76 apply(simp add: trm_assn.perm_bn_simps) |
75 apply(simp add: trm_assn.perm_bn_simps) |
77 apply(simp add: trm_assn.bn_defs) |
76 apply(simp add: trm_assn.bn_defs) |
78 apply(simp add: atom_eqvt) |
77 apply(simp add: atom_eqvt) |
79 done |
78 done |
80 |
79 |
81 (*lemma alpha_bn_permute: |
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82 assumes a: "alpha_bn x y" |
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83 and b: "q \<bullet> bn x = r \<bullet> bn y" |
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84 shows "alpha_bn (q \<bullet> x) (r \<bullet> y)" |
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85 proof - |
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86 have "alpha_bn x (permute_bn r y)" |
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87 by (rule alpha_bn_trans[OF a]) (rule trm_assn.perm_bn_alpha) |
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88 then have "alpha_bn (permute_bn r y) x" |
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89 by (rule alpha_bn_sym) |
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90 then have "alpha_bn (permute_bn r y) (permute_bn q x)" |
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91 by (rule alpha_bn_trans) (rule trm_assn.perm_bn_alpha) |
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92 then have "alpha_bn (permute_bn q x) (permute_bn r y)" |
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93 by (rule alpha_bn_sym) |
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94 moreover have "bn (permute_bn q x) = bn (permute_bn r y)" |
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95 using b trm_assn.permute_bn by simp |
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96 ultimately have "permute_bn q x = permute_bn r y" |
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97 using bn_inj by simp |
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98 *) |
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99 |
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100 |
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101 lemma max_eqvt[eqvt]: "p \<bullet> (max (a :: _ :: pure) b) = max (p \<bullet> a) (p \<bullet> b)" |
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102 by (simp add: permute_pure) |
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103 |
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104 |
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105 lemma Abs_lst_fcb2: |
80 lemma Abs_lst_fcb2: |
106 fixes as bs :: "'a :: fs" |
81 fixes as bs :: "atom list" |
107 and x y :: "'b :: fs" |
82 and x y :: "'b :: fs" |
108 assumes eq: "[ba as]lst. x = [ba bs]lst. y" |
83 and c::"'c::fs" |
109 and ctxt: "finite (supp c)" |
84 assumes eq: "[as]lst. x = [bs]lst. y" |
110 and fcb1: "set (ba as) \<sharp>* f as x c" |
85 and fcb1: "(set as) \<sharp>* c \<Longrightarrow> (set as) \<sharp>* f as x c" |
111 and fresh1: "set (ba as) \<sharp>* c" |
86 and fresh1: "set as \<sharp>* c" |
112 and fresh2: "set (ba bs) \<sharp>* c" |
87 and fresh2: "set bs \<sharp>* c" |
113 and perm1: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f as x c) = f (p \<bullet> as) (p \<bullet> x) c" |
88 and perm1: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f as x c) = f (p \<bullet> as) (p \<bullet> x) c" |
114 and perm2: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f bs y c) = f (p \<bullet> bs) (p \<bullet> y) c" |
89 and perm2: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f bs y c) = f (p \<bullet> bs) (p \<bullet> y) c" |
115 (* What we would like in this proof, and lets this proof finish *) |
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116 and ba_inj: "\<And>q r. q \<bullet> ba as = r \<bullet> ba bs \<Longrightarrow> pn q as = pn r bs" |
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117 shows "f as x c = f bs y c" |
90 shows "f as x c = f bs y c" |
118 proof - |
91 proof - |
119 have "supp (as, x, c) supports (f as x c)" |
