry |
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130 |
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131 lemma[quot_respect]: |
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132 "((R ===> R ===> op =) ===> list_rel R ===> list_rel R ===> op =) list_rel list_rel" |
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133 by (simp add: list_rel_rsp) |
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134 |
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135 lemma[quot_preserve]: |
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136 assumes a: "Quotient R abs1 rep1" |
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137 shows "((abs1 ---> abs1 ---> id) ---> map rep1 ---> map rep1 ---> id) list_rel = list_rel" |
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138 apply (simp add: expand_fun_eq) |
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139 apply clarify |
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140 apply (induct_tac xa xb rule: list_induct2') |
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141 apply (simp_all add: Quotient_abs_rep[OF a]) |
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142 done |
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143 |
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144 lemma[quot_preserve]: |
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145 assumes a: "Quotient R abs1 rep1" |
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146 shows "(list_rel ((rep1 ---> rep1 ---> id) R) l m) = (l = m)" |
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147 by (induct l m rule: list_induct2') (simp_all add: Quotient_rel_rep[OF a]) |
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148 |
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149 lemma bla: "(Ap4 trm4 list = Ap4 trm4a lista) = |
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150 (trm4 = trm4a \<and> list_rel (op =) list lista)" |
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151 by (lifting alpha4_inj(2)) |
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152 |
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153 thm bla[simplified list_rel_eq] |
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154 |
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155 lemma " (Lm4 name rtrm4 = Lm4 namea rtrm4a) = |
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156 (\<exists>pi\<Colon>perm. |
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157 fv_trm4 rtrm4 - {atom name} = fv_trm4 rtrm4a - {atom namea} \<and> |
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158 (fv_trm4 rtrm4 - {atom name}) \<sharp>* pi \<and> |
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159 pi \<bullet> rtrm4 = rtrm4a \<and> pi \<bullet> {atom name} = {atom namea})" |
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160 |
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161 ML {* lift_thm [@{typ trm4}] @{context} @{thm alpha4_inj(1)} *} |
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162 ML {* lift_thm [@{typ trm4}] @{context} @{thm alpha4_inj(2)} *} |
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163 ML {* lift_thm [@{typ trm4}] @{context} @{thm alpha4_inj(3)[unfolded alpha_gen]} *} |
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164 ML {* lift_thm [@{typ trm4}] @{context} @{thm rtrm4.induct} *} |
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165 . |
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166 |
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167 (*lemmas trm1_bp_induct = rtrm4.induct[quot_lifted]*) |
124 |
168 |
125 end |
169 end |