theory SingleLet+
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imports "../NewParser"+
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begin+
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+
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atom_decl name+
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+
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declare [[STEPS = 20]]+
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+
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+
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nominal_datatype trm  =+
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  Var "name"+
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| App "trm" "trm"+
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| Lam x::"name" t::"trm"  bind x in t+
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| Let a::"assg" t::"trm"  bind (set) "bn a" in t+
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| Foo x::"name" y::"name" t::"trm" t1::"trm" t2::"trm" bind (set) x in y t t1 t2+
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| Bar x::"name" y::"name" t::"trm" bind y x in t x y+
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| Baz x::"name" t1::"trm" t2::"trm" bind x in t1, bind x in t2 +
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and assg =+
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  As "name" x::"name" t::"trm" bind x in t+
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binder+
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  bn::"assg \<Rightarrow> atom set"+
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where+
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  "bn (As x y t) = {atom x}"+
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+
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+
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+
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+
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ML {* Function.prove_termination *}+
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+
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text {* can lift *}+
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+
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thm distinct+
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thm trm_raw_assg_raw.inducts+
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thm trm_raw.exhaust+
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thm assg_raw.exhaust+
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thm fv_defs+
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thm perm_simps+
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thm perm_laws+
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thm trm_raw_assg_raw.size(9 - 16)+
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thm eq_iff+
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thm eq_iff_simps+
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thm bn_defs+
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thm fv_eqvt+
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thm bn_eqvt+
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thm size_eqvt+
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+
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+
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ML {*+
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  val thms_d = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms distinct}+
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*}+
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+
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ML {* +
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  val thms_i = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms trm_raw_assg_raw.inducts}+
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*}+
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+
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ML {* +
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  val thms_i = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms trm_raw.exhaust}+
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*}+
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+
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ML {* +
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  val thms_i = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms assg_raw.exhaust}+
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*}+
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+
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ML {*+
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  val thms_f = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms fv_defs}+
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*}+
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+
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ML {* +
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  val thms_i = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms trm_raw_assg_raw.size(9 - 16)}+
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*}+
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+
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ML {*+
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  val thms_p = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms perm_simps}+
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*}+
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+
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ML {*+
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  val thms_f = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms perm_laws}+
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*}+
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+
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ML {*+
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 val thms_e = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) +
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   @{thms eq_iff[unfolded alphas permute_prod.simps prod_fv.simps prod_alpha_def prod_rel.simps+
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    prod.cases]}+
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*}+
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+
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ML {*+
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 val thms_e = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) +
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   @{thms eq_iff_simps[unfolded alphas permute_prod.simps prod_fv.simps prod_alpha_def prod_rel.simps+
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    prod.cases]}+
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*}+
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+
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ML {*+
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  val thms_f = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms bn_defs}+
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*}+
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+
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ML {*+
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  val thms_f = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms bn_eqvt}+
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*}+
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+
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ML {*+
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  val thms_f = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms fv_eqvt}+
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*}+
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+
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ML {*+
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  val thms_f = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms size_eqvt}+
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*}+
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lemma supp_fv:+
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  "supp t = fv_trm t"+
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  "supp b = fv_bn b"+
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apply(induct t and b rule: i1)+
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apply(simp_all add: f1)+
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apply(simp_all add: supp_def)+
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apply(simp_all add: b1)+
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sorry+
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+
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consts perm_bn_trm :: "perm \<Rightarrow> trm \<Rightarrow> trm"+
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consts perm_bn_assg :: "perm \<Rightarrow> assg \<Rightarrow> assg"+
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+
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lemma y:+
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  "perm_bn_trm p (Var x) = (Var x)"+
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  "perm_bn_trm p (App t1 t2) = (App t1 t2)"+
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  "perm_bn_trm p ("+
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+
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typ trm+
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typ assg+
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+
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thm trm_assg.fv+
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thm trm_assg.supp+
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thm trm_assg.eq_iff+
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thm trm_assg.bn+
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thm trm_assg.perm+
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thm trm_assg.induct+
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thm trm_assg.inducts+
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thm trm_assg.distinct+
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ML {* Sign.of_sort @{theory} (@{typ trm}, @{sort fs}) *}+
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+
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(* TEMPORARY+
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thm trm_assg.fv[simplified trm_assg.supp(1-2)]+
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*)+
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end+
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