92 have "supp (as, x, c) supports (f as x c)" |
120 unfolding supports_def fresh_def[symmetric] |
93 unfolding supports_def fresh_def[symmetric] |
121 apply (simp add: fresh_Pair perm1 fresh_star_def supp_swap swap_fresh_fresh) |
94 by (simp add: fresh_Pair perm1 fresh_star_def supp_swap swap_fresh_fresh) |
122 sorry |
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123 then have fin1: "finite (supp (f as x c))" |
95 then have fin1: "finite (supp (f as x c))" |
124 by (auto intro: supports_finite simp add: finite_supp supp_Pair ctxt) |
96 by (auto intro: supports_finite simp add: finite_supp) |
125 have "supp (bs, y, c) supports (f bs y c)" |
97 have "supp (bs, y, c) supports (f bs y c)" |
126 unfolding supports_def fresh_def[symmetric] |
98 unfolding supports_def fresh_def[symmetric] |
127 apply (simp add: fresh_Pair perm2 fresh_star_def supp_swap swap_fresh_fresh) |
99 by (simp add: fresh_Pair perm2 fresh_star_def supp_swap swap_fresh_fresh) |
128 sorry |
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129 then have fin2: "finite (supp (f bs y c))" |
100 then have fin2: "finite (supp (f bs y c))" |
130 by (auto intro: supports_finite simp add: finite_supp supp_Pair ctxt) |
101 by (auto intro: supports_finite simp add: finite_supp) |
131 obtain q::"perm" where |
102 obtain q::"perm" where |
132 fr1: "(q \<bullet> (set (ba as))) \<sharp>* (x, c, f as x c, f bs y c)" and |
103 fr1: "(q \<bullet> (set as)) \<sharp>* (x, c, f as x c, f bs y c)" and |
133 fr2: "supp q \<sharp>* ([ba as]lst. x)" and |
104 fr2: "supp q \<sharp>* Abs_lst as x" and |
134 inc: "supp q \<subseteq> (set (ba as)) \<union> q \<bullet> (set (ba as))" |
105 inc: "supp q \<subseteq> (set as) \<union> q \<bullet> (set as)" |
135 using at_set_avoiding3[where xs="set (ba as)" and c="(x, c, f as x c, f bs y c)" |
106 using at_set_avoiding3[where xs="set as" and c="(x, c, f as x c, f bs y c)" and x="[as]lst. x"] |
136 and x="[ba as]lst. x"] fin1 fin2 |
107 fin1 fin2 |
137 by (auto simp add: supp_Pair finite_supp ctxt Abs_fresh_star dest: fresh_star_supp_conv) |
108 by (auto simp add: supp_Pair finite_supp Abs_fresh_star dest: fresh_star_supp_conv) |
138 have "[q \<bullet> (ba as)]lst. (q \<bullet> x) = q \<bullet> ([ba as]lst. x)" by simp |
109 have "Abs_lst (q \<bullet> as) (q \<bullet> x) = q \<bullet> Abs_lst as x" by simp |
139 also have "\<dots> = [ba as]lst. x" |
110 also have "\<dots> = Abs_lst as x" |
140 by (simp only: fr2 perm_supp_eq) |
111 by (simp only: fr2 perm_supp_eq) |
141 finally have "[q \<bullet> (ba as)]lst. (q \<bullet> x) = [ba bs]lst. y" using eq by simp |
112 finally have "Abs_lst (q \<bullet> as) (q \<bullet> x) = Abs_lst bs y" using eq by simp |
142 then obtain r::perm where |
113 then obtain r::perm where |
143 qq1: "q \<bullet> x = r \<bullet> y" and |
114 qq1: "q \<bullet> x = r \<bullet> y" and |
144 qq2: "q \<bullet> (ba as) = r \<bullet> (ba bs)" and |
115 qq2: "q \<bullet> as = r \<bullet> bs" and |
145 qq3: "supp r \<subseteq> (q \<bullet> (set (ba as))) \<union> set (ba bs)" |
116 qq3: "supp r \<subseteq> (q \<bullet> (set as)) \<union> set bs" |
146 apply(drule_tac sym) |
117 apply(drule_tac sym) |
147 apply(simp only: Abs_eq_iff2 alphas) |
118 apply(simp only: Abs_eq_iff2 alphas) |
148 apply(erule exE) |
119 apply(erule exE) |
149 apply(erule conjE)+ |
120 apply(erule conjE)+ |
150 apply(drule_tac x="p" in meta_spec) |
121 apply(drule_tac x="p" in meta_spec) |
151 apply(simp add: set_eqvt) |
122 apply(simp add: set_eqvt) |
152 apply(blast) |
123 apply(blast) |
153 done |
124 done |
154 have "(set (ba as)) \<sharp>* f as x c" by (rule fcb1) |
125 have "(set as) \<sharp>* f as x c" |
155 then have "q \<bullet> ((set (ba as)) \<sharp>* f as x c)" |
126 apply(rule fcb1) |
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127 apply(rule fresh1) |
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128 done |
