(*notation ( output) "prop" ("#_" [1000] 1000) *)notation ( output) "Trueprop" ("#_" [1000] 1000)function(sequential) akind :: "kind \<Rightarrow> kind \<Rightarrow> bool" ("_ \<approx>ki _" [100, 100] 100)and aty :: "ty \<Rightarrow> ty \<Rightarrow> bool" ("_ \<approx>ty _" [100, 100] 100)and atrm :: "trm \<Rightarrow> trm \<Rightarrow> bool" ("_ \<approx>tr _" [100, 100] 100)where a1: "(Type) \<approx>ki (Type) = True"| a2: "(KPi A x K) \<approx>ki (KPi A' x' K') = (A \<approx>ty A' \<and> (\<exists>pi. (rfv_kind K - {atom x} = rfv_kind K' - {atom x'} \<and> (rfv_kind K - {atom x})\<sharp>* pi \<and> (pi \<bullet> K) \<approx>ki K' \<and> (pi \<bullet> x) = x')))"| "_ \<approx>ki _ = False"| a3: "(TConst i) \<approx>ty (TConst j) = (i = j)"| a4: "(TApp A M) \<approx>ty (TApp A' M') = (A \<approx>ty A' \<and> M \<approx>tr M')"| a5: "(TPi A x B) \<approx>ty (TPi A' x' B') = ((A \<approx>ty A') \<and> (\<exists>pi. rfv_ty B - {atom x} = rfv_ty B' - {atom x'} \<and> (rfv_ty B - {atom x})\<sharp>* pi \<and> (pi \<bullet> B) \<approx>ty B' \<and> (pi \<bullet> x) = x'))"| "_ \<approx>ty _ = False"| a6: "(Const i) \<approx>tr (Const j) = (i = j)"| a7: "(Var x) \<approx>tr (Var y) = (x = y)"| a8: "(App M N) \<approx>tr (App M' N') = (M \<approx>tr M' \<and> N \<approx>tr N')"| a9: "(Lam A x M) \<approx>tr (Lam A' x' M') = (A \<approx>ty A' \<and> (\<exists>pi. rfv_trm M - {atom x} = rfv_trm M' - {atom x'} \<and> (rfv_trm M - {atom x})\<sharp>* pi \<and> (pi \<bullet> M) \<approx>tr M' \<and> (pi \<bullet> x) = x'))"| "_ \<approx>tr _ = False"apply (pat_completeness)apply simp_alldoneterminationby (size_change)lemma regularize_to_injection: shows "(QUOT_TRUE l \<Longrightarrow> y) \<Longrightarrow> (l = r) \<longrightarrow> y" by(auto simp add: QUOT_TRUE_def)syntax "Bex1_rel" :: "id \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> bool" ("(3\<exists>!!_\<in>_./ _)" [0, 0, 10] 10)translations "\<exists>!!x\<in>A. P" == "Bex1_rel A (%x. P)"(* Atomize infrastructure *)(* FIXME/TODO: is this really needed? *)(*lemma atomize_eqv: shows "(Trueprop A \<equiv> Trueprop B) \<equiv> (A \<equiv> B)"proof assume "A \<equiv> B" then show "Trueprop A \<equiv> Trueprop B" by unfoldnext assume *: "Trueprop A \<equiv> Trueprop B" have "A = B" proof (cases A) case True have "A" by fact then show "A = B" using * by simp next case False have "\<not>A" by fact then show "A = B" using * by auto qed then show "A \<equiv> B" by (rule eq_reflection)qed*)ML {* fun dest_cbinop t = let val (t2, rhs) = Thm.dest_comb t; val (bop, lhs) = Thm.dest_comb t2; in (bop, (lhs, rhs)) end*}ML {* fun dest_ceq t = let val (bop, pair) = dest_cbinop t; val (bop_s, _) = Term.dest_Const (Thm.term_of bop); in if bop_s = "op =" then pair else (raise CTERM ("Not an equality", [t])) end*}ML {* fun split_binop_conv t = let val (lhs, rhs) = dest_ceq