theory SingleLet+
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imports "../NewParser"+
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begin+
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atom_decl name+
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declare [[STEPS = 100]]+
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nominal_datatype single_let: 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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thm single_let.distinct+
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thm single_let.induct+
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thm single_let.exhaust+
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thm single_let.fv_defs+
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thm single_let.bn_defs+
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thm single_let.perm_simps+
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thm single_let.eq_iff+
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thm single_let.fv_bn_eqvt+
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thm single_let.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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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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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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typ trm+
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typ assg+
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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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end+
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