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129 then have "q \<bullet> ((set as) \<sharp>* f as x c)" |
156 by (simp add: permute_bool_def) |
130 by (simp add: permute_bool_def) |
157 then have "set (q \<bullet> (ba as)) \<sharp>* f (q \<bullet> as) (q \<bullet> x) c" |
131 then have "set (q \<bullet> as) \<sharp>* f (q \<bullet> as) (q \<bullet> x) c" |
158 apply(simp add: fresh_star_eqvt set_eqvt) |
132 apply(simp add: fresh_star_eqvt set_eqvt) |
159 apply(subst (asm) perm1) |
133 apply(subst (asm) perm1) |
160 using inc fresh1 fr1 |
134 using inc fresh1 fr1 |
161 apply(auto simp add: fresh_star_def fresh_Pair) |
135 apply(auto simp add: fresh_star_def fresh_Pair) |
162 done |
136 done |
163 then have "set (r \<bullet> (ba bs)) \<sharp>* f (r \<bullet> bs) (r \<bullet> y) c" using qq1 qq2 ba_inj |
137 then have "set (r \<bullet> bs) \<sharp>* f (r \<bullet> bs) (r \<bullet> y) c" using qq1 qq2 by simp |
164 apply simp |
138 then have "r \<bullet> ((set bs) \<sharp>* f bs y c)" |
165 sorry |
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166 then have "r \<bullet> ((set (ba bs)) \<sharp>* f bs y c)" |
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167 apply(simp add: fresh_star_eqvt set_eqvt) |
139 apply(simp add: fresh_star_eqvt set_eqvt) |
168 apply(subst (asm) perm2[symmetric]) |
140 apply(subst (asm) perm2[symmetric]) |
169 using qq3 fresh2 fr1 |
141 using qq3 fresh2 fr1 |
170 apply(auto simp add: set_eqvt fresh_star_def fresh_Pair) |
142 apply(auto simp add: set_eqvt fresh_star_def fresh_Pair) |
171 done |
143 done |
172 then have fcb2: "(set (ba bs)) \<sharp>* f bs y c" by (simp add: permute_bool_def) |
144 then have fcb2: "(set bs) \<sharp>* f bs y c" by (simp add: permute_bool_def) |
173 have "f as x c = q \<bullet> (f as x c)" |
145 have "f as x c = q \<bullet> (f as x c)" |
174 apply(rule perm_supp_eq[symmetric]) |
146 apply(rule perm_supp_eq[symmetric]) |
175 using inc fcb1 fr1 by (auto simp add: fresh_star_def) |
147 using inc fcb1[OF fresh1] fr1 by (auto simp add: fresh_star_def) |
176 also have "\<dots> = f (q \<bullet> as) (q \<bullet> x) c" |
148 also have "\<dots> = f (q \<bullet> as) (q \<bullet> x) c" |
177 apply(rule perm1) |
149 apply(rule perm1) |
178 using inc fresh1 fr1 by (auto simp add: fresh_star_def) |
150 using inc fresh1 fr1 by (auto simp add: fresh_star_def) |
179 also have "\<dots> = f (r \<bullet> bs) (r \<bullet> y) c" using qq1 qq2 ba_inj |
151 also have "\<dots> = f (r \<bullet> bs) (r \<bullet> y) c" using qq1 qq2 by simp |
180 apply(simp) |
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181 sorry |
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182 also have "\<dots> = r \<bullet> (f bs y c)" |
152 also have "\<dots> = r \<bullet> (f bs y c)" |
183 apply(rule perm2[symmetric]) |
153 apply(rule perm2[symmetric]) |
184 using qq3 fresh2 fr1 by (auto simp add: fresh_star_def) |
154 using qq3 fresh2 fr1 by (auto simp add: fresh_star_def) |
185 also have "... = f bs y c" |
155 also have "... = f bs y c" |
186 apply(rule perm_supp_eq) |
156 apply(rule perm_supp_eq) |
187 using qq3 fr1 fcb2 by (auto simp add: fresh_star_def) |
157 using qq3 fr1 fcb2 by (auto simp add: fresh_star_def) |
188 finally show ?thesis by simp |
158 finally show ?thesis by simp |
189 qed |
159 qed |
190 |
160 |
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161 lemma Abs_lst1_fcb2: |
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162 fixes a b :: "atom" |
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163 and x y :: "'b :: fs" |
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164 and c::"'c :: fs" |
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165 assumes e: "(Abs_lst [a] x) = (Abs_lst [b] y)" |
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166 and fcb1: "a \<sharp> c \<Longrightarrow> a \<sharp> f a x c" |
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167 and fresh: "{a, b} \<sharp>* c" |
