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theory SingleLetFoo
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imports "../NewParser"
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begin
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declare [[STEPS = 5]]
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7 |
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atom_decl name
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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_set x in t
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| Let a::"assg" t::"trm" bind_set "bn a" in t
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| Foo1 a1::"assg" a2::"assg" t::"trm" bind_set "bn a1" "bn a2" in t
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| Foo2 x::name a::"assg" t::"trm" bind_set x "bn a" in t
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and assg =
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As "name" "trm"
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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 t) = {atom x}"
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thm trm_assg.distinct
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thm trm_assg.eq_iff
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thm trm_assg.supp
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thm trm_assg.perm
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thm trm_assg.fv[simplified trm_assg.supp(1-2),no_vars]
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thm permute_trm_raw_permute_assg_raw.simps
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thm fv_trm_raw.simps fv_assg_raw.simps fv_bn_raw.simps[no_vars]
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thm alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros[no_vars]
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lemmas all = alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros
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lemma test: "p \<bullet> bn_raw \<equiv> bn_raw" sorry
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lemma
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assumes "distinct [x,y, z, u]"
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shows "alpha_trm_raw (Foo2_raw z (As_raw x (Var_raw z)) (Var_raw z))
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(Foo2_raw u (As_raw y (Var_raw z)) (Var_raw u))"
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using assms
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apply(rule_tac all)
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apply(rule_tac x="(z \<leftrightarrow> u) + (x \<leftrightarrow> y)" in exI)
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apply(simp only: alphas)
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apply(rule conjI)
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apply(simp)
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apply(simp add: supp_at_base fresh_star_def)
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apply(rule conjI)
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apply(simp add: supp_at_base fresh_star_def)
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apply(rule conjI)
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apply(simp)
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apply(rule all)
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apply(simp)
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unfolding flip_def
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apply(perm_simp add: test)
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unfolding flip_def[symmetric]
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apply(simp)
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apply(subst flip_at_base_simps(3))
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apply(auto)[2]
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apply(simp)
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apply(rule all)
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apply(rule all)
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apply(simp)
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done
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lemma
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assumes "distinct [x,y,z,u]"
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shows "fv_trm_raw (Foo2_raw z (As_raw x (Var_raw z)) (Var_raw z)) = {atom z}"
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using assms
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apply(simp add: supp_at_base)
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done
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end
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