t; val (bop, _) = dest_cbinop lhs; val [clT, cr2] = bop |> Thm.ctyp_of_term |> Thm.dest_ctyp; val [cmT, crT] = Thm.dest_ctyp cr2; in Drule.instantiate' [SOME clT, SOME cmT, SOME crT] [NONE, NONE, NONE, NONE, SOME bop] @{thm arg_cong2} end*}ML {* fun split_arg_conv t = let val (lhs, rhs) = dest_ceq t; val (lop, larg) = Thm.dest_comb lhs; val [caT, crT] = lop |> Thm.ctyp_of_term |> Thm.dest_ctyp; in Drule.instantiate' [SOME caT, SOME crT] [NONE, NONE, SOME lop] @{thm arg_cong} end*}ML {* fun split_binop_tac n thm = let val concl = Thm.cprem_of thm n; val (_, cconcl) = Thm.dest_comb concl; val rewr = split_binop_conv cconcl; in rtac rewr n thm end handle CTERM _ => Seq.empty*}ML {* fun split_arg_tac n thm = let val concl = Thm.cprem_of thm n; val (_, cconcl) = Thm.dest_comb concl; val rewr = split_arg_conv cconcl; in rtac rewr n thm end handle CTERM _ => Seq.empty*}lemma trueprop_cong: shows "(a \<equiv> b) \<Longrightarrow> (Trueprop a \<equiv> Trueprop b)" by autolemma list_induct_hol4: fixes P :: "'a list \<Rightarrow> bool" assumes a: "((P []) \<and> (\<forall>t. (P t) \<longrightarrow> (\<forall>h. (P (h # t)))))" shows "\<forall>l. (P l)" using a apply (rule_tac allI) apply (induct_tac "l") apply (simp) apply (metis) doneML {*val no_vars = Thm.rule_attribute (fn context => fn th => let val ctxt = Variable.set_body false (Context.proof_of context); val ((_, [th']), _) = Variable.import true [th] ctxt; in th' end);*}(*lemma equality_twice: "a = c \<Longrightarrow> b = d \<Longrightarrow> (a = b \<longrightarrow> c = d)"by auto*)(*interpretation code *)(*val bindd = ((Binding.make ("", Position.none)), ([]: Attrib.src list)) val ((_, [eqn1pre]), lthy5) = Variable.import true [ABS_def] lthy4; val eqn1i = Thm.prop_of (symmetric eqn1pre) val ((_, [eqn2pre]), lthy6) = Variable.import true [REP_def] lthy5; val eqn2i = Thm.prop_of (symmetric eqn2pre) val exp_morphism = ProofContext.export_morphism lthy6 (ProofContext.init (ProofContext.theory_of lthy6)); val exp_term = Morphism.term exp_morphism; val exp = Morphism.thm exp_morphism; val mthd = Method.SIMPLE_METHOD ((rtac quot_thm 1) THEN ALLGOALS (simp_tac (HOL_basic_ss addsimps [(symmetric (exp ABS_def)), (symmetric (exp REP_def))]))) val mthdt = Method.Basic (fn _ => mthd) val bymt = Proof.global_terminal_proof (mthdt, NONE) val exp_i = [(@{const_name QUOT_TYPE}, ((("QUOT_TYPE_I_" ^ (Binding.name_of qty_name)), true), Expression.Named [("R", rel), ("Abs", abs), ("Rep", rep) ]))]*)(*||> Local_Theory.theory (fn thy => let val global_eqns = map exp_term [eqn2i, eqn1i]; (* Not sure if the following context should not be used *) val (global_eqns2, lthy7) = Variable.import_terms true global_eqns lthy6; val global_eqns3 = map (fn t => (bindd, t)) global_eqns2; in ProofContext.theory_of (bymt (Expression.interpretation (exp_i, []) global_eqns3 thy)) end)*)