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168 and perm1: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f a x c) = f (p \<bullet> a) (p \<bullet> x) c" |
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169 and perm2: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f b y c) = f (p \<bullet> b) (p \<bullet> y) c" |
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170 shows "f a x c = f b y c" |
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171 using e |
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172 apply(drule_tac Abs_lst_fcb2[where c="c" and f="\<lambda>(as::atom list) . f (hd as)"]) |
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173 apply(simp_all) |
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174 using fcb1 fresh perm1 perm2 |
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175 apply(simp_all add: fresh_star_def) |
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176 done |
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177 |
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178 |
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179 lemma max_eqvt[eqvt]: "p \<bullet> (max (a :: _ :: pure) b) = max (p \<bullet> a) (p \<bullet> b)" |
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180 by (simp add: permute_pure) |
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181 |
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182 function |
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183 apply_assn :: "(trm \<Rightarrow> nat) \<Rightarrow> assn \<Rightarrow> nat" |
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184 where |
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185 "apply_assn f ANil = (0 :: nat)" |
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186 | "apply_assn f (ACons x t as) = max (f t) (apply_assn f as)" |
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187 apply(case_tac x) |
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188 apply(case_tac b rule: trm_assn.exhaust(2)) |
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189 apply(simp_all) |
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190 apply(blast) |
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191 done |
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192 |
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193 termination by lexicographic_order |
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194 |
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195 lemma [eqvt]: |
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196 "p \<bullet> (apply_assn f a) = apply_assn (p \<bullet> f) (p \<bullet> a)" |
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197 apply(induct f a rule: apply_assn.induct) |
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198 apply simp_all |
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199 apply(perm_simp) |
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200 apply rule |
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201 apply(perm_simp) |
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202 apply simp |
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203 done |
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204 |
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205 lemma alpha_bn_apply_assn: |
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206 assumes "alpha_bn as bs" |
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207 shows "apply_assn f as = apply_assn f bs" |
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208 using assms |
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209 apply (induct rule: alpha_bn_inducts) |
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210 apply simp_all |
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211 done |
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212 |
191 nominal_primrec |
213 nominal_primrec |
192 height_trm :: "trm \<Rightarrow> nat" |
