0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : do_CVC4 %s 0.03/0.24 % Computer : n150.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 05:39:25 CDT 2018 0.03/0.24 % CPUTime : 0.06/0.29 %----Proving without arithmetic mode 0.06/0.30 ------- cvc4-fof casc j9 : /export/starexec/sandbox2/benchmark/theBenchmark.p at ... 0.06/0.30 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 8.80/9.07 % SZS status Theorem for theBenchmark 8.80/9.07 % SZS output start Proof for theBenchmark 8.80/9.07 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (forall ((C $$unsorted)) (or (not (hBOOL (hAPP _let_5 bool (hAPP _let_5 (fun _let_5 bool) (ord_less_eq _let_5) C) (hAPP _let_3 _let_5 (dom pname com) body)))) (not (hBOOL (hAPP _let_5 bool (finite_finite pname) C))) (not (= (ti _let_4 fa) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) C)))) )))))))) 8.80/9.07 ( skv_1 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (forall ((AA $$unsorted)) (or (not (hBOOL (hAPP _let_5 bool (hAPP _let_5 (fun _let_5 bool) (ord_less_eq _let_5) AA) (hAPP _let_3 _let_5 (dom pname com) body)))) (not (= (ti _let_4 fa) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) AA)))) )))))))) 8.80/9.07 ( skv_2 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (hAPP (fun pname (option com)) _let_3 (dom pname com) body))) (let ((_let_5 (fun pname _let_0))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_3 bool (hAPP pname (fun _let_3 bool) (member pname) X_1) _let_4))) (hBOOL (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_5 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) _let_4)) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 X_1))) (bot_bot _let_2))))) ))))))) 8.80/9.07 ( skv_3 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) X_1) fa))) ))) 8.80/9.07 ( skv_4 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (fun com bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP com (fun _let_0 bool) (member com) X_1) wt))) )) 8.80/9.07 ( skv_5 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP bool (fun _let_0 bool) (member bool) X_1) fNot))) )) 8.80/9.07 ( skv_6 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (hAPP _let_1 (fun _let_4 bool) (member _let_1) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_4 bool _let_7 fa))) (hBOOL (hAPP _let_4 bool _let_7 (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))) ))))))))) 8.80/9.07 ( skv_7 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (= (hAPP bool _let_0 fimplies X_1) (hAPP bool _let_0 fdisj X_1)) )) 8.80/9.07 ( skv_8 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (= (hAPP bool _let_0 fconj X_1) (hAPP bool _let_0 fdisj X_1)) )) 8.80/9.07 ( skv_9 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (= (hAPP bool _let_0 fimplies X_1) (hAPP bool _let_0 fconj X_1)) )) 8.80/9.07 ( skv_10 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (let ((_let_5 (hAPP _let_0 (fun _let_2 bool) (member _let_0) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_2 bool _let_5 (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2))))) (hBOOL (hAPP _let_2 bool _let_5 (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))) ))))))) 8.80/9.07 ( skv_11 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (fun pname bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP pname (fun _let_0 bool) (member pname) X_1) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))) )) 8.80/9.07 ( skv_12 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) X_1) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1))))) ))) 8.80/9.07 ( skv_13 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (forall ((X_1 $$unsorted)) (= (hAPP _let_0 bool (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2)) X_1) (hAPP _let_0 bool (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)) X_1)) )))))) 8.80/9.07 ( skv_14 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) X_1) (hAPP _let_0 _let_1 (ord_less_eq _let_0) fa)))) ))) 8.80/9.07 ( skv_15 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_3 bool (hAPP _let_2 (fun _let_3 bool) (member _let_2) X_1) (hAPP _let_2 _let_3 (hoare_122391849derivs state) (hAPP _let_4 _let_2 (hAPP _let_5 (fun _let_4 _let_2) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))))) ))))))) 8.80/9.07 ( skv_16 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_2 bool (hAPP _let_1 (fun _let_2 bool) (member _let_1) X_1) (finite_finite _let_0)))) )))) 8.80/9.07 ( skv_17 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) X_1) (finite_finite pname)))) ))) 8.80/9.07 ( skv_18 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) (hAPP com _let_0 hoare_Mirabelle_MGT y)) X_1))) ))) 8.80/9.07 ( skv_19 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_1 bool (hAPP _let_2 _let_2 (hAPP _let_5 _let_3 (combs _let_1 bool bool) (hAPP _let_2 _let_5 (hAPP (fun bool _let_0) (fun _let_2 _let_5) (combb bool _let_0 _let_1) fdisj) (hAPP _let_1 _let_2 (hAPP _let_4 _let_4 (combc _let_1 _let_1 bool) (fequal _let_1)) (hAPP com _let_1 hoare_Mirabelle_MGT y)))) (hAPP _let_2 _let_2 (hAPP (fun _let_1 (fun _let_2 bool)) _let_3 (combc _let_1 _let_2 bool) (member _let_1)) (bot_bot _let_2))) X_1))) ))))))) 8.80/9.07 ( skv_20 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (hoare_509422987triple state))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (fequal _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) X_1))) )) 8.80/9.07 ( skv_21 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (forall ((C $$unsorted)) (or (not (hBOOL (hAPP _let_5 bool (hAPP _let_5 (fun _let_5 bool) (ord_less_eq _let_5) C) skv_2))) (not (hBOOL (hAPP _let_5 bool (finite_finite pname) C))) (not (= (ti _let_4 fa) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) C)))) )))))))) 8.80/9.07 ( skv_22 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (forall ((AA $$unsorted)) (or (not (hBOOL (hAPP _let_5 bool (hAPP _let_5 (fun _let_5 bool) (ord_less_eq _let_5) AA) skv_2))) (not (= (ti _let_4 fa) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) AA)))) )))))))) 8.80/9.07 ( skv_23 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun com bool))) (forall ((C $$unsorted)) (or (not (hBOOL (hAPP _let_6 bool (hAPP _let_6 (fun _let_6 bool) (ord_less_eq _let_6) C) (hAPP _let_5 _let_6 (hAPP _let_2 (fun _let_5 _let_6) (image pname com) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) (hAPP _let_3 _let_5 (dom pname com) body))))) (not (hBOOL (hAPP _let_6 bool (finite_finite com) C))) (not (= (ti _let_4 fa) (hAPP _let_6 _let_4 (hAPP (fun com _let_1) (fun _let_6 _let_4) (image com _let_1) hoare_Mirabelle_MGT) C)))) )))))))) 8.80/9.07 ( skv_24 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun com bool))) (forall ((AA $$unsorted)) (or (not (hBOOL (hAPP _let_6 bool (hAPP _let_6 (fun _let_6 bool) (ord_less_eq _let_6) AA) (hAPP _let_5 _let_6 (hAPP _let_2 (fun _let_5 _let_6) (image pname com) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) (hAPP _let_3 _let_5 (dom pname com) body))))) (not (= (ti _let_4 fa) (hAPP _let_6 _let_4 (hAPP (fun com _let_1) (fun _let_6 _let_4) (image com _let_1) hoare_Mirabelle_MGT) AA)))) )))))))) 8.80/9.07 ( skv_25 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun _let_2 _let_0))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_2 bool (hAPP _let_3 _let_3 (hAPP _let_4 (fun _let_3 _let_3) (combs _let_2 bool bool) (hAPP _let_3 _let_4 (hAPP (fun bool _let_0) (fun _let_3 _let_4) (combb bool _let_0 _let_2) fconj) (hAPP _let_2 _let_3 (fequal _let_2) fa))) (finite_finite _let_1)) X_1))) )))))) 8.80/9.07 ( skv_26 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun _let_2 bool))) (not (hBOOL (hAPP _let_2 bool (hAPP _let_0 _let_0 (hAPP _let_3 (fun _let_0 _let_0) (combs _let_2 bool bool) (hAPP _let_0 _let_3 (hAPP (fun bool _let_0) (fun _let_0 _let_3) (combb bool _let_0 _let_2) fconj) (hAPP _let_2 _let_0 (hAPP _let_4 _let_4 (combc _let_2 _let_2 bool) (fequal _let_2)) fa))) (finite_finite _let_1)) X_1)))) )))))) 8.80/9.07 ( skv_27 ) 8.80/9.07 ) 8.80/9.07 (skolem (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (fun _let_3 _let_0))) (let ((_let_8 (fun _let_3 _let_4))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_3 bool (hAPP _let_4 _let_4 (hAPP _let_7 (fun _let_4 _let_4) (combs _let_3 bool bool) (hAPP _let_4 _let_7 (hAPP (fun bool _let_0) (fun _let_4 _let_7) (combb bool _let_0 _let_3) fconj) (hAPP _let_3 _let_4 (hAPP _let_8 _let_8 (combc _let_3 _let_3 bool) (fequal _let_3)) fa))) (hAPP _let_3 _let_4 (hoare_122391849derivs state) (hAPP _let_5 _let_3 (hAPP _let_6 (fun _let_5 _let_3) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_5 (dom pname com) body)))) X_1))) )))))))))) 8.80/9.08 ( skv_28 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (fun _let_3 _let_0))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_3 bool (hAPP _let_4 _let_4 (hAPP _let_7 (fun _let_4 _let_4) (combs _let_3 bool bool) (hAPP _let_4 _let_7 (hAPP (fun bool _let_0) (fun _let_4 _let_7) (combb bool _let_0 _let_3) fconj) (hAPP _let_3 _let_4 (fequal _let_3) fa))) (hAPP _let_3 _let_4 (hoare_122391849derivs state) (hAPP _let_5 _let_3 (hAPP _let_6 (fun _let_5 _let_3) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_5 (dom pname com) body)))) X_1))) ))))))))) 8.80/9.08 ( skv_29 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (option com))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun (hoare_509422987triple state) bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun pname (hoare_509422987triple state)))) (let ((_let_8 (fun _let_4 _let_1))) (let ((_let_9 (fun _let_4 _let_5))) (forall ((X_1 $$unsorted)) (let ((_let_0 (hoare_509422987triple state))) (not (hBOOL (hAPP _let_4 bool (hAPP _let_5 _let_5 (hAPP _let_8 (fun _let_5 _let_5) (combs _let_4 bool bool) (hAPP _let_5 _let_8 (hAPP (fun bool _let_1) (fun _let_5 _let_8) (combb bool _let_1 _let_4) fconj) (hAPP _let_4 _let_5 (hAPP _let_9 _let_9 (combc _let_4 _let_4 bool) (fequal _let_4)) (hAPP _let_6 _let_4 (hAPP _let_7 (fun _let_6 _let_4) (image pname _let_0) (hAPP _let_2 _let_7 (hAPP (fun com _let_0) (fun _let_2 _let_7) (combb com _let_0 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_6 (dom pname com) body))))) (hAPP _let_4 _let_5 (ord_less_eq _let_4) fa)) X_1)))) ))))))))))) 8.80/9.08 ( skv_30 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (option com))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun (hoare_509422987triple state) bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun pname (hoare_509422987triple state)))) (let ((_let_8 (fun _let_4 _let_1))) (forall ((X_1 $$unsorted)) (let ((_let_0 (hoare_509422987triple state))) (not (hBOOL (hAPP _let_4 bool (hAPP _let_5 _let_5 (hAPP _let_8 (fun _let_5 _let_5) (combs _let_4 bool bool) (hAPP _let_5 _let_8 (hAPP (fun bool _let_1) (fun _let_5 _let_8) (combb bool _let_1 _let_4) fconj) (hAPP _let_4 _let_5 (fequal _let_4) (hAPP _let_6 _let_4 (hAPP _let_7 (fun _let_6 _let_4) (image pname _let_0) (hAPP _let_2 _let_7 (hAPP (fun com _let_0) (fun _let_2 _let_7) (combb com _let_0 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_6 (dom pname com) body))))) (hAPP _let_4 _let_5 (ord_less_eq _let_4) fa)) X_1)))) )))))))))) 8.80/9.08 ( skv_31 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun pname bool))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 (fun _let_1 bool)))) (forall ((X_1 $$unsorted)) (let ((_let_0 (fun _let_1 bool))) (not (hBOOL (hAPP _let_1 bool (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs _let_1 bool bool) (hAPP _let_0 _let_2 (hAPP (fun bool _let_0) (fun _let_0 _let_2) (combb bool _let_0 _let_1) fconj) (hAPP _let_1 _let_0 (hAPP _let_3 _let_3 (combc _let_1 _let_1 bool) (fequal _let_1)) (hAPP (fun pname (option com)) _let_1 (dom pname com) body)))) (finite_finite pname)) X_1)))) ))))) 8.80/9.08 ( skv_32 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_4 bool (hAPP _let_1 (fun _let_4 bool) (member _let_1) X_1) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))) )))))))) 8.80/9.08 ( skv_33 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_2 bool (hAPP _let_0 (fun _let_2 bool) (member _let_0) X_1) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))) )))))) 8.80/9.08 ( skv_34 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (fun com bool))) (let ((_let_1 (hAPP com (fun _let_0 bool) (member com) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 wt))) (hBOOL (hAPP _let_0 bool _let_1 (bot_bot _let_0)))) ))) 8.80/9.08 ( skv_35 ) 8.80/9.08 ) 8.80/9.08 (skolem (forall ((X_1 $$unsorted)) (= (hAPP com bool wt X_1) (hAPP com bool (bot_bot (fun com bool)) X_1)) ) 8.80/9.08 ( skv_36 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (fun com bool))) (forall ((X_1 $$unsorted)) (or (not (= (ti com skv_5) (hAPP com com (combi com) X_1))) (not (hBOOL (hAPP _let_0 bool (hAPP com (fun _let_0 bool) (member com) X_1) wt)))) )) 8.80/9.08 ( skv_37 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_1))) (forall ((X_1 $$unsorted)) (or (not (= (hAPP pname _let_1 (hAPP _let_2 _let_5 (hAPP (fun com _let_1) (fun _let_2 _let_5) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) X_1) (ti _let_1 skv_7))) (not (hBOOL (hAPP _let_4 bool (hAPP pname (fun _let_4 bool) (member pname) X_1) (hAPP _let_3 _let_4 (dom pname com) body))))) ))))))) 8.80/9.08 ( skv_38 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP _let_0 (fun _let_1 bool) (member _let_0) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_2 fa))) (hBOOL (hAPP _let_1 bool _let_2 (bot_bot _let_1)))) )))) 8.80/9.08 ( skv_39 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (hoare_509422987triple state))) (forall ((X_1 $$unsorted)) (= (hAPP _let_0 bool fa X_1) (hAPP _let_0 bool (bot_bot (fun _let_0 bool)) X_1)) )) 8.80/9.08 ( skv_40 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP _let_0 (fun _let_1 bool) (member _let_0) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_2 fa))) (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1))))) )))) 8.80/9.08 ( skv_41 ) 8.80/9.08 ) 8.80/9.08 (skolem (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP (hoare_509422987triple state) bool fa X_1))) ) 8.80/9.08 ( skv_42 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_1))) (forall ((X_1 $$unsorted)) (or (not (= (hAPP pname _let_1 (hAPP _let_2 _let_5 (hAPP (fun com _let_1) (fun _let_2 _let_5) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) X_1) (ti _let_1 skv_7))) (not (hBOOL (hAPP _let_4 bool (hAPP pname (fun _let_4 bool) (member pname) X_1) skv_2)))) ))))))) 8.80/9.08 ( skv_43 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_1))) (forall ((X_1 $$unsorted)) (or (not (= (hAPP pname _let_1 (hAPP _let_2 _let_5 (hAPP (fun com _let_1) (fun _let_2 _let_5) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) X_1) (ti _let_1 skv_4))) (not (hBOOL (hAPP _let_4 bool (hAPP pname (fun _let_4 bool) (member pname) X_1) skv_2)))) ))))))) 8.80/9.08 ( skv_44 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (forall ((C $$unsorted)) (or (not (hBOOL (hAPP _let_3 bool (hAPP _let_3 (fun _let_3 bool) (ord_less_eq _let_3) C) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))) (not (hBOOL (hAPP _let_3 bool (finite_finite pname) C))) (not (= (ti _let_2 fa) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) C)))) )))))) 8.80/9.08 ( skv_45 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (forall ((AA $$unsorted)) (or (not (hBOOL (hAPP _let_3 bool (hAPP _let_3 (fun _let_3 bool) (ord_less_eq _let_3) AA) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))) (not (= (ti _let_2 fa) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) AA)))) )))))) 8.80/9.08 ( skv_46 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))))) (forall ((C $$unsorted)) (or (not (hBOOL (hAPP _let_5 bool (hAPP _let_5 (fun _let_5 bool) (ord_less_eq _let_5) C) skv_2))) (not (hBOOL (hAPP _let_5 bool (finite_finite pname) C))) (not (= (hAPP _let_5 _let_4 _let_7 C) (ti _let_4 (hAPP _let_5 _let_4 _let_7 (hAPP _let_3 _let_5 (dom pname com) body)))))) ))))))))) 8.80/9.08 ( skv_47 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))))) (forall ((AA $$unsorted)) (or (not (hBOOL (hAPP _let_5 bool (hAPP _let_5 (fun _let_5 bool) (ord_less_eq _let_5) AA) skv_2))) (not (= (ti _let_4 (hAPP _let_5 _let_4 _let_7 (hAPP _let_3 _let_5 (dom pname com) body))) (hAPP _let_5 _let_4 _let_7 AA)))) ))))))))) 8.80/9.08 ( skv_48 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (fun bool bool))) (let ((_let_1 (hAPP bool (fun _let_0 bool) (member bool) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 fNot))) (hBOOL (hAPP _let_0 bool _let_1 (bot_bot _let_0)))) ))) 8.80/9.08 ( skv_49 ) 8.80/9.08 ) 8.80/9.08 (skolem (forall ((X_1 $$unsorted)) (= (hAPP bool bool fNot X_1) (hAPP bool bool (bot_bot (fun bool bool)) X_1)) ) 8.80/9.08 ( skv_50 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (or (not (= (ti bool skv_6) (hAPP bool bool (combi bool) X_1))) (not (hBOOL (hAPP _let_0 bool (hAPP bool (fun _let_0 bool) (member bool) X_1) fNot)))) )) 8.80/9.08 ( skv_51 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP bool (fun _let_0 bool) (member bool) X_1) (combi bool)))) )) 8.80/9.08 ( skv_52 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_2 bool (hAPP _let_1 (fun _let_2 bool) (member _let_1) X_1) (hAPP _let_0 _let_2 (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))))) )))) 8.80/9.08 ( skv_53 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (forall ((X_1 $$unsorted)) (= (hAPP _let_2 bool (hAPP _let_0 _let_3 (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) X_1) (hAPP _let_2 bool (hAPP _let_2 _let_3 (hoare_122391849derivs state) (hAPP _let_4 _let_2 (hAPP _let_5 (fun _let_4 _let_2) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body))) X_1)) ))))))) 8.80/9.08 ( skv_54 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (bot_bot _let_1))) (let ((_let_3 (fun pname bool))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_3 bool (hAPP pname (fun _let_3 bool) (member pname) X_1) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))) (hBOOL (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (hoare_122391849derivs state) _let_2) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 X_1))) _let_2)))) ))))) 8.80/9.08 ( skv_55 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (fun pname bool))) (let ((_let_1 (hAPP pname (fun _let_0 bool) (member pname) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 skv_2))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))) ))) 8.80/9.08 ( skv_56 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (fun pname bool))) (let ((_let_1 (hAPP pname (fun _let_0 bool) (member pname) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 skv_1))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))) ))) 8.80/9.08 ( skv_57 ) 8.80/9.08 ) 8.80/9.08 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (let ((_let_5 (hAPP _let_0 (fun _let_2 bool) (member _let_0) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_2 bool _let_5 fa))) (hBOOL (hAPP _let_2 bool _let_5 (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))) ))))))) 8.80/9.08 ( skv_58 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (bot_bot _let_1))) (let ((_let_3 (hAPP _let_0 (fun _let_1 bool) (member _let_0) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool _let_3 _let_2))) (hBOOL (hAPP _let_1 bool _let_3 (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) _let_2)))) ))))) 8.80/9.09 ( skv_59 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (hAPP _let_1 (fun _let_4 bool) (member _let_1) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_4 bool _let_7 (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))) (hBOOL (hAPP _let_4 bool _let_7 fa))) ))))))))) 8.80/9.09 ( skv_60 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun pname bool))) (let ((_let_1 (finite_finite pname))) (let ((_let_2 (hAPP pname (fun _let_0 bool) (member pname) A_2))) (forall ((A_2 $$unsorted) (F_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 F_1))) (not (hBOOL (hAPP _let_0 bool _let_2 (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))) (hBOOL (hAPP _let_0 bool _let_2 F_1)) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP pname (fun _let_0 _let_0) (insert pname) A_2) F_1)))) )))) 8.80/9.09 ( skv_61 skv_62 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) fa))) (let ((_let_3 (hAPP _let_0 (fun _let_1 bool) (member _let_0) A_2))) (forall ((A_2 $$unsorted) (F_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (finite_finite _let_0) F_1))) (not (hBOOL (hAPP _let_1 bool _let_3 (bot_bot _let_1)))) (hBOOL (hAPP _let_1 bool _let_3 F_1)) (not (hBOOL (hAPP _let_1 bool _let_2 F_1))) (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) A_2) F_1)))) ))))) 8.80/9.09 ( skv_63 skv_64 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun com bool))) (let ((_let_1 (finite_finite com))) (let ((_let_2 (hAPP com (fun _let_0 bool) (member com) A_2))) (forall ((A_2 $$unsorted) (F_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 F_1))) (not (hBOOL (hAPP _let_0 bool _let_2 (bot_bot _let_0)))) (hBOOL (hAPP _let_0 bool _let_2 F_1)) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP com (fun _let_0 _let_0) (insert com) A_2) F_1)))) )))) 8.80/9.09 ( skv_65 skv_66 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun bool bool))) (let ((_let_1 (finite_finite bool))) (let ((_let_2 (hAPP bool (fun _let_0 bool) (member bool) A_2))) (forall ((A_2 $$unsorted) (F_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 F_1))) (not (hBOOL (hAPP _let_0 bool _let_2 (bot_bot _let_0)))) (hBOOL (hAPP _let_0 bool _let_2 F_1)) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP bool (fun _let_0 _let_0) (insert bool) A_2) F_1)))) )))) 8.80/9.09 ( skv_67 skv_68 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun (fun _let_0 bool) (fun _let_0 bool)))) (let ((_let_3 (insert _let_0))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (let ((_let_6 (hAPP (fun _let_0 bool) (fun (fun _let_0 bool) bool) (hoare_122391849derivs state) (hAPP _let_4 (fun _let_0 bool) (hAPP _let_5 (fun _let_4 (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body))))) (let ((_let_7 (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) A_2))) (forall ((A_2 $$unsorted) (F_1 $$unsorted)) (let ((_let_0 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite _let_0) F_1))) (not (hBOOL (hAPP _let_0 bool _let_7 (hAPP _let_0 _let_0 (hAPP _let_0 _let_2 _let_3 (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_0))))) (hBOOL (hAPP _let_0 bool _let_7 F_1)) (not (hBOOL (hAPP _let_0 bool _let_6 F_1))) (hBOOL (hAPP _let_0 bool _let_6 (hAPP _let_0 _let_0 (hAPP _let_0 _let_2 _let_3 A_2) F_1))))) ))))))))) 8.80/9.09 ( skv_69 skv_70 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun (fun _let_0 bool) (fun _let_0 bool)))) (let ((_let_2 (insert _let_0))) (let ((_let_3 (finite_finite _let_0))) (let ((_let_4 (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) A_2))) (forall ((A_2 $$unsorted) (F_1 $$unsorted)) (let ((_let_0 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool _let_3 F_1))) (not (hBOOL (hAPP _let_0 bool _let_4 (hAPP _let_0 _let_0 (hAPP _let_0 _let_1 _let_2 (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_0))))) (hBOOL (hAPP _let_0 bool _let_4 F_1)) (hBOOL (hAPP _let_0 bool _let_3 (hAPP _let_0 _let_0 (hAPP _let_0 _let_1 _let_2 A_2) F_1))))) )))))) 8.80/9.09 ( skv_71 skv_72 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP _let_0 (fun _let_1 bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)))) (let ((_let_3 (hAPP _let_0 (fun _let_1 bool) (member _let_0) A_2))) (forall ((A_2 $$unsorted) (F_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (finite_finite _let_0) F_1))) (not (hBOOL (hAPP _let_1 bool _let_3 fa))) (hBOOL (hAPP _let_1 bool _let_3 F_1)) (not (hBOOL (hAPP _let_1 bool _let_2 F_1))) (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) A_2) F_1)))) ))))) 8.80/9.09 ( skv_73 skv_74 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun (fun _let_0 bool) (fun _let_0 bool)))) (let ((_let_4 (insert _let_0))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_0))) (let ((_let_7 (hAPP _let_3 _let_2 (hAPP _let_2 (fun _let_3 _let_2) (combb (fun _let_0 bool) bool (fun _let_0 bool)) (hAPP (fun _let_0 bool) _let_2 (hoare_122391849derivs state) (hAPP _let_5 (fun _let_0 bool) (hAPP _let_6 (fun _let_5 (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_6 (hAPP (fun com _let_0) (fun _let_1 _let_6) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_5 (dom pname com) body)))) (hAPP _let_0 _let_3 _let_4 (hAPP com _let_0 hoare_Mirabelle_MGT y))))) (let ((_let_8 (hAPP _let_0 _let_2 (member _let_0) A_2))) (forall ((A_2 $$unsorted) (F_1 $$unsorted)) (let ((_let_0 (option com))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_2 bool (finite_finite _let_0) F_1))) (not (hBOOL (hAPP _let_2 bool _let_8 (hAPP _let_5 _let_2 (hAPP _let_6 (fun _let_5 _let_2) (image pname _let_0) (hAPP _let_1 _let_6 (hAPP (fun com _let_0) (fun _let_1 _let_6) (combb com _let_0 pname) hoare_Mirabelle_MGT) (hAPP _let_1 _let_1 (hAPP (fun _let_0 com) (fun _let_1 _let_1) (combb _let_0 com pname) (the com)) body))) (hAPP _let_1 _let_5 (dom pname com) body))))) (hBOOL (hAPP _let_2 bool _let_8 F_1)) (not (hBOOL (hAPP _let_2 bool _let_7 F_1))) (hBOOL (hAPP _let_2 bool _let_7 (hAPP _let_2 _let_2 (hAPP _let_0 _let_3 _let_4 A_2) F_1))))))) )))))))))) 8.80/9.09 ( skv_75 skv_76 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (option com))) (forall ((Y_1 $$unsorted)) (not (= (hAPP com _let_0 (some com) Y_1) (hAPP pname _let_0 body skv_3))) )) 8.80/9.09 ( skv_77 ) 8.80/9.09 ) 8.80/9.09 (skolem (forall ((X_1 $$unsorted)) (= (hAPP bool bool fNot X_1) (hAPP bool bool (combi bool) X_1)) ) 8.80/9.09 ( skv_78 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (= (hAPP bool _let_0 fimplies X_1) (hAPP bool _let_0 (combk bool bool) X_1)) )) 8.80/9.09 ( skv_79 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (fun _let_5 _let_4))) (let ((_let_8 (image pname _let_1))) (let ((_let_9 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT))) (forall ((X_1 $$unsorted)) (= (hAPP _let_5 _let_4 (hAPP _let_6 _let_7 _let_8 (hAPP _let_2 _let_6 _let_9 (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) X_1) (hAPP _let_5 _let_4 (hAPP _let_6 _let_7 _let_8 (hAPP _let_2 _let_6 _let_9 body_1)) X_1)) ))))))))))) 8.80/9.09 ( skv_80 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (forall ((X_1 $$unsorted)) (= (hAPP _let_1 bool fa X_1) (hAPP _let_1 bool (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body)) X_1)) )))))))) 8.80/9.09 ( skv_81 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (= (hAPP _let_0 _let_1 (fequal _let_0) X_1) (hAPP _let_0 _let_1 (ord_less_eq _let_0) X_1)) ))) 8.80/9.09 ( skv_82 ) 8.80/9.09 ) 8.80/9.09 (skolem (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP com bool wt X_1))) ) 8.80/9.09 ( skv_83 ) 8.80/9.09 ) 8.80/9.09 (skolem (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP bool bool fNot X_1))) ) 8.80/9.09 ( skv_84 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun pname bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_1 bool (hAPP _let_2 _let_2 (hAPP _let_3 (fun _let_2 _let_2) (combs _let_1 bool bool) (hAPP _let_2 _let_3 (hAPP (fun bool _let_0) (fun _let_2 _let_3) (combb bool _let_0 _let_1) fconj) (hAPP _let_1 _let_2 (fequal _let_1) (hAPP (fun pname (option com)) _let_1 (dom pname com) body)))) (finite_finite pname)) X_1))) ))))) 8.80/9.09 ( skv_85 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (forall ((C $$unsorted)) (or (not (hBOOL (hAPP _let_3 bool (hAPP _let_3 (fun _let_3 bool) (ord_less_eq _let_3) C) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))) (not (hBOOL (hAPP _let_3 bool (finite_finite pname) C))) (not (= (ti _let_2 (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) C)))) )))))) 8.80/9.09 ( skv_86 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (forall ((C $$unsorted)) (or (not (hBOOL (hAPP _let_3 bool (hAPP _let_3 (fun _let_3 bool) (ord_less_eq _let_3) C) (bot_bot _let_3)))) (not (hBOOL (hAPP _let_3 bool (finite_finite pname) C))) (not (= (ti _let_2 fa) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) C)))) )))))) 8.80/9.09 ( skv_87 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (= (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) X_1) (hAPP _let_1 _let_1 (collect _let_0) X_1)) ))) 8.80/9.09 ( skv_88 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (= (hAPP _let_0 _let_1 (fequal _let_0) X_1) (hAPP _let_0 _let_1 (hoare_122391849derivs state) X_1)) ))) 8.80/9.09 ( skv_89 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (= (hAPP _let_0 _let_1 (ord_less_eq _let_0) X_1) (hAPP _let_0 _let_1 (hoare_122391849derivs state) X_1)) ))) 8.80/9.09 ( skv_90 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (= (hAPP _let_1 _let_1 (combi _let_1) X_1) (hAPP _let_1 _let_1 (collect _let_0) X_1)) ))) 8.80/9.09 ( skv_91 ) 8.80/9.09 ) 8.80/9.09 (skolem (forall ((X_1 $$unsorted)) (= (hAPP bool bool (combi bool) X_1) (hAPP bool bool (bot_bot (fun bool bool)) X_1)) ) 8.80/9.09 ( skv_92 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (= (hAPP bool _let_0 fconj X_1) (hAPP bool _let_0 (fequal bool) X_1)) )) 8.80/9.09 ( skv_93 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (= (hAPP _let_0 bool (hAPP _let_0 _let_1 (ord_less_eq _let_0) fa) X_1) (hAPP _let_0 bool (bot_bot _let_1) X_1)) ))) 8.80/9.09 ( skv_94 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (forall ((X_1 $$unsorted)) (= (hAPP _let_2 bool (finite_finite _let_0) X_1) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))) X_1)) )))))) 8.80/9.09 ( skv_95 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun pname bool))) (forall ((X_1 $$unsorted)) (= (hAPP pname bool (hAPP (fun pname (option com)) _let_0 (dom pname com) body) X_1) (hAPP pname bool (bot_bot _let_0) X_1)) )) 8.80/9.09 ( skv_96 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (let ((_let_5 (hAPP (fun com _let_1) (fun _let_2 _let_4) (combb com _let_1 pname) hoare_Mirabelle_MGT))) (forall ((X_1 $$unsorted)) (= (hAPP pname _let_1 (hAPP _let_2 _let_4 _let_5 body_1) X_1) (hAPP pname _let_1 (hAPP _let_2 _let_4 _let_5 (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) X_1)) ))))))) 8.80/9.09 ( skv_97 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun (hoare_509422987triple state) bool))) (forall ((X_1 $$unsorted)) (let ((_let_0 (hoare_509422987triple state))) (= (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) X_1) (hAPP _let_0 _let_0 (combi _let_0) X_1))) )) 8.80/9.09 ( skv_98 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (= (hAPP _let_1 bool (finite_finite _let_0) X_1) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) X_1)) ))) 8.80/9.09 ( skv_99 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (forall ((X_1 $$unsorted)) (= (hAPP _let_1 bool (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body)) X_1) (hAPP _let_1 bool (bot_bot _let_4) X_1)) )))))))) 8.80/9.09 ( skv_100 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (= (hAPP bool _let_0 fconj X_1) (hAPP bool _let_0 (combk bool bool) X_1)) )) 8.80/9.09 ( skv_101 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (= (hAPP bool _let_0 fimplies X_1) (hAPP bool _let_0 (fequal bool) X_1)) )) 8.80/9.09 ( skv_102 ) 8.80/9.09 ) 8.80/9.09 (skolem (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (forall ((X_1 $$unsorted)) (= (hAPP pname com body_1 X_1) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) X_1)) )))) 8.80/9.10 ( skv_103 ) 8.80/9.10 ) 8.80/9.10 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0)) A_1)) )) 8.80/9.10 ( bool, fNot ) 8.80/9.10 ( bool, (bot_bot (fun bool bool)) ) 8.80/9.10 ( com, wt ) 8.80/9.10 ( com, (bot_bot (fun com bool)) ) 8.80/9.10 ( pname, (bot_bot (fun pname bool)) ) 8.80/9.10 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)) ) 8.80/9.10 ( (hoare_509422987triple state), fa ) 8.80/9.10 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 8.80/9.10 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 8.80/9.10 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (ti _let_1 (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1))))) ) 8.80/9.10 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 8.80/9.10 ( (fun (hoare_509422987triple state) bool), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 8.80/9.10 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) fa) (bot_bot _let_1)))) ) 8.80/9.10 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun pname _let_1))) (hAPP _let_5 _let_5 (hAPP 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_let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)) (bot_bot _let_1)))) ) 8.80/9.10 ) 8.80/9.10 (instantiation (forall ((P $$unsorted)) (or (not (hBOOL P)) (not (hBOOL (hAPP bool bool fNot P)))) ) 8.80/9.10 ( skv_6 ) 8.80/9.10 ( skv_50 ) 8.80/9.10 ( skv_78 ) 8.80/9.10 ( skv_84 ) 8.80/9.10 ) 8.80/9.10 (instantiation (let ((_let_0 (finite_finite X_a))) (forall ((X_a $$unsorted)) (= _let_0 (ti (fun (fun X_a bool) bool) _let_0)) )) 8.80/9.10 ( bool ) 8.80/9.10 ( com ) 8.80/9.10 ( (option com) ) 8.80/9.10 ( (fun bool bool) ) 8.80/9.10 ( pname ) 8.80/9.10 ( (hoare_509422987triple state) ) 8.80/9.10 ( (fun pname (option com)) ) 8.80/9.10 ( (fun (hoare_509422987triple state) bool) ) 8.80/9.10 ( (fun (fun (hoare_509422987triple state) bool) bool) ) 8.80/9.10 ( (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun _let_0 _let_0)) ) 8.80/9.10 ( (fun pname bool) ) 8.80/9.10 ( (fun (fun pname bool) bool) ) 8.80/9.10 ( (fun com bool) ) 8.80/9.10 ) 8.80/9.10 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (= (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 (hAPP _let_0 _let_0 (hAPP X_a (fun _let_0 _let_0) (insert X_a) X_2) A_1)) B)) (and (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 A_1) B)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (member X_a) X_2) B)))) )))) 8.80/9.10 ( bool, skv_6, fNot, fNot ) 8.80/9.10 ( bool, skv_6, fNot, (bot_bot (fun bool bool)) ) 8.80/9.10 ( com, skv_5, wt, wt ) 8.80/9.10 ( com, skv_5, wt, (bot_bot (fun com bool)) ) 8.80/9.10 ( pname, skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (bot_bot (fun pname bool)) ) 8.80/9.10 ( pname, skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP pname (fun _let_0 _let_0) (insert pname) pn) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 8.80/9.10 ( pname, skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_1 ) 8.80/9.10 ( pname, skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_2 ) 8.80/9.10 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 8.80/9.10 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)), fa ) 8.80/9.10 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 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(hoare_509422987triple state), skv_7, fa, (bot_bot (fun (hoare_509422987triple state) bool)) ) 8.80/9.10 ( (hoare_509422987triple state), skv_7, fa, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 8.80/9.10 ( (hoare_509422987triple state), skv_7, fa, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP 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com) body))) fa)))))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (let ((_let_5 (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) _let_5) _let_5))))))) ) 9.06/9.29 ( (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (hAPP pname (fun _let_0 bool) (member pname) pn) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (finite_finite _let_0) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (finite_finite _let_0) (bot_bot _let_1)))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (finite_finite _let_0) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1))))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))) (bot_bot _let_2))))))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (bot_bot _let_1))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) _let_2) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) _let_2))))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 bool))) (hAPP _let_2 bool (hAPP _let_1 (fun _let_2 bool) (member _let_1) fa) (hAPP _let_0 _let_2 (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)))))) ) 9.06/9.29 ( (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun (hoare_509422987triple state) bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname (hoare_509422987triple state)))) (hAPP _let_4 bool (hAPP _let_3 (fun _let_4 bool) (member _let_3) (hAPP _let_5 _let_3 (hAPP _let_6 (fun _let_5 _let_3) (image pname (hoare_509422987triple state)) (hAPP _let_1 _let_6 (hAPP (fun com (hoare_509422987triple state)) (fun _let_1 _let_6) (combb com (hoare_509422987triple state) pname) hoare_Mirabelle_MGT) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body))) (hAPP _let_2 _let_5 (dom pname com) body))) (hAPP _let_3 _let_4 (ord_less_eq _let_3) fa))))))))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 bool (hAPP _let_2 (fun _let_3 bool) (member _let_2) fa) (hAPP _let_2 _let_3 (hoare_122391849derivs state) (hAPP _let_4 _let_2 (hAPP _let_5 (fun _let_4 _let_2) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))))))))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 bool (hAPP _let_2 (fun _let_3 bool) (member _let_2) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2))) (hAPP _let_2 _let_3 (hoare_122391849derivs state) (hAPP _let_4 _let_2 (hAPP _let_5 (fun _let_4 _let_2) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))))))))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 bool))) (hAPP _let_2 bool (hAPP _let_1 (fun _let_2 bool) (member _let_1) fa) (finite_finite _let_0))))) ) 9.06/9.29 ( (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)) (finite_finite pname)))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 bool fa (hAPP com _let_0 hoare_Mirabelle_MGT y))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP com _let_0 hoare_Mirabelle_MGT y))) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) _let_2) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) _let_2) (bot_bot _let_1)))))) ) 9.06/9.29 ( (let ((_let_0 (fun bool bool))) (hAPP _let_0 bool (finite_finite bool) (bot_bot _let_0))) ) 9.06/9.29 ( (let ((_let_0 (fun com bool))) (hAPP _let_0 bool (finite_finite com) (bot_bot _let_0))) ) 9.06/9.29 ( (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (finite_finite pname) (bot_bot _let_0))) ) 9.06/9.29 ( (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (finite_finite _let_0) (bot_bot _let_1)))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) fa) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1))))) ) 9.06/9.29 ( (hAPP com bool wt y) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (bot_bot _let_1))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (hoare_122391849derivs state) _let_2) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) _let_2))))) ) 9.06/9.29 ( (let ((_let_0 (fun bool bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot) (bot_bot _let_0))) ) 9.06/9.29 ( (let ((_let_0 (fun com bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) wt) (bot_bot _let_0))) ) 9.06/9.29 ( (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa) (bot_bot _let_0))) ) 9.06/9.29 ( (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_4 bool (hAPP _let_4 (fun _let_4 bool) (hoare_122391849derivs state) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))) fa)))))))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (ord_less_eq _let_2) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (ord_less_eq _let_2) fa) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 9.06/9.29 ( (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_1) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 9.06/9.29 ( (hAPP (fun pname bool) bool (finite_finite pname) skv_1) ) 9.06/9.29 ( (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_2) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 9.06/9.29 ( (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (hAPP pname (fun _let_0 bool) (member pname) skv_3) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_2)))))))) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) skv_4) fa))) ) 9.06/9.29 ( (let ((_let_0 (fun com bool))) (hAPP _let_0 bool (hAPP com (fun _let_0 bool) (member com) skv_5) wt)) ) 9.06/9.29 ( skv_6 ) 9.06/9.29 ( (let ((_let_0 (fun bool bool))) (hAPP _let_0 bool (hAPP bool (fun _let_0 bool) (member bool) skv_6) fNot)) ) 9.06/9.29 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) skv_7) fa))) ) 9.06/9.29 ) 9.06/9.29 (instantiation (forall ((P $$unsorted)) (or (hBOOL (hAPP bool bool fNot P)) (hBOOL P)) ) 9.06/9.29 ( skv_6 ) 9.06/9.29 ( skv_50 ) 9.06/9.29 ( skv_78 ) 9.06/9.29 ( skv_84 ) 9.06/9.29 ) 9.06/9.29 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (finite_finite X_a))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (= (hBOOL (hAPP _let_0 bool _let_1 A_1)) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_a (fun _let_0 _let_0) (insert X_a) A_3) A_1)))) ))) 9.06/9.29 ( bool, fTrue, (bot_bot (fun bool bool)) ) 9.06/9.29 ( bool, fFalse, (bot_bot (fun bool bool)) ) 9.06/9.29 ( bool, skv_6, fNot ) 9.06/9.29 ( bool, skv_67, skv_68 ) 9.06/9.29 ( com, y, (bot_bot (fun com bool)) ) 9.06/9.29 ( com, y, (hAPP (fun com (option com)) (fun com bool) (dom com com) (some com)) ) 9.06/9.29 ( com, (hAPP pname com body_1 pn), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun com bool))) (hAPP _let_0 _let_1 (hAPP (fun pname com) (fun _let_0 _let_1) (image pname com) body_1) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))) ) 9.06/9.29 ( com, skv_5, wt ) 9.06/9.29 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let 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(hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (finite_finite _let_0) (bot_bot _let_1)))) ) 9.43/9.45 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (finite_finite _let_0) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1))))) ) 9.43/9.45 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))) (bot_bot _let_2))))))) ) 9.43/9.45 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (bot_bot _let_1))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) _let_2) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) _let_2))))) ) 9.43/9.46 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 bool))) (hAPP _let_2 bool (hAPP _let_1 (fun _let_2 bool) (member _let_1) fa) (hAPP _let_0 _let_2 (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)))))) ) 9.43/9.46 ( bool, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun (hoare_509422987triple state) bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname (hoare_509422987triple state)))) (hAPP _let_4 bool (hAPP _let_3 (fun _let_4 bool) (member _let_3) (hAPP _let_5 _let_3 (hAPP _let_6 (fun _let_5 _let_3) (image pname (hoare_509422987triple state)) (hAPP _let_1 _let_6 (hAPP (fun com (hoare_509422987triple state)) (fun _let_1 _let_6) (combb com (hoare_509422987triple state) pname) hoare_Mirabelle_MGT) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body))) (hAPP _let_2 _let_5 (dom pname com) body))) (hAPP _let_3 _let_4 (ord_less_eq _let_3) fa))))))))) ) 9.43/9.46 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 bool (hAPP _let_2 (fun _let_3 bool) (member _let_2) fa) (hAPP _let_2 _let_3 (hoare_122391849derivs state) (hAPP _let_4 _let_2 (hAPP _let_5 (fun _let_4 _let_2) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))))))))) ) 9.43/9.46 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 bool (hAPP _let_2 (fun _let_3 bool) (member _let_2) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2))) (hAPP _let_2 _let_3 (hoare_122391849derivs state) (hAPP _let_4 _let_2 (hAPP _let_5 (fun _let_4 _let_2) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))))))))) ) 9.43/9.46 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 bool))) (hAPP _let_2 bool (hAPP _let_1 (fun _let_2 bool) (member _let_1) fa) (finite_finite _let_0))))) ) 9.43/9.46 ( bool, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)) (finite_finite pname)))) ) 9.43/9.46 ( bool, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 bool fa (hAPP com _let_0 hoare_Mirabelle_MGT y))) ) 9.43/9.46 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP com _let_0 hoare_Mirabelle_MGT y))) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) _let_2) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) _let_2) (bot_bot _let_1)))))) ) 9.43/9.46 ( bool, (let ((_let_0 (fun bool bool))) (hAPP _let_0 bool (finite_finite bool) (bot_bot _let_0))) ) 9.43/9.46 ( bool, (let ((_let_0 (fun com bool))) (hAPP _let_0 bool (finite_finite com) (bot_bot _let_0))) ) 9.43/9.46 ( bool, (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (finite_finite pname) (bot_bot _let_0))) ) 9.43/9.48 ( bool, (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (finite_finite _let_0) (bot_bot _let_1)))) ) 9.43/9.48 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) fa) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1))))) ) 9.43/9.48 ( bool, (hAPP com bool wt y) ) 9.43/9.48 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (bot_bot _let_1))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (hoare_122391849derivs state) _let_2) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) _let_2))))) ) 9.43/9.48 ( bool, (let ((_let_0 (fun bool bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot) (bot_bot _let_0))) ) 9.43/9.48 ( bool, (let ((_let_0 (fun com bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) wt) (bot_bot _let_0))) ) 9.43/9.48 ( bool, (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa) (bot_bot _let_0))) ) 9.43/9.48 ( bool, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_4 bool (hAPP _let_4 (fun _let_4 bool) (hoare_122391849derivs state) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))) fa)))))))) ) 9.43/9.48 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (ord_less_eq _let_2) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 9.43/9.49 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (ord_less_eq _let_2) fa) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 9.43/9.49 ( bool, (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_1) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 9.43/9.49 ( bool, (hAPP (fun pname bool) bool (finite_finite pname) skv_1) ) 9.43/9.49 ( bool, (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_2) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 9.43/9.49 ( bool, (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (hAPP pname (fun _let_0 bool) (member pname) skv_3) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 9.43/9.49 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_2)))))))) ) 9.43/9.49 ( bool, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) skv_4) fa))) ) 9.43/9.49 ( bool, (let ((_let_0 (fun com bool))) (hAPP _let_0 bool (hAPP com (fun _let_0 bool) (member com) skv_5) wt)) ) 9.43/9.49 ( bool, skv_6 ) 9.43/9.49 ( bool, (let ((_let_0 (fun bool bool))) (hAPP _let_0 bool (hAPP bool (fun _let_0 bool) (member 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(hAPP _let_1 _let_1 (collect X_a) (hAPP _let_1 _let_1 (hAPP _let_3 _let_2 (combs X_a bool bool) (hAPP _let_1 _let_3 (hAPP (fun bool _let_0) (fun _let_1 _let_3) (combb bool _let_0 X_a) fconj) (hAPP X_a _let_1 (fequal X_a) A_3))) P_1)) (hAPP _let_1 _let_1 (hAPP X_a _let_2 (insert X_a) A_3) (bot_bot _let_1)))) ))))) 9.65/9.59 ( bool, fNot, skv_6 ) 9.65/9.59 ( bool, fNot, skv_50 ) 9.65/9.59 ( bool, fNot, skv_78 ) 9.65/9.59 ( bool, fNot, skv_84 ) 9.65/9.59 ( bool, (combi bool), fTrue ) 9.65/9.59 ( bool, (combi bool), fFalse ) 9.65/9.59 ( bool, (combi bool), skv_51 ) 9.65/9.59 ( bool, (combi bool), skv_78 ) 9.65/9.59 ( bool, (combi bool), skv_92 ) 9.65/9.59 ( bool, (bot_bot (fun bool bool)), skv_50 ) 9.65/9.59 ( bool, (bot_bot (fun bool bool)), skv_92 ) 9.65/9.59 ( bool, (let ((_let_0 (fun bool bool))) (hAPP _let_0 _let_0 (hAPP (fun bool (fun _let_0 bool)) (fun _let_0 _let_0) (combc bool _let_0 bool) (member bool)) fNot)), skv_6 ) 9.65/9.59 ( bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fTrue ) 9.65/9.59 ( bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fFalse ) 9.65/9.59 ( com, wt, y ) 9.65/9.59 ( com, wt, (hAPP pname com body_1 skv_3) ) 9.65/9.59 ( com, wt, skv_5 ) 9.65/9.59 ( com, wt, skv_36 ) 9.65/9.59 ( com, wt, skv_83 ) 9.65/9.59 ( com, (bot_bot (fun com bool)), skv_36 ) 9.65/9.59 ( com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun com bool))) (let ((_let_4 (fun com _let_2))) (hAPP (fun _let_0 bool) _let_3 (hAPP _let_4 (fun (fun _let_0 bool) _let_3) (combc com (fun _let_0 bool) bool) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_4) (combb _let_0 _let_2 com) (member _let_0)) hoare_Mirabelle_MGT)) fa)))))), y ) 9.65/9.59 ( com, (let ((_let_0 (fun com bool))) (hAPP _let_0 _let_0 (hAPP (fun com (fun _let_0 bool)) (fun _let_0 _let_0) (combc com _let_0 bool) (member com)) wt)), skv_5 ) 9.65/9.59 ( com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun com bool))) (hAPP _let_1 _let_3 (hAPP _let_2 (fun _let_1 _let_3) (combb _let_0 bool com) (hAPP _let_2 _let_2 (hAPP (fun _let_0 (fun _let_2 bool)) (fun _let_2 _let_2) (combc _let_0 _let_2 bool) (member _let_0)) fa)) hoare_Mirabelle_MGT))))), y ) 9.65/9.59 ( com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun com bool))) (hAPP _let_1 _let_2 (hAPP (fun _let_0 bool) (fun _let_1 _let_2) (combb _let_0 bool com) fa) hoare_Mirabelle_MGT)))), y ) 9.65/9.59 ( com, (let ((_let_0 (fun com bool))) (let ((_let_1 (fun com com))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb com bool com) wt) (combi com)))), y ) 9.65/9.59 ( (fun bool bool), (finite_finite bool), fNot ) 9.65/9.59 ( (fun bool bool), (finite_finite bool), (bot_bot (fun bool bool)) ) 9.65/9.60 ( (fun bool bool), (finite_finite bool), skv_68 ) 9.65/9.60 ( (fun bool bool), (finite_finite bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 _let_0 (hAPP bool (fun _let_0 _let_0) (insert bool) skv_67) skv_68)) ) 9.65/9.60 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), fNot ) 9.65/9.60 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), (bot_bot (fun bool bool)) ) 9.65/9.60 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6), fNot ) 9.65/9.60 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6), (bot_bot (fun bool bool)) ) 9.65/9.60 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 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bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_67), skv_68 ) 9.69/9.60 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn ) 9.69/9.60 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3 ) 9.69/9.60 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_96 ) 9.69/9.60 ( pname, (bot_bot (fun pname bool)), skv_96 ) 9.69/9.60 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), pn ) 9.69/9.60 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), skv_3 ) 9.69/9.60 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) 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skv_64))) ) 9.69/9.61 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), skv_94 ) 9.69/9.61 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 9.69/9.61 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) 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(hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)))))))))))))), skv_2 ) 9.73/9.70 ( (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (bot_bot (fun pname bool)) ) 9.73/9.70 ( (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP pname (fun _let_0 _let_0) (insert pname) pn) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 9.73/9.70 ( (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), skv_1 ) 9.73/9.70 ( (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP (fun pname 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$$unsorted) (A_3 $$unsorted)) (or (hBOOL (hAPP X_a bool P_1 A_3)) (= (bot_bot _let_1) (hAPP _let_1 _let_1 (collect X_a) (hAPP _let_1 _let_1 (hAPP _let_2 (fun _let_1 _let_1) (combs X_a bool bool) (hAPP _let_1 _let_2 (hAPP (fun bool _let_0) (fun _let_1 _let_2) (combb bool _let_0 X_a) fconj) (hAPP X_a _let_1 (fequal X_a) A_3))) P_1)))) )))) 9.88/9.72 ( bool, fNot, skv_6 ) 9.88/9.72 ( bool, fNot, skv_50 ) 9.88/9.72 ( bool, fNot, skv_78 ) 9.88/9.72 ( bool, fNot, skv_84 ) 9.88/9.72 ( bool, (combi bool), fTrue ) 9.88/9.72 ( bool, (combi bool), fFalse ) 9.88/9.72 ( bool, (combi bool), skv_51 ) 9.88/9.72 ( bool, (combi bool), skv_78 ) 9.88/9.72 ( bool, (combi bool), skv_92 ) 9.88/9.72 ( bool, (bot_bot (fun bool bool)), skv_50 ) 9.88/9.72 ( bool, (bot_bot (fun bool bool)), skv_92 ) 9.88/9.72 ( bool, (let ((_let_0 (fun bool bool))) (hAPP _let_0 _let_0 (hAPP (fun bool (fun _let_0 bool)) (fun _let_0 _let_0) (combc bool _let_0 bool) (member bool)) fNot)), skv_6 ) 9.88/9.72 ( bool, (let ((_let_0 (fun 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fa)))))), y ) 9.88/9.72 ( com, (let ((_let_0 (fun com bool))) (hAPP _let_0 _let_0 (hAPP (fun com (fun _let_0 bool)) (fun _let_0 _let_0) (combc com _let_0 bool) (member com)) wt)), skv_5 ) 9.88/9.72 ( com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun com bool))) (hAPP _let_1 _let_3 (hAPP _let_2 (fun _let_1 _let_3) (combb _let_0 bool com) (hAPP _let_2 _let_2 (hAPP (fun _let_0 (fun _let_2 bool)) (fun _let_2 _let_2) (combc _let_0 _let_2 bool) (member _let_0)) fa)) hoare_Mirabelle_MGT))))), y ) 9.88/9.72 ( com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun com bool))) (hAPP _let_1 _let_2 (hAPP (fun _let_0 bool) (fun _let_1 _let_2) (combb _let_0 bool com) fa) hoare_Mirabelle_MGT)))), y ) 9.88/9.72 ( com, (let ((_let_0 (fun com bool))) (let ((_let_1 (fun com com))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb com bool com) wt) (combi com)))), y ) 9.88/9.72 ( (fun bool bool), (finite_finite bool), fNot ) 9.88/9.72 ( (fun bool bool), (finite_finite bool), (bot_bot (fun bool bool)) ) 9.88/9.72 ( (fun bool bool), (finite_finite bool), skv_68 ) 9.88/9.72 ( (fun bool bool), (finite_finite bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 _let_0 (hAPP bool (fun _let_0 _let_0) (insert bool) skv_67) skv_68)) ) 9.88/9.72 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), fNot ) 9.88/9.72 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), (bot_bot (fun bool bool)) ) 9.88/9.72 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6), fNot ) 9.88/9.72 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6), (bot_bot (fun bool bool)) ) 9.88/9.72 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (ord_less_eq _let_0)) (bot_bot _let_0)))), fNot ) 9.88/9.72 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb _let_0 bool _let_0) (finite_finite bool)) (collect bool))))), (hAPP bool (fun bool bool) (combk bool bool) fFalse) ) 9.88/9.72 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb _let_0 bool _let_0) (hAPP _let_0 _let_1 (ord_less_eq _let_0) fNot)) (collect bool))))), (hAPP bool (fun bool bool) (combk bool bool) fFalse) ) 9.88/9.72 ( (fun bool bool), (let ((_let_0 (fun (fun bool bool) bool))) (let ((_let_1 (fun (fun bool bool) (fun bool bool)))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb (fun bool bool) bool (fun bool bool)) (hAPP bool _let_0 (member bool) skv_6)) (hAPP (fun bool bool) _let_1 (image bool bool) (combi bool))))), fNot ) 9.88/9.72 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), fNot ) 9.88/9.72 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), (bot_bot (fun bool bool)) ) 9.88/9.72 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) fTrue), (combi bool) ) 9.88/9.72 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) fTrue), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun pname bool))) (let ((_let_2 (finite_finite pname))) (let ((_let_3 (fun _let_1 bool))) (hAPP _let_3 _let_0 (hAPP _let_3 (fun _let_3 _let_0) (image _let_1 bool) _let_2) _let_2))))) ) 9.88/9.72 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) fFalse), (combi bool) ) 9.88/9.72 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) fFalse), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (hAPP _let_1 (fun (fun _let_1 bool) bool) (member _let_1) (hAPP com _let_1 hoare_Mirabelle_MGT y)))) (hAPP (fun (fun _let_1 bool) bool) _let_0 (hAPP (fun (fun _let_1 bool) bool) (fun (fun (fun _let_1 bool) bool) _let_0) (image (fun _let_1 bool) bool) _let_2) _let_2)))) ) 9.88/9.72 ( (fun bool bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP bool (fun (fun bool bool) bool) (member bool) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) fa)))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun (hoare_509422987triple state) bool))) (let ((_let_2 (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) fa))) (hAPP (fun _let_1 bool) _let_0 (hAPP (fun _let_1 bool) (fun (fun _let_1 bool) _let_0) (image _let_1 bool) _let_2) _let_2)))) ) 9.88/9.72 ( (fun bool bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP bool (fun (fun bool bool) bool) (member bool) (hAPP _let_4 bool (hAPP _let_4 (fun _let_4 bool) (ord_less_eq _let_4) fa) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_1))) (let ((_let_6 (hAPP _let_3 (fun _let_3 bool) (hoare_122391849derivs state) (hAPP _let_4 _let_3 (hAPP _let_5 (fun 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(fun (hoare_509422987triple state) bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (finite_finite (hoare_509422987triple state)))) (hAPP _let_2 _let_0 (hAPP _let_2 (fun _let_2 _let_0) (image _let_1 bool) _let_3) _let_3))))) ) 9.88/9.73 ( (fun bool bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP bool (fun (fun bool bool) bool) (member bool) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2))))))))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (hAPP _let_2 _let_0 (hAPP _let_2 (fun _let_2 _let_0) (image _let_1 bool) (hAPP _let_2 _let_2 (hAPP (fun _let_1 (fun _let_2 bool)) (fun _let_2 _let_2) (combc _let_1 _let_2 bool) (member _let_1)) fa)) (bot_bot _let_2))))) ) 9.88/9.73 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (combi bool))), (bot_bot (fun bool bool)) ) 9.88/9.73 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_49), fNot ) 9.88/9.73 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_49), (bot_bot (fun bool bool)) ) 9.88/9.73 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_51), fNot ) 9.88/9.73 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_52), (combi bool) ) 9.88/9.73 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_67), (bot_bot (fun bool bool)) ) 9.88/9.73 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_67), skv_68 ) 9.88/9.73 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn ) 9.88/9.73 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3 ) 9.88/9.73 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_96 ) 9.88/9.73 ( pname, (bot_bot (fun pname bool)), skv_96 ) 9.88/9.73 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), pn ) 9.88/9.73 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), skv_3 ) 9.88/9.73 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 9.88/9.73 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), skv_40 ) 9.88/9.73 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), skv_100 ) 9.88/9.73 ( (hoare_509422987triple state), fa, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 9.88/9.73 ( (hoare_509422987triple state), fa, skv_4 ) 9.88/9.73 ( (hoare_509422987triple state), fa, skv_7 ) 9.88/9.73 ( (hoare_509422987triple state), fa, skv_40 ) 9.88/9.73 ( (hoare_509422987triple state), fa, skv_42 ) 9.88/9.73 ( (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 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(fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), skv_14 ) 9.88/9.73 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 9.88/9.73 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), skv_14 ) 9.88/9.73 ( 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skv_21 ) 9.88/9.73 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) (hAPP com _let_0 hoare_Mirabelle_MGT y)))), skv_19 ) 9.88/9.73 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) (bot_bot _let_1)))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 9.88/9.73 ( (hoare_509422987triple state), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_2 _let_2))) (let ((_let_4 (fun _let_1 _let_2))) (let ((_let_5 (fun _let_1 _let_0))) (hAPP _let_2 _let_2 (hAPP _let_5 _let_3 (combs _let_1 bool bool) (hAPP _let_2 _let_5 (hAPP (fun bool _let_0) (fun 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(hAPP _let_3 _let_1 (hAPP _let_4 (fun _let_3 _let_1) (combb _let_2 bool _let_0) (hAPP _let_1 _let_4 (member _let_1) fa)) (member _let_0))))))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 9.88/9.73 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_1))) (hAPP _let_2 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_2 _let_1) (combs _let_0 _let_1 bool) (member _let_0)) (hAPP _let_1 _let_2 (hAPP (fun _let_0 (fun _let_1 _let_1)) (fun _let_1 _let_2) (combc _let_0 _let_1 _let_1) (insert _let_0)) (bot_bot _let_1)))))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 9.88/9.73 ( (fun pname (option com)), (let ((_let_0 (fun pname (option com)))) (let ((_let_1 (fun pname bool))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 bool))) (hAPP _let_2 _let_3 (hAPP (fun _let_1 bool) (fun _let_2 _let_3) (combb _let_1 bool _let_0) (finite_finite pname)) (dom pname com)))))), body ) 9.88/9.73 ( (fun pname (option com)), (let ((_let_0 (fun pname (option com)))) (let ((_let_1 (fun pname bool))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 bool))) (let ((_let_4 (fun _let_0 _let_0))) (hAPP _let_4 _let_3 (hAPP _let_3 (fun _let_4 _let_3) (combb _let_0 bool _let_0) (hAPP _let_2 _let_3 (hAPP (fun _let_1 bool) (fun _let_2 _let_3) (combb _let_1 bool _let_0) (finite_finite pname)) (dom pname com))) (combi _let_0))))))), body ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), fa ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) fa))) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) fa))) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), skv_54 ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), skv_74 ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) skv_73) skv_74))) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), skv_99 ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (hoare_122391849derivs state) (bot_bot _let_0))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (hoare_122391849derivs state) (bot_bot _let_0))), fa ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (hoare_122391849derivs state) (bot_bot _let_0))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (hoare_122391849derivs state) (bot_bot _let_0))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (hoare_122391849derivs state) (bot_bot _let_0))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (hoare_122391849derivs state) (bot_bot _let_0))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_55))) (bot_bot _let_1)))) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), fa ) 9.88/9.73 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 9.88/9.74 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 9.88/9.74 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 9.88/9.74 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) fa))) ) 9.88/9.74 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), skv_64 ) 9.88/9.74 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) skv_63) skv_64))) ) 9.88/9.74 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), skv_94 ) 9.88/9.74 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 9.88/9.74 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), fa ) 9.88/9.74 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 9.88/9.74 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP 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_let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1))))), fconj ) 10.34/10.05 ( (fun bool (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) bool), (combb bool (fun bool bool) (fun (hoare_509422987triple state) bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) fa))), fconj ) 10.34/10.05 ( (fun bool (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) bool), (combb bool (fun bool bool) (fun (hoare_509422987triple state) bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) fa))), fdisj ) 10.34/10.05 ( (fun bool (fun bool bool)), (fun (fun 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_let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))))), fdisj ) 10.34/10.05 ( (fun bool (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) bool), (combb bool (fun bool bool) (fun (hoare_509422987triple state) bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP (fun _let_0 bool) (fun _let_0 bool) (hAPP (fun bool bool) (fun (fun _let_0 bool) (fun _let_0 bool)) (combb bool bool _let_0) fNot) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) fa)))), fimplies ) 10.34/10.05 ( (fun bool (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) bool), (combb bool (fun bool bool) (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 (fun _let_1 bool)))) (hAPP (fun _let_1 bool) (fun _let_1 bool) (hAPP (fun bool bool) (fun (fun _let_1 bool) (fun _let_1 bool)) (combb bool bool _let_1) fNot) (hAPP _let_1 (fun _let_1 bool) (hAPP _let_2 _let_2 (combc _let_1 _let_1 bool) (fequal _let_1)) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1))))))), fimplies ) 10.34/10.05 ( (fun bool (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (fun (hoare_509422987triple state) bool))) (let ((_let_3 (fun (fun _let_2 bool) (fun _let_2 _let_0)))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (fun 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(hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (fequal _let_0) (bot_bot _let_0))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (fun (hoare_509422987triple state) bool))) (let ((_let_3 (fun (fun _let_2 bool) (fun _let_2 _let_0)))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (fequal _let_2) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (fun (hoare_509422987triple state) bool))) (let ((_let_3 (fun (fun _let_2 bool) (fun _let_2 _let_0)))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 (fun _let_1 bool) (fequal _let_1) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1))))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (fun (hoare_509422987triple state) bool))) (let ((_let_3 (fun (fun _let_2 bool) (fun _let_2 _let_0)))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) (bot_bot _let_0)))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (fun 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body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) (fun bool bool)), (fun (fun (hoare_509422987triple state) bool) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (fun (hoare_509422987triple state) bool))) (let ((_let_3 (fun (fun _let_2 bool) (fun _let_2 _let_0)))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 (fun _let_1 bool)))) (hAPP _let_1 (fun _let_1 bool) (hAPP _let_2 _let_2 (combc _let_1 _let_1 bool) (fequal _let_1)) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (fun pname bool) (fun bool bool)), (fun (fun pname bool) bool), (combb bool (fun bool bool) (fun pname bool)), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (fequal _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (fun pname bool) (fun bool bool)), (fun (fun pname bool) bool), (combb bool (fun bool bool) (fun pname bool)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (fun pname bool) (fun bool bool)), (fun (fun pname bool) bool), (combb bool (fun bool bool) (fun pname bool)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun 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(fun (fun _let_2 bool) (fun _let_2 _let_0)))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (fun pname bool) (fun bool bool)), (fun (fun pname bool) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun (fun _let_2 bool) (fun _let_2 _let_0)))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (fun pname 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(hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) (bot_bot _let_0)))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (fun pname bool) (fun bool bool)), (fun (fun pname bool) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun (fun _let_2 bool) (fun _let_2 _let_0)))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) skv_1))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (hoare_509422987triple state) (fun bool bool)), (fun (hoare_509422987triple state) bool), (combb bool (fun bool bool) (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun _let_0 bool) (fequal _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (hoare_509422987triple state) (fun bool bool)), (fun (hoare_509422987triple state) bool), (combb bool (fun bool bool) (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) (hAPP com _let_0 hoare_Mirabelle_MGT y)))), fdisj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (hoare_509422987triple state) (fun bool bool)), (fun (hoare_509422987triple state) bool), (combb bool (fun bool bool) (hoare_509422987triple state)), (let ((_let_0 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(fun bool bool)), (fun (hoare_509422987triple state) (fun bool bool)), (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (hoare_509422987triple state))) (let ((_let_3 (fun (fun _let_2 bool) (fun _let_2 _let_0)))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) (hAPP com _let_0 hoare_Mirabelle_MGT y)))), fdisj ) 10.34/10.06 ( (fun bool (fun bool bool)), (fun (hoare_509422987triple state) (fun bool bool)), (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (hoare_509422987triple state))) (let ((_let_3 (fun (fun _let_2 bool) (fun _let_2 _let_0)))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))))), fdisj ) 10.34/10.06 ( (fun bool (fun bool bool)), (let ((_let_0 (fun bool bool))) (fun _let_0 _let_0)), (fun (fun bool bool) bool), (let ((_let_0 (fun bool bool))) (combb bool _let_0 _let_0)), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (fequal _let_0) (bot_bot _let_0))), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (let ((_let_0 (fun bool bool))) (fun _let_0 _let_0)), (fun (fun bool bool) bool), (let ((_let_0 (fun bool bool))) (combb bool _let_0 _let_0)), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (fequal _let_0) fNot)), fconj ) 10.34/10.06 ( (fun bool (fun bool bool)), (let ((_let_0 (fun bool bool))) (fun _let_0 _let_0)), (fun (fun bool bool) bool), (let ((_let_0 (fun bool bool))) (combb bool _let_0 _let_0)), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) (bot_bot _let_0)))), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (let ((_let_0 (fun bool bool))) (fun _let_0 _let_0)), (fun (fun bool bool) bool), (let ((_let_0 (fun bool bool))) (combb bool _let_0 _let_0)), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) fNot))), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun com (fun bool bool)), (fun com bool), (combb bool (fun bool bool) com), (hAPP com (fun com bool) (fequal com) y), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun com (fun bool bool)), (fun com bool), (combb bool (fun bool bool) com), (let ((_let_0 (fun com (fun com bool)))) (hAPP com (fun com bool) (hAPP _let_0 _let_0 (combc com com bool) (fequal com)) y)), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun (fun pname (option com)) (fun bool bool)), (fun (fun pname (option com)) bool), (combb bool (fun bool bool) (fun pname (option com))), (let ((_let_0 (fun pname (option com)))) (hAPP _let_0 (fun _let_0 bool) (fequal _let_0) body)), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun (fun pname (option com)) (fun bool bool)), (fun (fun pname (option com)) bool), (combb bool (fun bool bool) (fun pname (option com))), (let ((_let_0 (fun pname (option com)))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) body))), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combb bool (fun bool bool) (fun (fun (hoare_509422987triple state) bool) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun (fun _let_0 bool) bool))) (hAPP _let_1 (fun _let_1 bool) (fequal _let_1) (hAPP _let_0 _let_1 (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))))), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combb bool (fun bool bool) (fun (fun (hoare_509422987triple state) bool) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 (fun _let_3 bool) (fequal _let_3) (hAPP _let_2 _let_3 (hoare_122391849derivs state) (hAPP _let_4 _let_2 (hAPP _let_5 (fun _let_4 _let_2) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))))))))), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combb bool (fun bool bool) (fun (fun (hoare_509422987triple state) bool) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun (fun _let_0 bool) bool))) (hAPP _let_1 (fun _let_1 bool) (fequal _let_1) (finite_finite _let_0)))), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combb bool (fun bool bool) (fun (fun (hoare_509422987triple state) bool) bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 (fun _let_1 bool) (fequal _let_1) (hAPP _let_0 _let_1 (ord_less_eq _let_0) fa)))), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combb bool (fun bool bool) (fun (fun (hoare_509422987triple state) bool) bool)), (let ((_let_0 (fun (fun (hoare_509422987triple state) bool) bool))) (hAPP _let_0 (fun _let_0 bool) (fequal _let_0) (bot_bot _let_0))), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combb bool (fun bool bool) (fun (fun (hoare_509422987triple state) bool) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun (fun _let_0 bool) bool))) (let ((_let_2 (fun _let_1 (fun _let_1 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(combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body))))))))))), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combb bool (fun bool bool) (fun (fun (hoare_509422987triple state) bool) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun (fun _let_0 bool) bool))) (let ((_let_2 (fun _let_1 (fun _let_1 bool)))) (hAPP _let_1 (fun _let_1 bool) (hAPP _let_2 _let_2 (combc _let_1 _let_1 bool) (fequal _let_1)) (finite_finite _let_0))))), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combb bool (fun bool bool) (fun (fun (hoare_509422987triple state) bool) bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 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(fun com bool) (fun bool bool)), (fun (fun com bool) bool), (combb bool (fun bool bool) (fun com bool)), (let ((_let_0 (fun com bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) (bot_bot _let_0)))), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun (fun com bool) (fun bool bool)), (fun (fun com bool) bool), (combb bool (fun bool bool) (fun com bool)), (let ((_let_0 (fun com bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)) wt))), fconj ) 10.34/10.07 ( (fun bool (fun bool bool)), (fun pname (fun bool bool)), (fun pname bool), (combb bool (fun bool bool) pname), (let ((_let_0 (fun pname (fun pname bool)))) (hAPP pname (fun pname bool) (hAPP _let_0 _let_0 (combc pname pname bool) (fequal pname)) pn)), fdisj ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_12 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_38 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_55 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_56 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_57 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_61 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), (bot_bot (fun pname bool)), skv_3 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), skv_1, skv_57 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), skv_2, skv_3 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), skv_2, skv_43 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), skv_2, skv_44 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), skv_2, skv_56 ) 10.34/10.07 ( pname, bool, (fun pname bool), (member pname), skv_62, skv_61 ) 10.34/10.07 ( pname, bool, (fun pname bool), (let ((_let_0 (fun (fun pname bool) bool))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname pname))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb pname _let_0 pname) (member pname)) (combi pname))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn ) 10.34/10.07 ( pname, bool, (fun pname bool), (let ((_let_0 (fun (fun pname bool) bool))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname pname))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb pname _let_0 pname) (member pname)) (combi pname))))), (bot_bot (fun pname bool)), pn ) 10.34/10.07 ( pname, bool, (fun pname bool), (let ((_let_0 (fun (fun pname bool) bool))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname pname))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb pname _let_0 pname) (member pname)) (combi pname))))), skv_1, pn ) 10.34/10.07 ( pname, bool, (fun pname bool), (let ((_let_0 (fun (fun pname bool) bool))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname pname))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb pname _let_0 pname) (member pname)) (combi pname))))), skv_2, pn ) 10.45/10.10 ( pname, com, (fun pname com), (let ((_let_0 (fun pname com))) (hAPP (fun _let_0 _let_0) (fun pname (fun _let_0 com)) (combc _let_0 pname com) (combi _let_0))), body_1, skv_3 ) 10.45/10.10 ( pname, (option com), (fun pname (option com)), (let ((_let_0 (option com))) (let ((_let_1 (fun pname _let_0))) (hAPP (fun _let_1 _let_1) (fun pname (fun _let_1 _let_0)) (combc _let_1 pname _let_0) (combi _let_1)))), body, pn ) 10.45/10.10 ( pname, (fun pname bool), (fun pname bool), (insert pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn ) 10.45/10.10 ( pname, (fun pname bool), (fun pname bool), (insert pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3 ) 10.45/10.10 ( pname, (fun pname bool), (fun pname bool), (insert pname), skv_62, skv_61 ) 10.45/10.10 ( pname, (fun pname bool), (fun pname bool), (let ((_let_0 (fun (fun pname bool) (fun pname bool)))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname pname))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb pname _let_0 pname) (insert pname)) (combi pname))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn ) 10.45/10.10 ( pname, (fun pname bool), (fun pname bool), (let ((_let_0 (fun (fun pname bool) (fun pname bool)))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname pname))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb pname _let_0 pname) (insert pname)) (combi pname))))), (bot_bot (fun pname bool)), pn ) 10.45/10.10 ( (hoare_509422987triple state), bool, (hoare_509422987triple state), (fequal (hoare_509422987triple state)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 10.45/10.10 ( (hoare_509422987triple state), bool, (hoare_509422987triple state), (fequal (hoare_509422987triple state)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), skv_14 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (hoare_509422987triple state), (fequal (hoare_509422987triple state)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), skv_19 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (hoare_509422987triple state), (fequal (hoare_509422987triple state)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), skv_20 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (hoare_509422987triple state), (fequal (hoare_509422987triple state)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), skv_21 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)) ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)), skv_4 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)), skv_7 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)), skv_39 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)), skv_59 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)), skv_63 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), fa, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), fa, skv_4 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), fa, skv_7 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), fa, skv_39 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), fa, skv_41 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), fa, skv_58 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), fa, skv_73 ) 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((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), skv_7 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com 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(hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), skv_75 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), skv_11 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun 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(let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), skv_11 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), skv_13 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), skv_41 ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun 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) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) fa))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) fa))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 10.45/10.10 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun 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(let ((_let_1 (fun pname bool))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 bool))) (hAPP _let_2 _let_3 (hAPP (fun _let_1 bool) (fun _let_2 _let_3) (combb _let_1 bool _let_0) (finite_finite pname)) (dom pname com)))))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun pname (option com)))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 (fun _let_1 bool)))) (hAPP (fun _let_1 bool) _let_2 (hAPP (fun bool _let_0) (fun (fun _let_1 bool) _let_2) (combb bool _let_0 _let_1) fconj) (hAPP _let_1 (fun _let_1 bool) (hAPP _let_3 _let_3 (combc _let_1 _let_1 bool) (fequal _let_1)) body)))))) ) 11.37/10.71 ( (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combs (fun (fun (hoare_509422987triple state) bool) bool) bool bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun (fun _let_0 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(let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (fun _let_4 bool))) (let ((_let_8 (fun _let_4 _let_0))) (hAPP _let_7 _let_8 (hAPP (fun bool _let_0) (fun _let_7 _let_8) (combb bool _let_0 _let_4) fconj) (hAPP _let_4 _let_7 (fequal _let_4) (hAPP _let_3 _let_4 (hoare_122391849derivs state) (hAPP _let_5 _let_3 (hAPP _let_6 (fun _let_5 _let_3) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_5 (dom pname com) body)))))))))))))) ) 11.37/10.71 ( (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combs (fun (fun (hoare_509422987triple state) bool) bool) bool bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun (fun _let_0 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(let ((_let_8 (fun _let_4 (fun _let_4 bool)))) (hAPP (fun _let_4 bool) _let_7 (hAPP (fun bool _let_0) (fun (fun _let_4 bool) _let_7) (combb bool _let_0 _let_4) fconj) (hAPP _let_4 (fun _let_4 bool) (hAPP _let_8 _let_8 (combc _let_4 _let_4 bool) (fequal _let_4)) (hAPP _let_3 _let_4 (hoare_122391849derivs state) (hAPP _let_5 _let_3 (hAPP _let_6 (fun _let_5 _let_3) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_5 (dom pname com) body)))))))))))))) ) 11.37/10.71 ( (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combs (fun (fun (hoare_509422987triple state) bool) bool) bool bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) fa)), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun (fun _let_1 bool) bool))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (hAPP (fun _let_2 bool) _let_3 (hAPP (fun bool _let_0) (fun (fun _let_2 bool) _let_3) (combb bool _let_0 _let_2) fconj) (hAPP _let_2 (fun _let_2 bool) (hAPP _let_4 _let_4 (combc _let_2 _let_2 bool) (fequal _let_2)) (finite_finite _let_1)))))))) ) 11.37/10.71 ( (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combs (fun (fun (hoare_509422987triple state) bool) bool) bool bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_4 (fun (fun _let_4 bool) bool) (member _let_4) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body)))))))))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun (hoare_509422987triple state) bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun _let_2 _let_0))) (hAPP _let_3 _let_4 (hAPP (fun bool _let_0) (fun _let_3 _let_4) (combb bool _let_0 _let_2) fconj) (hAPP _let_2 _let_3 (fequal _let_2) (hAPP _let_1 _let_2 (ord_less_eq _let_1) fa)))))))) ) 11.37/10.71 ( (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (combs (fun (fun 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_let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 11.37/10.76 ( (hoare_509422987triple state), skv_7, (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 11.37/10.76 ( (hoare_509422987triple state), skv_7, fa, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) 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_let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 11.37/10.76 ( (hoare_509422987triple state), skv_33, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 11.37/10.76 ( (hoare_509422987triple state), skv_34, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), fa ) 11.37/10.76 ( (hoare_509422987triple state), skv_39, (bot_bot (fun (hoare_509422987triple state) bool)), fa ) 11.37/10.76 ( (hoare_509422987triple state), skv_41, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 11.37/10.76 ( (hoare_509422987triple state), skv_58, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), fa ) 11.37/10.76 ( (hoare_509422987triple state), skv_59, (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 11.37/10.76 ( (hoare_509422987triple state), skv_60, (bot_bot (fun (hoare_509422987triple state) bool)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 11.51/10.76 ( (hoare_509422987triple state), skv_63, fa, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP 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(hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 11.51/10.77 ( (fun (hoare_509422987triple state) bool), (bot_bot (fun (hoare_509422987triple state) bool)), (finite_finite (hoare_509422987triple state)), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 11.51/10.77 ( (fun (hoare_509422987triple state) bool), fa, (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) fa) (bot_bot _let_1)))) ) 11.51/10.77 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 11.51/10.77 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP _let_0 _let_0 (hAPP (hoare_509422987triple state) (fun _let_0 _let_0) (insert (hoare_509422987triple state)) (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y)) (bot_bot _let_0))) (bot_bot _let_1)))) ) 11.51/10.77 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 11.51/10.77 ( (fun (hoare_509422987triple state) bool), skv_15, (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 11.51/10.77 ( (fun (hoare_509422987triple state) bool), skv_16, (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 11.51/10.77 ( (fun pname bool), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (bot_bot (fun (fun pname bool) bool)), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)) (bot_bot _let_1)))) ) 11.51/10.77 ( (fun pname bool), (bot_bot (fun pname bool)), (finite_finite pname), (bot_bot (fun (fun pname bool) bool)) ) 11.51/10.77 ) 11.51/10.77 (instantiation (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (fequal X_a) X) Y)) (not (= (ti X_a Y) (ti X_a X)))) ) 11.51/10.77 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 11.51/10.77 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), skv_14 ) 11.51/10.77 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), skv_19 ) 11.51/10.77 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), skv_20 ) 11.51/10.77 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), skv_21 ) 11.51/10.77 ) 11.51/10.77 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (fun X_a X_b))) (forall ((X_b $$unsorted) (X_a $$unsorted) (C_1 $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) X_2) A_1))) (= (hAPP _let_1 _let_1 (hAPP X_b (fun _let_1 _let_1) (insert X_b) C_1) (bot_bot _let_1)) (hAPP _let_0 _let_1 (hAPP _let_2 (fun _let_0 _let_1) (image X_a X_b) (hAPP X_b _let_2 (combk X_b X_a) C_1)) A_1))) )))) 11.51/10.77 ( bool, bool, skv_6, fFalse, (combi bool) ) 11.51/10.77 ( bool, (fun (hoare_509422987triple state) bool), fTrue, fa, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 11.51/10.77 ( bool, (fun (hoare_509422987triple state) bool), fFalse, fa, (finite_finite (hoare_509422987triple state)) ) 11.51/10.77 ( bool, (fun (hoare_509422987triple state) bool), skv_67, (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 11.51/10.77 ( com, bool, skv_5, fTrue, (combi bool) ) 11.51/10.77 ( com, (fun bool bool), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), fNot, (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6) ) 11.51/10.77 ( com, (hoare_509422987triple state), (hAPP pname com body_1 pn), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) fa))) ) 11.51/10.77 ( com, (fun (hoare_509422987triple state) bool), skv_65, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (hoare_122391849derivs state) (bot_bot _let_0))) ) 11.51/10.77 ( com, (fun pname bool), y, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (finite_finite pname) ) 11.51/10.77 ( (fun bool bool), pname, fNot, skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 11.51/10.77 ( (fun bool bool), (hoare_509422987triple state), (bot_bot (fun bool bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 11.51/10.77 ( pname, (hoare_509422987triple state), skv_3, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 11.51/10.77 ( pname, (fun (hoare_509422987triple state) bool), pn, fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))) ) 11.51/10.77 ( pname, (fun (hoare_509422987triple state) bool), pn, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)) ) 11.51/10.77 ( pname, (fun (hoare_509422987triple state) bool), skv_61, (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))) ) 11.51/10.77 ( (hoare_509422987triple state), com, skv_7, y, wt ) 11.51/10.77 ( (hoare_509422987triple state), (fun bool bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (hAPP pname _let_1 (hAPP _let_2 _let_4 (hAPP (fun com _let_1) (fun _let_2 _let_4) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) pn)))))), (bot_bot (fun bool bool)), (finite_finite bool) ) 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pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), pn, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 11.51/10.78 ( (fun (hoare_509422987triple state) bool), (hoare_509422987triple state), fa, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 11.51/10.78 ( (fun (hoare_509422987triple state) bool), (hoare_509422987triple state), fa, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), fa ) 11.51/10.78 ( (fun (hoare_509422987triple state) bool), (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 11.51/10.78 ( (fun (hoare_509422987triple state) bool), 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com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 11.57/10.82 ( (hoare_509422987triple state), com, hoare_Mirabelle_MGT, y, skv_25 ) 11.57/10.82 ( (hoare_509422987triple state), com, hoare_Mirabelle_MGT, (hAPP pname com body_1 skv_3), (bot_bot (fun com bool)) ) 11.57/10.82 ( (hoare_509422987triple state), (hoare_509422987triple state), (combi (hoare_509422987triple state)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 11.57/10.82 ( (hoare_509422987triple state), (hoare_509422987triple state), (combi (hoare_509422987triple state)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) 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body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 11.57/10.82 ( (fun (hoare_509422987triple state) bool), (fun (hoare_509422987triple state) bool), (combi (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (finite_finite (hoare_509422987triple state)) ) 11.57/10.82 ( (fun (hoare_509422987triple state) bool), (fun (hoare_509422987triple state) bool), (combi (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 11.57/10.82 ( (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun _let_0 _let_0)), 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(finite_finite pname) ) 11.57/10.82 ) 11.57/10.82 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_b bool))) (let ((_let_2 (hAPP (fun X_b X_a) (fun _let_1 _let_0) (image X_b X_a) F))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_a) B))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) B) (hAPP _let_1 _let_0 _let_2 A_1)))) (not (forall ((C $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) C) A_1))) (not (hBOOL (hAPP _let_1 bool (finite_finite X_b) C))) (not (= (hAPP _let_1 _let_0 _let_2 C) (ti _let_0 B)))) ))) )))) 11.57/10.82 ( bool, bool, (combi bool), (bot_bot (fun bool bool)), fNot ) 11.57/10.82 ( bool, bool, (combi bool), (bot_bot (fun bool bool)), (combi bool) ) 11.57/10.82 ( bool, bool, (combi bool), (bot_bot (fun bool bool)), (bot_bot (fun bool bool)) ) 11.57/10.82 ( bool, bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fNot, fNot ) 11.57/10.82 ( bool, bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fNot, (bot_bot (fun bool bool)) ) 11.57/10.82 ( com, com, (combi com), (bot_bot (fun com bool)), wt ) 11.57/10.82 ( com, com, (combi com), (bot_bot (fun com bool)), (bot_bot (fun com bool)) ) 11.57/10.82 ( com, com, (let ((_let_0 (combi com))) (let ((_let_1 (fun com com))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb com com com) _let_0) _let_0))), wt, wt ) 11.57/10.82 ( com, com, (let ((_let_0 (combi com))) (let ((_let_1 (fun com com))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb com com com) _let_0) _let_0))), wt, (bot_bot (fun com bool)) ) 11.57/10.82 ( com, (hoare_509422987triple state), hoare_Mirabelle_MGT, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))), fa ) 11.57/10.82 ( pname, com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_24 ) 11.57/10.82 ( pname, com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_25 ) 11.57/10.82 ( pname, pname, (combi pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 11.57/10.82 ( pname, pname, (combi pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_1 ) 11.57/10.82 ( pname, pname, (combi pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_2 ) 11.57/10.82 ( pname, pname, (combi pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_45 ) 11.57/10.82 ( pname, pname, (combi pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_46 ) 11.57/10.82 ( pname, pname, (combi pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_86 ) 11.57/10.82 ( pname, pname, (combi pname), (bot_bot (fun pname bool)), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 11.57/10.82 ( pname, pname, (combi pname), (bot_bot (fun pname bool)), (bot_bot (fun pname bool)) ) 11.57/10.82 ( pname, pname, (combi pname), (bot_bot (fun pname bool)), skv_1 ) 11.57/10.82 ( pname, pname, (combi pname), (bot_bot (fun pname bool)), skv_2 ) 11.57/10.82 ( pname, pname, (combi pname), (bot_bot (fun pname bool)), skv_87 ) 11.57/10.82 ( pname, (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (hAPP _let_2 _let_4 (hAPP (fun com _let_1) (fun _let_2 _let_4) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), fa ) 11.57/10.82 ( pname, (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun 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_let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 11.57/10.83 ( pname, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (bot_bot (fun (hoare_509422987triple state) bool)) ) 11.57/10.83 ( pname, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), fa ) 11.57/10.83 ( pname, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 11.57/10.83 ( pname, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 11.57/10.83 ( pname, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 11.60/10.83 ( pname, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), (bot_bot (fun pname bool)), fa ) 11.60/10.83 ( pname, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), skv_86, (bot_bot (fun (hoare_509422987triple state) bool)) ) 11.60/10.83 ( pname, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), skv_86, fa ) 11.60/10.83 ( pname, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), skv_86, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 11.60/10.83 ( pname, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 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(hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), skv_87, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 11.60/10.83 ( pname, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), skv_87, (let ((_let_0 (hoare_509422987triple 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bool) bool)) ) 11.60/10.83 ( (hoare_509422987triple state), (hoare_509422987triple state), (combi (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 11.60/10.83 ( (hoare_509422987triple state), (hoare_509422987triple state), (combi (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)), fa ) 11.60/10.83 ( (hoare_509422987triple state), (hoare_509422987triple state), (combi (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 11.60/10.83 ( (hoare_509422987triple state), (hoare_509422987triple state), (combi (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 11.60/10.83 ( (hoare_509422987triple state), (hoare_509422987triple state), (combi (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), fa ) 11.60/10.83 ( (hoare_509422987triple state), (hoare_509422987triple state), (combi (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 11.60/10.83 ( (fun (hoare_509422987triple state) bool), (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_0 (fun _let_1 _let_0) (combk _let_0 _let_1) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com 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_let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs bool bool bool) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb bool _let_0 bool) fconj) (hAPP bool _let_0 (fequal bool) fTrue))) (combi bool)))) ) 11.60/10.83 ( bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs bool bool bool) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb bool _let_0 bool) fconj) (hAPP bool _let_0 (fequal bool) fFalse))) (combi bool)))) ) 11.60/10.83 ( bool, (let ((_let_0 (fun bool (fun bool bool)))) (hAPP (fun bool bool) (fun bool bool) (hAPP _let_0 (fun (fun bool bool) (fun bool bool)) (combs bool bool bool) (hAPP (fun bool bool) _let_0 (hAPP _let_0 (fun (fun bool bool) _let_0) (combb bool (fun bool bool) bool) fconj) (hAPP bool (fun bool bool) (hAPP _let_0 _let_0 (combc bool bool bool) (fequal bool)) fTrue))) (combi bool))) ) 11.60/10.83 ( bool, (let ((_let_0 (fun bool (fun bool bool)))) (hAPP (fun bool bool) 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( (hoare_509422987triple state), skv_7, skv_39, fa ) 11.60/10.89 ( (hoare_509422987triple state), skv_7, skv_41, fa ) 11.60/10.89 ( (hoare_509422987triple state), skv_7, skv_58, fa ) 11.60/10.89 ( (hoare_509422987triple state), skv_7, skv_60, fa ) 11.60/10.89 ( (hoare_509422987triple state), skv_7, skv_73, fa ) 11.60/10.89 ( (hoare_509422987triple state), skv_7, skv_75, fa ) 11.60/10.89 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) 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(let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb bool _let_0 bool) fconj))), (fequal bool), fTrue ) 11.60/10.89 ( bool, (fun bool (fun bool bool)), (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb bool _let_0 bool) fconj))), (fequal bool), fFalse ) 11.60/10.89 ( bool, (fun bool (fun bool bool)), (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb bool _let_0 bool) fconj))), (let ((_let_0 (fun bool (fun bool bool)))) (hAPP _let_0 _let_0 (combc bool bool bool) (fequal bool))), fTrue ) 11.60/10.89 ( bool, (fun bool (fun bool bool)), (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (hAPP _let_1 (fun _let_0 _let_1) (combb bool _let_0 bool) fconj))), (let ((_let_0 (fun bool (fun bool bool)))) (hAPP _let_0 _let_0 (combc bool bool bool) (fequal bool))), fFalse ) 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bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fdisj ) 11.73/10.98 ( (fun bool (fun bool bool)), (fun bool bool), (fun bool (fun bool bool)), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (fun _let_1 _let_0))) (hAPP bool _let_2 (hAPP (fun _let_1 _let_1) (fun bool _let_2) (combc _let_1 bool _let_0) (combi _let_1)) skv_10)))), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fconj ) 11.73/10.98 ( (fun bool (fun bool bool)), (fun bool bool), (fun bool (fun bool bool)), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (fun _let_1 _let_0))) (hAPP bool _let_2 (hAPP 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(hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fimplies ) 11.73/10.99 ( (fun bool (fun bool bool)), (fun bool (fun bool bool)), (fun bool (fun bool bool)), (combi (fun bool (fun bool bool))), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fdisj ) 11.73/10.99 ( (fun bool (fun bool bool)), (fun bool (fun bool bool)), (fun bool (fun bool bool)), (combc bool bool bool), (combi (fun bool (fun bool bool))), (fequal bool) ) 11.73/10.99 ( (fun bool (fun bool bool)), (fun bool (fun bool bool)), (fun bool (fun bool bool)), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) 