214 height_trm :: "trm \<Rightarrow> nat" |
193 and height_assn :: "assn \<Rightarrow> nat" |
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194 where |
215 where |
195 "height_trm (Var x) = 1" |
216 "height_trm (Var x) = 1" |
196 | "height_trm (App l r) = max (height_trm l) (height_trm r)" |
217 | "height_trm (App l r) = max (height_trm l) (height_trm r)" |
197 | "height_trm (Lam v b) = 1 + (height_trm b)" |
218 | "height_trm (Lam v b) = 1 + (height_trm b)" |
198 | "height_trm (Let as b) = max (height_assn as) (height_trm b)" |
219 | "height_trm (Let as b) = max (apply_assn height_trm as) (height_trm b)" |
199 | "height_assn ANil = 0" |
220 apply (simp only: eqvt_def height_trm_graph_def) |
200 | "height_assn (ACons v t as) = max (height_trm t) (height_assn as)" |
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201 apply (simp only: eqvt_def height_trm_height_assn_graph_def) |
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202 apply (rule, perm_simp, rule, rule TrueI) |
221 apply (rule, perm_simp, rule, rule TrueI) |
203 apply (case_tac x) |
222 apply (case_tac x rule: trm_assn.exhaust(1)) |
204 apply (case_tac a rule: trm_assn.exhaust(1)) |
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205 apply (auto)[4] |
223 apply (auto)[4] |
206 apply (drule_tac x="assn" in meta_spec) |
224 apply (drule_tac x="assn" in meta_spec) |
207 apply (drule_tac x="trm" in meta_spec) |
225 apply (drule_tac x="trm" in meta_spec) |
208 apply (simp add: alpha_bn_refl) |
226 apply (simp add: alpha_bn_refl) |
209 apply (case_tac b rule: trm_assn.exhaust(2)) |
227 apply(simp_all) |
210 apply (auto)[2] |
228 apply (erule_tac c="()" in Abs_lst1_fcb2) |
211 apply(simp_all del: trm_assn.eq_iff) |
229 apply (simp_all add: pure_fresh fresh_star_def eqvt_at_def)[4] |
212 apply(simp) |
230 apply (erule conjE) |
213 prefer 3 |
231 apply (subst alpha_bn_apply_assn) |
214 apply(simp) |
232 apply assumption |
215 apply(simp) |
233 apply (rule arg_cong) back |
216 apply (erule_tac c="()" and pn="permute" in Abs_lst_fcb2) |
234 apply (erule_tac c="()" in Abs_lst_fcb2) |
217 apply(simp add: finite_supp) |
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218 apply (simp_all add: pure_fresh fresh_star_def)[3] |
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219 apply (simp add: eqvt_at_def) |
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220 apply (simp add: eqvt_at_def) |
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221 apply(auto)[1] |
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222 --"other case" |
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223 apply (simp only: meta_eq_to_obj_eq[OF height_trm_def, symmetric, unfolded fun_eq_iff]) |
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224 apply (simp only: meta_eq_to_obj_eq[OF height_assn_def, symmetric, unfolded fun_eq_iff]) |
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225 apply (subgoal_tac "eqvt_at height_assn as") |
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226 apply (subgoal_tac "eqvt_at height_assn asa") |
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227 apply (subgoal_tac "eqvt_at height_trm b") |
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228 apply (subgoal_tac "eqvt_at height_trm ba") |
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229 apply (thin_tac "eqvt_at height_trm_height_assn_sumC (Inr as)") |
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230 apply (thin_tac "eqvt_at height_trm_height_assn_sumC (Inr asa)") |
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231 apply (thin_tac "eqvt_at height_trm_height_assn_sumC (Inl b)") |
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232 apply (thin_tac "eqvt_at height_trm_height_assn_sumC (Inl ba)") |
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233 defer |
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234 apply (simp add: eqvt_at_def height_trm_def) |