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(fun bool (fun bool bool))) _let_0) _let_0))), fconj ) 11.85/10.99 ( (fun bool (fun bool bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (fun (hoare_509422987triple state) bool)), (combi (fun bool (fun bool bool))), fconj ) 11.85/10.99 ( (fun bool (fun bool bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (fun (hoare_509422987triple state) bool)), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fconj ) 11.85/10.99 ( (fun bool (fun bool bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (fun (hoare_509422987triple state) bool)), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fimplies ) 11.85/10.99 ( (fun bool (fun bool bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (fun (hoare_509422987triple state) bool)), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fdisj 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bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_1 _let_4))) (hAPP _let_3 _let_5 (hAPP (fun _let_1 (fun _let_3 _let_4)) (fun _let_3 _let_5) (combc _let_1 _let_3 _let_4) (combb bool _let_0 _let_2)) (hAPP _let_2 _let_3 (fequal _let_2) (hAPP (fun pname (option com)) _let_2 (dom pname com) body))))))))), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fconj ) 11.85/10.99 ( (fun bool (fun bool bool)), (fun (fun pname bool) (fun bool bool)), (fun bool (fun bool bool)), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP (fun _let_2 bool) _let_5 (hAPP (fun _let_1 (fun (fun _let_2 bool) _let_3)) (fun (fun _let_2 bool) _let_5) (combc _let_1 (fun _let_2 bool) _let_3) (combb bool _let_0 _let_2)) (hAPP _let_2 (fun _let_2 bool) (hAPP _let_4 _let_4 (combc _let_2 _let_2 bool) (fequal _let_2)) (hAPP (fun pname (option com)) _let_2 (dom pname com) body))))))))), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fconj ) 11.85/10.99 ( (fun bool (fun bool bool)), (let ((_let_0 (fun pname bool))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (fun pname bool)), (combi (fun bool (fun bool bool))), fconj ) 11.85/10.99 ( (fun bool (fun bool bool)), (let ((_let_0 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state))) (let ((_let_3 (fun _let_2 (fun _let_2 bool)))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_1 _let_4))) (hAPP (fun _let_2 bool) _let_5 (hAPP (fun _let_1 (fun (fun _let_2 bool) _let_4)) (fun (fun _let_2 bool) _let_5) (combc _let_1 (fun _let_2 bool) _let_4) (combb bool _let_0 _let_2)) (hAPP _let_2 (fun _let_2 bool) (hAPP _let_3 _let_3 (combc _let_2 _let_2 bool) (fequal _let_2)) (hAPP com _let_2 hoare_Mirabelle_MGT y))))))))), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fdisj ) 11.85/10.99 ( (fun bool (fun bool bool)), (let ((_let_0 (hoare_509422987triple state))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (hoare_509422987triple state)), (combi (fun bool (fun 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bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fimplies ) 11.85/11.00 ( (fun bool (fun bool bool)), (let ((_let_0 (hoare_509422987triple state))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (hoare_509422987triple state)), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fdisj ) 11.85/11.00 ( (fun bool (fun bool bool)), (let ((_let_0 (hoare_509422987triple state))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (hoare_509422987triple state))) (let ((_let_3 (fun (fun _let_2 bool) (fun _let_2 _let_0)))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fdisj ) 11.85/11.00 ( (fun bool (fun bool bool)), (let ((_let_0 (fun bool bool))) (fun _let_0 (fun bool _let_0))), (fun bool (fun bool bool)), (combb bool (fun bool bool) bool), (combi (fun bool (fun bool bool))), (combk bool bool) ) 11.85/11.00 ( (fun bool (fun bool bool)), (let ((_let_0 (fun bool bool))) (fun _let_0 (fun bool _let_0))), (fun bool (fun bool bool)), (combb bool (fun bool bool) bool), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP 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(combb bool _let_0 _let_2)) (combi _let_1)))))))), fdisj ) 11.85/11.00 ( (fun bool (fun bool bool)), (fun (fun com bool) (fun com (fun bool bool))), (fun bool (fun bool bool)), (combb bool (fun bool bool) com), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fconj ) 11.85/11.00 ( (fun bool (fun bool bool)), (let ((_let_0 (fun bool bool))) (fun (fun _let_0 bool) (fun _let_0 _let_0))), (fun bool (fun bool bool)), (let ((_let_0 (fun bool bool))) (combb bool _let_0 _let_0)), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fconj ) 11.85/11.00 ( (fun bool (fun bool bool)), (let ((_let_0 (fun pname (option com)))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (fun pname (option com))), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fconj ) 11.85/11.00 ( (fun bool (fun bool bool)), (let ((_let_0 (fun (fun (hoare_509422987triple state) bool) bool))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (fun (fun (hoare_509422987triple state) bool) bool)), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fconj ) 11.85/11.00 ( (fun bool (fun bool bool)), (let ((_let_0 (fun (fun pname bool) bool))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (fun (fun pname bool) bool)), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fconj ) 11.85/11.00 ( (fun bool (fun bool bool)), (let ((_let_0 (fun com bool))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (fun bool (fun bool bool)), (combb bool (fun bool bool) (fun com bool)), (let ((_let_0 (combi (fun bool (fun bool bool))))) (let ((_let_1 (fun (fun bool (fun bool bool)) (fun bool (fun bool bool))))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb (fun bool (fun bool bool)) (fun bool (fun bool bool)) (fun bool (fun bool bool))) _let_0) _let_0))), fconj ) 11.85/11.00 ( (fun bool (fun bool bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun (fun _let_0 (fun _let_0 bool)) (fun _let_0 (fun _let_0 (fun bool bool))))), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun (fun _let_0 bool) (fun _let_0 (fun bool bool)))), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (combb (fun _let_0 bool) (fun _let_0 (fun bool bool)) _let_0)), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (let ((_let_2 (fun (hoare_509422987triple state) bool))) (let ((_let_3 (fun (fun _let_2 bool) (fun _let_2 _let_0)))) (let ((_let_4 (fun _let_1 _let_1))) (let ((_let_5 (fun _let_1 _let_3))) (hAPP _let_4 _let_5 (hAPP _let_5 (fun _let_4 _let_5) (combb _let_1 _let_3 _let_1) (combb bool _let_0 _let_2)) (combi _let_1)))))))), fconj ) 11.85/11.00 ( (fun bool (fun bool bool)), (let ((_let_0 (fun 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((_let_0 (combi pname))) (let ((_let_1 (fun pname pname))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb pname pname pname) _let_0) _let_0))), pn ) 11.85/11.00 ( pname, (option com), pname, (let ((_let_0 (option com))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname pname))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb pname _let_0 pname) body) (combi pname))))), (let ((_let_0 (combi pname))) (let ((_let_1 (fun pname pname))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb pname pname pname) _let_0) _let_0))), pn ) 11.85/11.00 ( pname, pname, pname, (combi pname), (combi pname), pn ) 11.85/11.00 ( pname, pname, pname, (combi pname), (let ((_let_0 (combi pname))) (let ((_let_1 (fun pname pname))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb pname pname pname) _let_0) _let_0))), pn ) 11.85/11.00 ( pname, pname, pname, (let ((_let_0 (combi pname))) (let ((_let_1 (fun pname pname))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun 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body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 12.47/11.38 ( (fun (fun (hoare_509422987triple state) bool) bool), (fun (fun (hoare_509422987triple state) bool) bool), (fun (fun (hoare_509422987triple state) bool) bool), (collect (fun (hoare_509422987triple state) bool)), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun (hoare_509422987triple state) bool))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 (fun _let_1 bool)))) (hAPP _let_2 (fun (fun _let_1 bool) (fun _let_1 bool)) (combs _let_1 bool bool) (hAPP (fun _let_1 bool) _let_2 (hAPP (fun bool _let_0) (fun (fun _let_1 bool) _let_2) (combb bool _let_0 _let_1) fdisj) (hAPP _let_1 (fun _let_1 bool) (hAPP _let_3 _let_3 (combc _let_1 _let_1 bool) (fequal _let_1)) fa))))))), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) 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12.69/11.54 ( (fun pname bool), (fun (fun (hoare_509422987triple state) bool) bool), (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_1))) (hAPP _let_1 _let_2 (hAPP (fun _let_0 (fun _let_1 _let_1)) (fun _let_1 _let_2) (combc _let_0 _let_1 _let_1) (insert _let_0)) (bot_bot _let_1))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_2 (fun (fun pname bool) (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1))))), skv_87 ) 12.69/11.54 ( (fun pname bool), (fun (fun (hoare_509422987triple state) bool) bool), (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (let ((_let_2 (combc _let_0 _let_0 bool))) (hAPP 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pname (fun pname com) (hoare_509422987triple state)) ) 13.15/11.89 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname bool))) (fun (fun _let_0 (fun _let_1 bool)) (fun _let_1 (fun _let_0 bool))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname bool))) (fun (fun _let_0 (fun _let_1 bool)) (fun _let_1 (fun _let_0 bool))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname bool))) (fun (fun _let_0 (fun _let_1 bool)) (fun _let_1 (fun _let_0 bool))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname bool))) (combi (fun (fun _let_0 (fun _let_1 bool)) (fun _let_1 (fun _let_0 bool)))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname bool))) (combi (fun (fun _let_0 (fun _let_1 bool)) (fun _let_1 (fun _let_0 bool)))))), (combc (hoare_509422987triple state) (fun pname bool) bool) ) 13.15/11.89 ( (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun (fun (hoare_509422987triple 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(let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun (fun (hoare_509422987triple state) (fun _let_0 bool)) (fun _let_0 _let_0))), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (combc (fun (hoare_509422987triple state) (fun _let_0 bool)) _let_0 _let_0)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (combi (fun (fun (hoare_509422987triple state) (fun _let_0 bool)) (fun _let_0 _let_0)))), (let ((_let_0 (hoare_509422987triple state))) (combc _let_0 (fun _let_0 bool) bool)) ) 13.15/11.89 ) 13.15/11.89 (instantiation (let ((_let_0 (image X_a X_b))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (= _let_0 (ti (fun (fun X_a X_b) (fun (fun X_a bool) (fun X_b bool))) _let_0)) )) 13.15/11.89 ( bool, bool ) 13.15/11.89 ( bool, (fun bool bool) ) 13.15/11.89 ( bool, (hoare_509422987triple state) ) 13.15/11.89 ( com, bool ) 13.15/11.89 ( com, com ) 13.15/11.89 ( com, (hoare_509422987triple state) ) 13.15/11.89 ( com, (fun (hoare_509422987triple state) bool) ) 13.15/11.89 ( com, (fun com bool) ) 13.15/11.89 ( (option com), com ) 13.15/11.89 ( (fun bool bool), (fun bool bool) ) 13.28/11.89 ( pname, bool ) 13.28/11.89 ( pname, com ) 13.28/11.89 ( pname, (option com) ) 13.28/11.89 ( pname, pname ) 13.28/11.89 ( pname, (hoare_509422987triple state) ) 13.28/11.89 ( pname, (fun (hoare_509422987triple state) bool) ) 13.28/11.89 ( pname, (fun (fun (hoare_509422987triple state) bool) bool) ) 13.28/11.89 ( pname, (fun pname bool) ) 13.28/11.89 ( pname, (fun (fun pname bool) bool) ) 13.28/11.89 ( pname, (fun (fun pname bool) (fun (hoare_509422987triple state) bool)) ) 13.28/11.89 ( (hoare_509422987triple state), bool ) 13.28/11.89 ( (hoare_509422987triple state), com ) 13.28/11.89 ( (hoare_509422987triple state), pname ) 13.28/11.89 ( (hoare_509422987triple state), (hoare_509422987triple state) ) 13.28/11.89 ( (hoare_509422987triple state), (fun (hoare_509422987triple state) bool) ) 13.28/11.89 ( (hoare_509422987triple state), (fun (fun (hoare_509422987triple state) bool) bool) ) 13.28/11.89 ( (hoare_509422987triple state), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun _let_0 _let_0)) ) 13.28/11.89 ( (hoare_509422987triple state), (fun pname bool) ) 13.28/11.89 ( (fun pname (option com)), (fun pname (option com)) ) 13.28/11.89 ( (fun (hoare_509422987triple state) bool), bool ) 13.28/11.89 ( (fun (hoare_509422987triple state) bool), pname ) 13.28/11.89 ( (fun (hoare_509422987triple state) bool), (hoare_509422987triple state) ) 13.28/11.89 ( (fun (hoare_509422987triple state) bool), (fun (hoare_509422987triple state) bool) ) 13.28/11.89 ( (fun (hoare_509422987triple state) bool), (fun (fun (hoare_509422987triple state) bool) bool) ) 13.28/11.89 ( (fun (hoare_509422987triple state) bool), (fun pname bool) ) 13.28/11.89 ( (fun (fun (hoare_509422987triple state) bool) bool), (fun (fun (hoare_509422987triple state) bool) bool) ) 13.28/11.89 ( (fun pname bool), bool ) 13.28/11.89 ( (fun pname bool), (fun pname (option com)) ) 13.28/11.89 ( (fun pname bool), (fun pname bool) ) 13.28/11.89 ( (fun pname bool), (fun (fun pname bool) bool) ) 13.28/11.89 ( (fun (fun pname bool) bool), (fun (fun pname bool) bool) ) 13.28/11.89 ( (fun com bool), (fun com bool) ) 13.28/11.89 ) 13.28/11.89 (instantiation (let ((_let_0 (fun (hoare_509422987triple X_a) bool))) (let ((_let_1 (hAPP _let_0 (fun _let_0 bool) (hoare_122391849derivs X_a) G))) (forall ((X_a $$unsorted) (G $$unsorted) (G_2 $$unsorted) (Ts $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (hoare_122391849derivs X_a) G_2) Ts))) (not (hBOOL (hAPP _let_0 bool _let_1 G_2))) (hBOOL (hAPP _let_0 bool _let_1 Ts))) ))) 13.28/11.89 ( state, (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), fa ) 13.28/11.89 ( state, (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 13.28/11.89 ( state, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 13.28/11.89 ( state, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 13.28/11.89 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), fa ) 13.28/11.89 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 13.28/11.89 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 13.28/11.89 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), fa ) 13.28/11.89 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 13.28/11.89 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 13.28/11.89 ( state, skv_89, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 13.28/11.89 ( state, skv_90, (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 13.28/11.89 ) 13.28/11.89 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (Y_3 $$unsorted) (A_1 $$unsorted) (X_2 $$unsorted)) (= (hBOOL (hAPP X_a bool (hAPP _let_0 _let_0 (hAPP X_a (fun _let_0 _let_0) (insert X_a) Y_3) A_1) X_2)) (or (hBOOL (hAPP X_a bool A_1 X_2)) (= (ti X_a Y_3) (ti X_a X_2)))) )) 13.28/11.89 ( bool, skv_6, fNot, skv_6 ) 13.28/11.89 ( bool, skv_6, fNot, skv_50 ) 13.28/11.89 ( bool, skv_6, fNot, skv_78 ) 13.28/11.89 ( bool, skv_6, fNot, skv_84 ) 13.28/11.89 ( com, skv_5, wt, y ) 13.28/11.89 ( com, skv_5, wt, (hAPP pname com body_1 skv_3) ) 13.28/11.89 ( com, skv_5, wt, skv_5 ) 13.28/11.89 ( com, skv_5, wt, skv_36 ) 13.28/11.89 ( com, skv_5, wt, skv_83 ) 13.28/11.89 ( pname, skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn ) 13.28/11.89 ( pname, skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3 ) 13.28/11.89 ( pname, skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_96 ) 13.28/11.89 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 13.28/11.89 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)), skv_14 ) 13.28/11.89 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)), skv_19 ) 13.28/11.90 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)), skv_20 ) 13.28/11.90 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)), skv_21 ) 13.28/11.90 ( (hoare_509422987triple state), skv_7, fa, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 13.28/11.90 ( (hoare_509422987triple state), skv_7, fa, skv_4 ) 13.28/11.90 ( (hoare_509422987triple state), skv_7, fa, skv_7 ) 13.28/11.90 ( (hoare_509422987triple state), skv_7, fa, skv_40 ) 13.28/11.90 ( (hoare_509422987triple state), skv_7, fa, skv_42 ) 13.28/11.90 ( (hoare_509422987triple state), skv_7, fa, skv_81 ) 13.28/11.90 ( (hoare_509422987triple state), skv_7, fa, skv_100 ) 13.28/11.90 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), skv_14 ) 13.28/11.90 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 13.28/11.90 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), fa ) 13.28/11.90 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 13.28/11.90 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 13.28/11.90 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 13.28/11.90 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), skv_54 ) 13.28/11.90 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), skv_70 ) 13.28/11.90 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) skv_69) skv_70))) ) 13.28/11.90 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), skv_95 ) 13.28/11.90 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (fun 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(hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 13.28/11.90 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 13.28/11.90 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) fa))) ) 13.28/11.91 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), skv_64 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) skv_63) skv_64))) ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), skv_94 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)), fa ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 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_let_1 _let_1 (collect _let_0) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) (bot_bot _let_1))))) ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)), skv_64 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)), skv_70 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)), skv_72 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) skv_71) skv_72))) ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)), skv_74 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)), skv_76 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)), skv_95 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)), skv_99 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), skv_26 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), skv_27 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), skv_28 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), skv_29 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), skv_30 ) 13.28/11.92 ( (fun (hoare_509422987triple state) bool), fa, 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hoare_Mirabelle_MGT y)) (bot_bot _let_1))))) ) 13.64/12.17 ( (hAPP com bool wt y) ) 13.64/12.17 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (bot_bot _let_1))) (hAPP _let_1 bool (hAPP _let_1 (fun _let_1 bool) (hoare_122391849derivs state) _let_2) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) _let_2))))) ) 13.64/12.17 ( (let ((_let_0 (fun bool bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot) (bot_bot _let_0))) ) 13.64/12.17 ( (let ((_let_0 (fun com bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) wt) (bot_bot _let_0))) ) 13.64/12.17 ( (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa) (bot_bot _let_0))) ) 13.64/12.17 ( (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_4 bool (hAPP _let_4 (fun _let_4 bool) (hoare_122391849derivs state) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))) fa)))))))) ) 13.64/12.18 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (ord_less_eq _let_2) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 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skv_1) ) 13.64/12.18 ( (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_2) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 13.64/12.18 ( (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (hAPP pname (fun _let_0 bool) (member pname) skv_3) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 13.64/12.18 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_2)))))))) ) 13.64/12.18 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) skv_4) fa))) ) 13.64/12.18 ( (let ((_let_0 (fun com bool))) (hAPP _let_0 bool (hAPP com (fun _let_0 bool) (member com) skv_5) wt)) ) 13.64/12.18 ( skv_6 ) 13.64/12.18 ( (let ((_let_0 (fun bool bool))) (hAPP _let_0 bool (hAPP bool (fun _let_0 bool) (member bool) skv_6) fNot)) ) 13.64/12.18 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) skv_7) fa))) ) 13.64/12.18 ) 13.64/12.18 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (fun X_a bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B $$unsorted) (F $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_1 bool (finite_finite X_a) A_1))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 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13.64/12.18 ( pname, pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (combi pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.64/12.18 ( pname, pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (combi pname), (bot_bot (fun pname bool)) ) 13.64/12.18 ( pname, pname, (bot_bot (fun pname bool)), (combi pname), (bot_bot (fun pname bool)) ) 13.64/12.18 ( pname, pname, skv_1, (combi pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.64/12.18 ( pname, pname, skv_1, (combi pname), (bot_bot (fun pname bool)) ) 13.64/12.18 ( pname, pname, skv_2, (combi pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.64/12.18 ( pname, pname, skv_2, (combi pname), (bot_bot (fun pname bool)) ) 13.64/12.18 ( pname, pname, skv_45, (combi pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.64/12.18 ( pname, pname, skv_46, (combi pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.64/12.18 ( pname, pname, skv_86, (combi pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.64/12.18 ( pname, pname, skv_87, (combi pname), (bot_bot (fun pname bool)) ) 13.64/12.18 ( (hoare_509422987triple state), com, fa, hoare_Mirabelle_MGT, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 13.64/12.18 ( (hoare_509422987triple state), pname, (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com 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(fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (hAPP _let_2 _let_4 (hAPP (fun com _let_1) (fun _let_2 _let_4) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.64/12.18 ( (hoare_509422987triple state), pname, fa, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (hAPP _let_2 _let_4 (hAPP (fun com _let_1) (fun _let_2 _let_4) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))))))), skv_2 ) 13.64/12.18 ( (hoare_509422987triple state), pname, fa, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun 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(hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), skv_87 ) 13.64/12.18 ( (hoare_509422987triple state), pname, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (hAPP _let_2 _let_4 (hAPP (fun com _let_1) (fun _let_2 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(hoare_509422987triple state), pname, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))), skv_86 ) 13.64/12.18 ( (hoare_509422987triple state), pname, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 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13.64/12.19 (instantiation (let ((_let_0 (option X_a))) (let ((_let_1 (fun X_b bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (M $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted)) (or (not (= (hAPP X_a _let_0 (some X_a) B_1) (hAPP X_b _let_0 M A_3))) (hBOOL (hAPP _let_1 bool (hAPP X_b (fun _let_1 bool) (member X_b) A_3) (hAPP (fun X_b _let_0) _let_1 (dom X_b X_a) M)))) ))) 13.64/12.19 ( com, com, (some com), y, y ) 13.64/12.19 ( (option com), com, (combi (option com)), (hAPP com (option com) (some com) y), y ) 13.64/12.19 ( pname, com, body, pn, y ) 13.64/12.19 ( pname, com, body, pn, skv_77 ) 13.64/12.19 ) 13.64/12.19 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (= (hAPP _let_0 _let_0 (hAPP X_a (fun _let_0 _let_0) (insert X_a) A_3) (bot_bot _let_0)) (hAPP _let_0 _let_0 (collect X_a) (hAPP X_a _let_0 (fequal X_a) A_3))) )) 13.64/12.19 ( bool, fTrue ) 13.64/12.19 ( bool, fFalse ) 13.64/12.19 ( bool, skv_6 ) 13.64/12.19 ( bool, skv_67 ) 13.64/12.19 ( bool, skv_93 ) 13.64/12.19 ( bool, skv_102 ) 13.64/12.19 ( com, y ) 13.64/12.19 ( com, (hAPP pname com body_1 pn) ) 13.64/12.19 ( com, skv_5 ) 13.64/12.19 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))) ) 13.64/12.19 ( com, skv_65 ) 13.64/12.19 ( (fun bool bool), fNot ) 13.64/12.19 ( (fun bool bool), (bot_bot (fun bool bool)) ) 13.64/12.19 ( pname, pn ) 13.64/12.19 ( pname, skv_3 ) 13.64/12.19 ( pname, skv_61 ) 13.64/12.19 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 13.64/12.19 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)) ) 13.64/12.19 ( (hoare_509422987triple state), skv_4 ) 13.64/12.19 ( (hoare_509422987triple state), skv_7 ) 13.64/12.19 ( 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13.64/12.19 ) 13.64/12.19 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_b bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (H $$unsorted) (Fa $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_a) Fa))) (hBOOL (hAPP _let_1 bool (finite_finite X_b) (hAPP _let_0 _let_1 (hAPP (fun X_a X_b) (fun _let_0 _let_1) (image X_a X_b) H) Fa)))) ))) 13.64/12.19 ( bool, bool, (combi bool), fNot ) 13.64/12.19 ( bool, bool, (combi bool), (combi bool) ) 13.64/12.19 ( bool, bool, (combi bool), (bot_bot (fun bool bool)) ) 13.64/12.19 ( bool, bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fNot ) 13.64/12.19 ( bool, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) fa))), (bot_bot 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(combi (fun pname bool)), (finite_finite pname) ) 13.79/12.20 ( (fun (fun pname bool) bool), pname, (member pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.79/12.20 ) 13.79/12.20 (instantiation (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (hoare_122391849derivs state))) (let ((_let_5 (fun _let_2 _let_2))) (let ((_let_6 (insert _let_1))) (let ((_let_7 (hAPP _let_1 _let_5 _let_6 (hAPP com _let_1 hoare_Mirabelle_MGT (hAPP pname com body_1 Pn_1))))) (let ((_let_8 (bot_bot _let_2))) (forall ((Pn_1 $$unsorted) (G $$unsorted)) (or (not (hBOOL (hAPP _let_2 bool (hAPP _let_2 _let_3 _let_4 (hAPP _let_2 _let_2 _let_7 G)) (hAPP _let_2 _let_2 (hAPP _let_1 _let_5 _let_6 (hAPP com _let_1 hoare_Mirabelle_MGT (hAPP _let_0 com (the com) (hAPP pname _let_0 body Pn_1)))) _let_8)))) (hBOOL (hAPP _let_2 bool (hAPP _let_2 _let_3 _let_4 G) (hAPP _let_2 _let_2 _let_7 _let_8)))) )))))))))) 13.79/12.20 ( skv_3, (bot_bot (fun (hoare_509422987triple state) bool)) ) 13.79/12.20 ( skv_3, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 13.79/12.20 ( skv_3, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 13.79/12.20 ( skv_3, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 13.79/12.20 ( skv_55, (bot_bot (fun (hoare_509422987triple state) bool)) ) 13.79/12.20 ) 13.79/12.20 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) A_3) A_1))) (= (hAPP _let_0 _let_0 (hAPP X_a (fun _let_0 _let_0) (insert X_a) A_3) A_1) (ti _let_0 A_1))) )) 13.79/12.20 ( bool, fTrue, (combi bool) ) 13.79/12.20 ( bool, fTrue, (bot_bot (fun bool bool)) ) 13.79/12.20 ( bool, fTrue, (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun pname bool))) (let ((_let_2 (finite_finite pname))) (let ((_let_3 (fun _let_1 bool))) (hAPP _let_3 _let_0 (hAPP _let_3 (fun _let_3 _let_0) (image _let_1 bool) _let_2) _let_2))))) ) 13.79/12.20 ( bool, fTrue, (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_1))) (let ((_let_6 (hAPP _let_3 (fun _let_3 bool) (hoare_122391849derivs state) (hAPP _let_4 _let_3 (hAPP _let_5 (fun _let_4 _let_3) (image pname _let_1) (hAPP _let_2 _let_5 (hAPP (fun com _let_1) (fun _let_2 _let_5) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body))))) (hAPP (fun _let_3 bool) _let_0 (hAPP (fun _let_3 bool) (fun (fun _let_3 bool) _let_0) (image _let_3 bool) _let_6) _let_6)))))))) ) 13.79/12.20 ( bool, fTrue, (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun (hoare_509422987triple state) bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (finite_finite (hoare_509422987triple state)))) (hAPP _let_2 _let_0 (hAPP _let_2 (fun _let_2 _let_0) (image _let_1 bool) _let_3) _let_3))))) ) 13.79/12.20 ( bool, fFalse, (combi bool) ) 13.79/12.20 ( bool, fFalse, (bot_bot (fun bool bool)) ) 13.79/12.20 ( bool, fFalse, (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (hAPP _let_1 (fun (fun _let_1 bool) bool) (member _let_1) (hAPP com _let_1 hoare_Mirabelle_MGT y)))) (hAPP (fun (fun _let_1 bool) bool) _let_0 (hAPP (fun (fun _let_1 bool) bool) (fun (fun (fun _let_1 bool) bool) _let_0) (image (fun _let_1 bool) bool) _let_2) _let_2)))) ) 13.79/12.20 ( bool, fFalse, (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun (hoare_509422987triple state) bool))) (let ((_let_2 (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) fa))) (hAPP (fun _let_1 bool) _let_0 (hAPP (fun _let_1 bool) (fun (fun _let_1 bool) _let_0) (image _let_1 bool) _let_2) _let_2)))) ) 13.79/12.20 ( bool, fFalse, (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (hAPP _let_2 _let_0 (hAPP _let_2 (fun _let_2 _let_0) (image _let_1 bool) (hAPP _let_2 _let_2 (hAPP (fun _let_1 (fun _let_2 bool)) (fun _let_2 _let_2) (combc _let_1 _let_2 bool) (member _let_1)) fa)) (bot_bot _let_2))))) ) 13.79/12.20 ( bool, skv_6, fNot ) 13.79/12.20 ( bool, skv_6, (bot_bot (fun bool bool)) ) 13.79/12.20 ( bool, skv_49, fNot ) 13.79/12.20 ( bool, skv_49, (bot_bot (fun bool bool)) ) 13.79/12.20 ( bool, skv_51, fNot ) 13.79/12.20 ( bool, skv_52, (combi bool) ) 13.79/12.20 ( bool, skv_67, (bot_bot (fun bool bool)) ) 13.79/12.21 ( bool, skv_67, skv_68 ) 13.79/12.21 ( com, y, wt ) 13.79/12.21 ( com, y, (bot_bot (fun com bool)) ) 13.79/12.21 ( com, y, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 13.79/12.21 ( com, y, (hAPP (fun com (option com)) (fun com bool) (dom com com) (some com)) ) 13.79/12.21 ( com, (hAPP pname com body_1 pn), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun com bool))) (hAPP _let_0 _let_1 (hAPP (fun pname com) (fun _let_0 _let_1) (image pname com) body_1) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))) ) 13.79/12.21 ( com, skv_5, wt ) 13.79/12.21 ( com, skv_5, (bot_bot (fun com bool)) ) 13.79/12.21 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 13.79/12.21 ( com, skv_35, wt ) 13.79/12.21 ( com, skv_35, (bot_bot (fun com bool)) ) 13.79/12.21 ( com, skv_37, wt ) 13.79/12.21 ( com, skv_65, (bot_bot (fun com bool)) ) 13.79/12.21 ( com, skv_65, skv_66 ) 13.79/12.21 ( (option com), (hAPP com (option com) (some com) y), (let ((_let_0 (option com))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun _let_0 bool))) (hAPP _let_2 _let_3 (hAPP _let_1 (fun _let_2 _let_3) (image pname _let_0) body) (hAPP _let_1 _let_2 (dom pname com) body)))))) ) 13.79/12.21 ( (fun bool bool), fNot, (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6) ) 13.79/12.21 ( (fun bool bool), fNot, (bot_bot (fun (fun bool bool) bool)) ) 13.79/12.21 ( (fun bool bool), (bot_bot (fun bool bool)), (finite_finite bool) ) 13.79/12.21 ( (fun bool bool), (bot_bot (fun bool bool)), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)) ) 13.79/12.21 ( (fun bool bool), (bot_bot (fun bool bool)), (bot_bot (fun (fun bool bool) bool)) ) 13.79/12.21 ( pname, pn, (hAPP (fun 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state), skv_41, fa ) 13.79/12.23 ( (hoare_509422987triple state), skv_41, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 13.79/12.23 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_55)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 13.79/12.23 ( (hoare_509422987triple state), skv_58, fa ) 13.79/12.23 ( (hoare_509422987triple state), skv_58, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 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((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_1 _let_0))) (let ((_let_4 (fun _let_1 _let_2))) (hAPP _let_2 _let_2 (hAPP _let_3 (fun _let_2 _let_2) (combs _let_1 bool bool) (hAPP _let_2 _let_3 (hAPP (fun bool _let_0) (fun _let_2 _let_3) (combb bool _let_0 _let_1) fconj) (hAPP _let_1 _let_2 (hAPP _let_4 _let_4 (combc _let_1 _let_1 bool) (fequal _let_1)) (bot_bot _let_1)))) (hAPP _let_1 _let_2 (ord_less_eq _let_1) wt))))))) ) 13.92/12.29 ) 13.92/12.29 (instantiation (let ((_let_0 (fun X_a bool))) (forall ((X_a $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (= (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) B_1) (hAPP _let_0 _let_0 (hAPP X_a (fun _let_0 _let_0) (insert X_a) A_3) (bot_bot _let_0)))) (= (ti X_a A_3) (ti X_a B_1))) )) 13.92/12.29 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 13.92/12.29 ( (hoare_509422987triple state), (hAPP com 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13.92/12.29 ( (fun (hoare_509422987triple state) bool), fa, fa ) 13.92/12.29 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 13.92/12.29 ( (fun pname bool), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.92/12.29 ) 13.92/12.29 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_1))) (forall ((X_a $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 B))) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_a (fun _let_0 _let_0) (insert X_a) B_1) B)))) ))) 13.92/12.29 ( bool, skv_6, fNot, fNot ) 13.92/12.29 ( bool, skv_6, (bot_bot (fun bool bool)), fNot ) 13.92/12.29 ( com, skv_5, wt, wt ) 13.92/12.29 ( com, skv_5, (bot_bot (fun com bool)), wt ) 13.92/12.29 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), skv_24, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 13.92/12.29 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), skv_25, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 13.92/12.29 ( pname, pn, skv_1, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.92/12.29 ( pname, pn, skv_2, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.92/12.29 ( pname, skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.92/12.29 ( pname, skv_3, skv_1, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.92/12.29 ( pname, skv_3, skv_2, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.92/12.29 ( pname, skv_3, skv_45, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.92/12.29 ( pname, skv_3, skv_46, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.92/12.29 ( pname, skv_3, skv_86, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.92/12.29 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 13.92/12.30 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 13.92/12.30 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), fa, (bot_bot (fun (hoare_509422987triple state) bool)) ) 13.92/12.30 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), fa, fa ) 13.92/12.30 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), fa, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 13.92/12.30 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 13.92/12.30 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 13.92/12.30 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)), (bot_bot (fun (hoare_509422987triple state) bool)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 13.92/12.30 ( (hoare_509422987triple state), skv_7, (bot_bot (fun (hoare_509422987triple state) bool)), fa ) 13.92/12.30 ( (hoare_509422987triple state), skv_7, fa, fa ) 13.92/12.30 ( (hoare_509422987triple state), skv_7, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), fa ) 13.92/12.30 ( (hoare_509422987triple state), skv_7, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), fa ) 13.92/12.30 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 13.92/12.30 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), fa, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 13.95/12.30 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 13.95/12.30 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 13.95/12.30 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 13.95/12.30 ( (hoare_509422987triple state), skv_63, fa, skv_64 ) 13.95/12.30 ( (fun (hoare_509422987triple state) bool), fa, (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 13.95/12.30 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 13.95/12.30 ( (fun pname bool), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (bot_bot (fun (fun pname bool) bool)), (bot_bot (fun (fun pname bool) bool)) ) 13.95/12.30 ) 13.95/12.30 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (= (ti _let_0 B) (ti _let_0 A_1))) (and (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 A_1) B)) (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 B) A_1)))) )))) 13.95/12.30 ( bool, fNot, fNot ) 13.95/12.30 ( bool, fNot, (bot_bot (fun bool bool)) ) 13.95/12.30 ( bool, (combi bool), (bot_bot (fun bool bool)) ) 13.95/12.30 ( bool, (bot_bot (fun bool bool)), fNot ) 13.95/12.30 ( bool, (bot_bot (fun bool bool)), (combi bool) ) 13.95/12.30 ( bool, (bot_bot (fun bool bool)), (bot_bot (fun bool bool)) ) 13.95/12.30 ( com, wt, wt ) 13.95/12.30 ( com, wt, (bot_bot (fun com bool)) ) 13.95/12.30 ( com, (bot_bot (fun com bool)), wt ) 13.95/12.30 ( com, (bot_bot (fun com bool)), (bot_bot (fun com bool)) ) 13.95/12.30 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))), skv_24 ) 13.95/12.30 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))), skv_25 ) 13.95/12.30 ( com, skv_24, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 13.95/12.30 ( com, skv_25, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 13.95/12.30 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (bot_bot (fun pname bool)) ) 13.95/12.30 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP pname (fun _let_0 _let_0) (insert pname) pn) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 13.95/12.30 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_1 ) 13.95/12.30 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_2 ) 13.95/12.30 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_45 ) 13.95/12.30 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_46 ) 13.95/12.30 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_86 ) 13.95/12.30 ( pname, (bot_bot (fun pname bool)), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.95/12.30 ( pname, (bot_bot (fun pname bool)), (bot_bot (fun pname bool)) ) 13.95/12.30 ( pname, (bot_bot (fun pname bool)), skv_1 ) 13.95/12.30 ( pname, (bot_bot (fun pname bool)), skv_2 ) 13.95/12.30 ( pname, (bot_bot (fun pname bool)), skv_87 ) 13.95/12.30 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP pname (fun _let_0 _let_0) (insert pname) pn) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.95/12.30 ( pname, skv_1, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.95/12.30 ( pname, skv_1, (bot_bot (fun pname bool)) ) 13.95/12.30 ( pname, skv_1, skv_1 ) 13.95/12.30 ( pname, skv_2, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.95/12.30 ( pname, skv_2, (bot_bot (fun pname bool)) ) 13.95/12.30 ( pname, skv_2, skv_2 ) 13.95/12.30 ( pname, skv_2, skv_22 ) 13.95/12.30 ( pname, skv_2, skv_23 ) 13.95/12.30 ( pname, skv_2, skv_47 ) 13.95/12.30 ( pname, skv_2, skv_48 ) 13.95/12.30 ( pname, skv_22, skv_2 ) 13.95/12.30 ( pname, skv_23, skv_2 ) 13.95/12.30 ( pname, skv_45, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.95/12.30 ( pname, skv_46, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.95/12.30 ( pname, skv_47, skv_2 ) 13.95/12.30 ( pname, skv_48, skv_2 ) 13.95/12.30 ( pname, skv_86, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 13.95/12.30 ( pname, skv_87, (bot_bot (fun pname bool)) ) 13.95/12.30 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 13.95/12.30 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), fa ) 13.95/12.30 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let 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(let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (combi (fun (hoare_509422987triple state) bool)), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 14.12/12.42 ( (fun (hoare_509422987triple state) bool), (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), (combi (fun (hoare_509422987triple state) bool)), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 14.12/12.42 ( (fun (hoare_509422987triple