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235 apply (simp add: eqvt_at_def height_trm_def) |
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236 apply (simp add: eqvt_at_def height_assn_def) |
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237 apply (simp add: eqvt_at_def height_assn_def) |
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238 apply (subgoal_tac "height_assn as = height_assn asa") |
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239 apply (subgoal_tac "height_trm b = height_trm ba") |
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240 apply simp |
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241 apply(simp) |
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242 apply(erule conjE) |
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243 apply (erule_tac c="()" and pn="permute_bn" in Abs_lst_fcb2) |
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244 apply(simp add: finite_supp) |
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245 apply (simp_all add: pure_fresh fresh_star_def)[3] |
235 apply (simp_all add: pure_fresh fresh_star_def)[3] |
246 apply (simp_all add: eqvt_at_def)[2] |
236 apply (simp_all add: eqvt_at_def)[2] |
247 apply(simp add: bn_inj2) |
237 done |
248 apply(simp) |
238 |
249 apply(erule conjE) |
239 definition "height_assn = apply_assn height_trm" |
250 thm trm_assn.fv_defs |
240 |
251 (*apply(simp add: Abs_eq_iff alphas)*) |
241 function |
252 apply (erule_tac c="()" and pn="permute_bn" and ba="bn" in Abs_lst_fcb2) |
242 apply_assn2 :: "(trm \<Rightarrow> trm) \<Rightarrow> assn \<Rightarrow> assn" |
253 defer |
243 where |
254 apply (simp_all add: pure_fresh fresh_star_def)[3] |
244 "apply_assn2 f ANil = ANil" |
255 defer |
245 | "apply_assn2 f (ACons x t as) = ACons x (f t) (apply_assn2 f as)" |
256 defer |
246 apply(case_tac x) |
257 apply (simp_all add: eqvt_at_def)[2] |
247 apply(case_tac b rule: trm_assn.exhaust(2)) |
258 apply (rule bn_inj) |
248 apply(simp_all) |
259 prefer 2 |
249 apply(blast) |
260 apply (simp add: eqvts) |
250 done |
261 oops |
251 |
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252 termination by lexicographic_order |
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253 |
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254 lemma [eqvt]: |
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255 "p \<bullet> (apply_assn2 f a) = apply_assn2 (p \<bullet> f) (p \<bullet> a)" |
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256 apply(induct f a rule: apply_assn2.induct) |
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257 apply simp_all |
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258 apply(perm_simp) |
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259 apply rule |
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260 done |
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261 |
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262 lemma bn_apply_assn2: "bn (apply_assn2 f as) = bn as" |
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263 apply (induct as rule: trm_assn.inducts(2)) |
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264 apply (rule TrueI) |
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265 apply (simp_all add: trm_assn.bn_defs) |
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266 done |
262 |
267 |
263 nominal_primrec |
268 nominal_primrec |
264 subst :: "name \<Rightarrow> trm \<Rightarrow> trm \<Rightarrow> trm" |
269 subst :: "name \<Rightarrow> trm \<Rightarrow> trm \<Rightarrow> trm" |
265 and substa :: "name \<Rightarrow> trm \<Rightarrow> assn \<Rightarrow> assn" |
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266 where |
270 where |
267 "subst s t (Var x) = (if (s = x) then t else (Var x))" |
271 "subst s t (Var x) = (if (s = x) then t else (Var x))" |
268 | "subst s t (App l r) = App (subst s t l) (subst s t r)" |
272 | "subst s t (App l r) = App (subst s t l) (subst s t r)" |
269 | "atom v \<sharp> (s, t) \<Longrightarrow> subst s t (Lam v b) = Lam v (subst s t b)" |
273 | "atom v \<sharp> (s, t) \<Longrightarrow> subst s t (Lam v b) = Lam v (subst s t b)" |
270 | "set (bn as) \<sharp>* (s, t) \<Longrightarrow> subst s t (Let as b) = Let (substa s t as) (subst s t b)" |
274 | "set (bn as) \<sharp>* (s, t) \<Longrightarrow> subst s t (Let as b) = Let (apply_assn2 (subst s t) as) (subst s t b)" |
271 | "substa s t ANil = ANil" |
275 apply (simp only: eqvt_def subst_graph_def) |
272 | "substa s t (ACons v t' as) = ACons v (subst v t t') as" |
276 apply (rule, perm_simp, rule) |
273 (*unfolding eqvt_def subst_substa_graph_def |
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274 apply (rule, perm_simp)*) |
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275 defer |
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276 apply (rule TrueI) |
277 apply (rule TrueI) |
277 apply (case_tac x) |
278 apply (case_tac x) |
278 apply (case_tac a) |
279 apply (rule_tac y="c" and c="(a,b)" in trm_assn.strong_exhaust(1)) |
279 apply (rule_tac y="c" and c="(aa,b)" in trm_assn.strong_exhaust(1)) |
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280 apply (auto simp add: fresh_star_def)[3] |
280 apply (auto simp add: fresh_star_def)[3] |
281 apply (drule_tac x="assn" in meta_spec) |
281 apply (drule_tac x="assn" in meta_spec) |
282 apply (simp add: Abs1_eq_iff alpha_bn_refl) |
282 apply (simp add: Abs1_eq_iff alpha_bn_refl) |
283 apply (case_tac b) |
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284 apply (case_tac c rule: trm_assn.exhaust(2)) |
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285 apply (auto)[2] |
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286 apply blast |
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287 apply blast |
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288 apply auto |
283 apply auto |
289 apply (simp_all add: meta_eq_to_obj_eq[OF subst_def, symmetric, unfolded fun_eq_iff]) |
284 apply (erule_tac c="(sa, ta)" in Abs_lst1_fcb2) |
290 apply (simp_all add: meta_eq_to_obj_eq[OF substa_def, symmetric, unfolded fun_eq_iff]) |
285 apply (simp add: Abs_fresh_iff) |
291 prefer 2 |
286 apply (simp add: fresh_star_def) |
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287 apply (simp_all add: fresh_star_Pair_elim perm_supp_eq eqvt_at_def)[2] |
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288 apply (simp add: bn_apply_assn2) |
292 apply (erule_tac c="(sa, ta)" in Abs_lst_fcb2) |
289 apply (erule_tac c="(sa, ta)" in Abs_lst_fcb2) |
293 apply (simp_all add: fresh_star_Pair) |
290 apply (simp add: fresh_star_def Abs_fresh_iff) |
294 prefer 6 |
291 apply assumption+ |
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292 apply (simp_all add: fresh_star_Pair_elim perm_supp_eq eqvt_at_def trm_assn.fv_bn_eqvt)[2] |
295 apply (erule alpha_bn_inducts) |
293 apply (erule alpha_bn_inducts) |
296 oops |
294 apply simp_all |
297 |
295 done |
298 |
296 |
299 lemma lets_bla: |
297 lemma lets_bla: |
300 "x \<noteq> z \<Longrightarrow> y \<noteq> z \<Longrightarrow> x \<noteq> y \<Longrightarrow>(Let (ACons x (Var y) ANil) (Var x)) \<noteq> (Let (ACons x (Var z) ANil) (Var x))" |
298 "x \<noteq> z \<Longrightarrow> y \<noteq> z \<Longrightarrow> x \<noteq> y \<Longrightarrow>(Let (ACons x (Var y) ANil) (Var x)) \<noteq> (Let (ACons x (Var z) ANil) (Var x))" |
301 by (simp add: trm_assn.eq_iff) |
299 by (simp add: trm_assn.eq_iff) |
302 |
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303 |
300 |
304 lemma lets_ok: |
301 lemma lets_ok: |
305 "(Let (ACons x (Var y) ANil) (Var x)) = (Let (ACons y (Var y) ANil) (Var y))" |
302 "(Let (ACons x (Var y) ANil) (Var x)) = (Let (ACons y (Var y) ANil) (Var y))" |
306 apply (simp add: trm_assn.eq_iff Abs_eq_iff ) |
303 apply (simp add: trm_assn.eq_iff Abs_eq_iff ) |
307 apply (rule_tac x="(x \<leftrightarrow> y)" in exI) |
304 apply (rule_tac x="(x \<leftrightarrow> y)" in exI) |