state) bool), (fun (hoare_509422987triple state) bool), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), (combi (fun (hoare_509422987triple state) 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bool) bool)) ) 14.12/12.44 ( (fun com bool), (finite_finite com) ) 14.12/12.44 ( (fun com bool), (let ((_let_0 (fun com bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) wt)) ) 14.12/12.44 ( (fun com bool), (hAPP com (fun (fun com bool) bool) (member com) skv_5) ) 14.12/12.44 ( (fun com bool), (bot_bot (fun (fun com bool) bool)) ) 14.12/12.44 ) 14.12/12.44 (instantiation (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (insert _let_0))) (let ((_let_4 (bot_bot _let_1))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (hAPP _let_1 (fun _let_1 bool) (hoare_122391849derivs state) G))) (forall ((C_1 $$unsorted) (G $$unsorted)) (or (not (hBOOL (hAPP com bool wt C_1))) (not (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_5 bool (hAPP pname (fun _let_5 bool) (member pname) X_1) (hAPP (fun pname (option com)) _let_5 (dom pname com) body)))) (hBOOL (hAPP _let_1 bool _let_6 (hAPP _let_1 _let_1 (hAPP _let_0 _let_2 _let_3 (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 X_1))) _let_4)))) )) (hBOOL (hAPP _let_1 bool _let_6 (hAPP _let_1 _let_1 (hAPP _let_0 _let_2 _let_3 (hAPP com _let_0 hoare_Mirabelle_MGT C_1)) _let_4)))) )))))))) 14.12/12.44 ( y, (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.12/12.44 ( y, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.12/12.44 ( y, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 14.12/12.44 ( (hAPP pname com body_1 skv_3), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.12/12.44 ( (hAPP pname com body_1 skv_3), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.12/12.44 ( (let ((_let_0 (option com))) (hAPP _let_0 com (the com) (hAPP pname _let_0 body skv_3))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 14.12/12.44 ( (let ((_let_0 (option com))) (hAPP _let_0 com (the com) (hAPP pname _let_0 body skv_3))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 14.12/12.44 ( (hAPP pname com body_1 skv_55), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.12/12.44 ) 14.12/12.44 (instantiation (let ((_let_0 (hAPP X_a (fun (fun X_a bool) (fun X_a bool)) (insert X_a) X_2))) (let ((_let_1 (hAPP (fun X_a bool) (fun X_a bool) _let_0 A_1))) (forall ((X_a $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun X_a bool))) (= _let_1 (hAPP _let_0 _let_0 _let_0 _let_1))) ))) 14.12/12.44 ( bool, skv_6, fNot ) 14.12/12.44 ( com, y, (hAPP (fun com (option com)) (fun com bool) (dom com com) (some com)) ) 14.12/12.44 ( com, (hAPP pname com body_1 pn), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun com bool))) (hAPP _let_0 _let_1 (hAPP (fun pname com) (fun _let_0 _let_1) (image pname com) body_1) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))) ) 14.12/12.44 ( com, skv_5, wt ) 14.12/12.44 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 14.12/12.44 ( pname, pn, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.12/12.44 ( pname, skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.12/12.44 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.12/12.44 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.12/12.44 ( (hoare_509422987triple state), skv_4, fa ) 14.12/12.44 ( (hoare_509422987triple state), skv_7, fa ) 14.12/12.44 ( (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (hAPP pname _let_1 (hAPP _let_2 _let_4 (hAPP (fun com _let_1) (fun _let_2 _let_4) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) pn)))))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 14.12/12.44 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.12/12.44 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))) ) 14.12/12.44 ( (fun (hoare_509422987triple state) bool), fa, (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)) ) 14.12/12.44 ( (fun (hoare_509422987triple state) bool), fa, (finite_finite (hoare_509422987triple state)) ) 14.12/12.44 ( (fun (hoare_509422987triple state) bool), fa, (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 14.12/12.44 ( (fun pname bool), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (finite_finite pname) ) 14.12/12.44 ) 14.12/12.44 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (forall ((X_a $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite X_a) A_1))) (hBOOL (hAPP _let_0 bool (finite_finite _let_0) (hAPP _let_0 _let_0 (collect _let_0) (hAPP _let_0 _let_0 (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (ord_less_eq _let_0)) A_1)))))) ))) 14.12/12.44 ( bool, (bot_bot (fun bool bool)) ) 14.12/12.44 ( com, (bot_bot (fun com bool)) ) 14.12/12.44 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.12/12.44 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.12/12.44 ( (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 14.12/12.44 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.12/12.44 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 14.12/12.44 ) 14.12/12.44 (instantiation (let ((_let_0 (hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= _let_0 (ti X_c _let_0)) )) 14.12/12.44 ( bool, bool, fNot, skv_6 ) 14.12/12.44 ( bool, bool, fNot, skv_50 ) 14.12/12.44 ( bool, bool, fNot, skv_78 ) 14.12/12.44 ( bool, bool, fNot, skv_84 ) 14.12/12.44 ( bool, bool, (combi bool), fTrue ) 14.12/12.44 ( bool, bool, (combi bool), fFalse ) 14.12/12.44 ( bool, bool, (combi bool), skv_51 ) 14.12/12.44 ( bool, bool, (combi bool), skv_78 ) 14.12/12.44 ( bool, bool, (combi bool), skv_92 ) 14.12/12.44 ( bool, bool, (bot_bot (fun bool bool)), skv_50 ) 14.12/12.44 ( bool, bool, (bot_bot (fun bool bool)), skv_92 ) 14.12/12.44 ( bool, bool, (let ((_let_0 (fun bool bool))) (hAPP _let_0 _let_0 (hAPP (fun bool (fun _let_0 bool)) (fun _let_0 _let_0) (combc bool _let_0 bool) (member bool)) fNot)), skv_6 ) 14.12/12.44 ( bool, bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fTrue ) 14.12/12.44 ( bool, bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fFalse ) 14.12/12.44 ( bool, com, wt, y ) 14.12/12.44 ( bool, com, wt, (hAPP pname com body_1 skv_3) ) 14.12/12.44 ( bool, com, wt, skv_5 ) 14.12/12.44 ( bool, com, wt, skv_36 ) 14.12/12.44 ( bool, com, wt, skv_83 ) 14.12/12.44 ( bool, com, (bot_bot (fun com bool)), skv_36 ) 14.12/12.44 ( bool, com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun com bool))) (let ((_let_4 (fun com _let_2))) (hAPP (fun _let_0 bool) _let_3 (hAPP _let_4 (fun (fun _let_0 bool) _let_3) (combc com (fun _let_0 bool) bool) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_4) (combb _let_0 _let_2 com) (member _let_0)) hoare_Mirabelle_MGT)) fa)))))), y ) 14.12/12.45 ( bool, com, (let ((_let_0 (fun com bool))) (hAPP _let_0 _let_0 (hAPP (fun com (fun _let_0 bool)) (fun _let_0 _let_0) (combc com _let_0 bool) (member com)) wt)), skv_5 ) 14.12/12.45 ( bool, com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun com bool))) (hAPP _let_1 _let_3 (hAPP _let_2 (fun _let_1 _let_3) (combb _let_0 bool com) (hAPP _let_2 _let_2 (hAPP (fun _let_0 (fun _let_2 bool)) (fun _let_2 _let_2) (combc _let_0 _let_2 bool) (member _let_0)) fa)) hoare_Mirabelle_MGT))))), y ) 14.12/12.45 ( bool, com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun com bool))) (hAPP _let_1 _let_2 (hAPP (fun _let_0 bool) (fun _let_1 _let_2) (combb _let_0 bool com) fa) hoare_Mirabelle_MGT)))), y ) 14.12/12.45 ( bool, com, (let ((_let_0 (fun com bool))) (let ((_let_1 (fun com com))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb com bool com) wt) (combi com)))), y ) 14.12/12.45 ( bool, (fun bool bool), (finite_finite bool), fNot ) 14.12/12.45 ( bool, (fun bool bool), (finite_finite bool), (bot_bot (fun bool bool)) ) 14.12/12.45 ( bool, (fun bool bool), (finite_finite bool), skv_68 ) 14.12/12.45 ( bool, (fun bool bool), (finite_finite bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 _let_0 (hAPP bool (fun _let_0 _let_0) (insert bool) skv_67) skv_68)) ) 14.12/12.45 ( bool, (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), fNot ) 14.12/12.45 ( bool, (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), (bot_bot (fun bool bool)) ) 14.12/12.45 ( bool, (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6), fNot ) 14.12/12.45 ( bool, (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6), (bot_bot (fun bool bool)) ) 14.12/12.45 ( bool, (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (ord_less_eq _let_0)) (bot_bot _let_0)))), fNot ) 14.12/12.45 ( bool, (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb _let_0 bool _let_0) (finite_finite bool)) (collect bool))))), (hAPP bool (fun bool bool) (combk bool bool) fFalse) ) 14.12/12.45 ( bool, (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb _let_0 bool _let_0) (hAPP _let_0 _let_1 (ord_less_eq _let_0) fNot)) (collect bool))))), (hAPP bool (fun bool bool) (combk bool bool) fFalse) ) 14.12/12.45 ( bool, (fun bool bool), (let ((_let_0 (fun (fun bool bool) bool))) (let ((_let_1 (fun (fun bool bool) (fun bool bool)))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb (fun bool bool) bool (fun bool bool)) (hAPP bool _let_0 (member bool) skv_6)) (hAPP (fun bool bool) _let_1 (image bool bool) (combi bool))))), fNot ) 14.12/12.45 ( bool, (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), fNot ) 14.12/12.45 ( bool, (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), (bot_bot (fun bool bool)) ) 14.12/12.45 ( bool, (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) fTrue), (combi bool) ) 14.12/12.45 ( bool, (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) fTrue), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun pname bool))) (let ((_let_2 (finite_finite pname))) (let ((_let_3 (fun _let_1 bool))) (hAPP _let_3 _let_0 (hAPP _let_3 (fun _let_3 _let_0) (image _let_1 bool) _let_2) _let_2))))) ) 14.12/12.45 ( bool, (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) fFalse), (combi bool) ) 14.12/12.45 ( bool, (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) fFalse), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (hAPP _let_1 (fun (fun _let_1 bool) bool) (member _let_1) (hAPP com _let_1 hoare_Mirabelle_MGT y)))) (hAPP (fun (fun _let_1 bool) bool) _let_0 (hAPP (fun (fun _let_1 bool) bool) (fun (fun (fun _let_1 bool) bool) _let_0) (image (fun _let_1 bool) bool) _let_2) _let_2)))) ) 14.12/12.45 ( bool, 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_let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_1))) (let ((_let_6 (hAPP _let_3 (fun _let_3 bool) (hoare_122391849derivs state) (hAPP _let_4 _let_3 (hAPP _let_5 (fun _let_4 _let_3) (image pname _let_1) (hAPP _let_2 _let_5 (hAPP (fun com _let_1) (fun _let_2 _let_5) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body))))) (hAPP (fun _let_3 bool) _let_0 (hAPP (fun _let_3 bool) (fun (fun _let_3 bool) _let_0) (image _let_3 bool) _let_6) _let_6)))))))) ) 14.12/12.45 ( bool, 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((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP bool (fun (fun bool bool) bool) (member bool) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2))))))))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (hAPP _let_2 _let_0 (hAPP _let_2 (fun _let_2 _let_0) (image _let_1 bool) (hAPP _let_2 _let_2 (hAPP (fun _let_1 (fun _let_2 bool)) (fun _let_2 _let_2) (combc _let_1 _let_2 bool) (member _let_1)) fa)) (bot_bot _let_2))))) ) 14.12/12.45 ( bool, (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (combi bool))), (bot_bot (fun bool bool)) ) 14.12/12.45 ( bool, (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_49), fNot ) 14.12/12.45 ( bool, (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_49), (bot_bot (fun bool bool)) ) 14.12/12.45 ( bool, (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_51), fNot ) 14.12/12.45 ( bool, (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_52), (combi bool) ) 14.12/12.45 ( bool, (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_67), (bot_bot (fun bool bool)) ) 14.12/12.45 ( bool, (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_67), skv_68 ) 14.12/12.45 ( bool, pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn ) 14.12/12.45 ( bool, pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3 ) 14.12/12.45 ( bool, pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_96 ) 14.12/12.45 ( bool, pname, (bot_bot (fun pname bool)), skv_96 ) 14.12/12.45 ( bool, pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), pn ) 14.12/12.45 ( bool, pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), skv_3 ) 14.12/12.45 ( bool, (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 14.12/12.45 ( bool, (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), skv_40 ) 14.12/12.45 ( bool, 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com)))))), body ) 14.12/12.45 ( bool, (fun pname (option com)), (let ((_let_0 (fun pname (option com)))) (let ((_let_1 (fun pname bool))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_0 bool))) (let ((_let_4 (fun _let_0 _let_0))) (hAPP _let_4 _let_3 (hAPP _let_3 (fun _let_4 _let_3) (combb _let_0 bool _let_0) (hAPP _let_2 _let_3 (hAPP (fun _let_1 bool) (fun _let_2 _let_3) (combb _let_1 bool _let_0) (finite_finite pname)) (dom pname com))) (combi _let_0))))))), body ) 14.12/12.45 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.12/12.46 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), fa ) 14.12/12.46 ( bool, (fun 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(fun _let_1 _let_1) (insert _let_0) skv_69) skv_70))) ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), skv_95 ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), fa ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite 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(hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) fa))) ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (collect _let_0) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) (bot_bot _let_1))))) ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), skv_64 ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), skv_70 ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), skv_72 ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) skv_71) skv_72))) ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), skv_74 ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), skv_76 ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), skv_95 ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (finite_finite (hoare_509422987triple state)), skv_99 ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), skv_94 ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (option com))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun (hoare_509422987triple state) bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun pname (hoare_509422987triple state)))) (let ((_let_8 (fun _let_4 _let_1))) (hAPP _let_5 _let_5 (hAPP _let_8 (fun _let_5 _let_5) (combs _let_4 bool bool) (hAPP _let_5 _let_8 (hAPP (fun bool _let_1) (fun _let_5 _let_8) (combb bool _let_1 _let_4) fconj) (hAPP _let_4 _let_5 (fequal _let_4) (hAPP _let_6 _let_4 (hAPP _let_7 (fun _let_6 _let_4) (image pname (hoare_509422987triple state)) (hAPP _let_2 _let_7 (hAPP (fun com (hoare_509422987triple state)) (fun _let_2 _let_7) (combb com (hoare_509422987triple state) pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_6 (dom pname com) body))))) (hAPP _let_4 _let_5 (ord_less_eq _let_4) fa))))))))))), skv_31 ) 14.12/12.48 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (fun _let_3 _let_0))) (hAPP _let_4 _let_4 (hAPP _let_7 (fun _let_4 _let_4) (combs _let_3 bool bool) (hAPP _let_4 _let_7 (hAPP (fun bool _let_0) (fun _let_4 _let_7) (combb bool _let_0 _let_3) fconj) (hAPP _let_3 _let_4 (fequal _let_3) fa))) (hAPP _let_3 _let_4 (hoare_122391849derivs state) (hAPP _let_5 _let_3 (hAPP _let_6 (fun _let_5 _let_3) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_5 (dom pname com) body)))))))))))), skv_29 ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun _let_2 _let_0))) (hAPP _let_3 _let_3 (hAPP _let_4 (fun _let_3 _let_3) (combs _let_2 bool bool) (hAPP _let_3 _let_4 (hAPP (fun bool _let_0) (fun _let_3 _let_4) (combb bool _let_0 _let_2) fconj) (hAPP _let_2 _let_3 (fequal _let_2) fa))) (finite_finite _let_1))))))), skv_26 ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (fun _let_4 (fun _let_4 bool)))) (hAPP _let_4 (fun _let_4 bool) (hAPP _let_7 _let_7 (combc _let_4 _let_4 bool) (ord_less_eq _let_4)) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))))), fa ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 (fun _let_1 bool)))) (hAPP _let_1 (fun _let_1 bool) (hAPP _let_2 _let_2 (combc _let_1 _let_1 bool) (hoare_122391849derivs state)) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 (fun _let_1 bool)))) (hAPP _let_1 (fun _let_1 bool) (hAPP _let_2 _let_2 (combc _let_1 _let_1 bool) (hoare_122391849derivs state)) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (hoare_122391849derivs state)) fa))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (hoare_122391849derivs state)) fa))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun (fun _let_0 bool) (fun _let_0 bool)))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_2 (fun _let_3 _let_2) (combb (fun _let_0 bool) bool (fun _let_0 bool)) (hAPP (fun _let_0 bool) _let_2 (hoare_122391849derivs state) (hAPP _let_4 (fun _let_0 bool) (hAPP _let_5 (fun _let_4 (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))) (hAPP _let_0 _let_3 (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))))))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun (fun _let_0 bool) (fun _let_0 bool)))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_2 (fun _let_3 _let_2) (combb (fun _let_0 bool) bool (fun _let_0 bool)) (hAPP (fun _let_0 bool) _let_2 (hoare_122391849derivs state) (hAPP _let_4 (fun _let_0 bool) (hAPP _let_5 (fun _let_4 (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))) (hAPP _let_0 _let_3 (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))))))))), fa ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun (fun _let_0 bool) (fun _let_0 bool)))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_2 (fun _let_3 _let_2) (combb (fun _let_0 bool) bool (fun _let_0 bool)) (hAPP (fun _let_0 bool) _let_2 (hoare_122391849derivs state) (hAPP _let_4 (fun _let_0 bool) (hAPP _let_5 (fun _let_4 (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))) (hAPP _let_0 _let_3 (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))))))))), skv_76 ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun (fun _let_0 bool) (fun _let_0 bool)))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_2 (fun _let_3 _let_2) (combb (fun _let_0 bool) bool (fun _let_0 bool)) (hAPP (fun 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pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body)))))))))), fa ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), fa ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_4 (fun _let_4 bool) (hoare_122391849derivs state) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body)))))))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.12/12.49 ( bool, (fun 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((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (option com))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun (hoare_509422987triple state) bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun pname (hoare_509422987triple state)))) (let ((_let_8 (fun _let_4 _let_1))) (let ((_let_9 (fun _let_4 _let_5))) (hAPP _let_5 _let_5 (hAPP _let_8 (fun _let_5 _let_5) (combs _let_4 bool bool) (hAPP _let_5 _let_8 (hAPP (fun bool _let_1) (fun _let_5 _let_8) (combb bool _let_1 _let_4) fconj) (hAPP _let_4 _let_5 (hAPP _let_9 _let_9 (combc _let_4 _let_4 bool) (fequal _let_4)) (hAPP _let_6 _let_4 (hAPP _let_7 (fun _let_6 _let_4) (image pname (hoare_509422987triple state)) (hAPP _let_2 _let_7 (hAPP (fun com (hoare_509422987triple state)) (fun _let_2 _let_7) (combb com (hoare_509422987triple state) pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_6 (dom pname com) body))))) (hAPP _let_4 _let_5 (ord_less_eq _let_4) fa)))))))))))), skv_30 ) 14.12/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (fun _let_3 _let_0))) (let ((_let_8 (fun _let_3 _let_4))) (hAPP _let_4 _let_4 (hAPP _let_7 (fun _let_4 _let_4) (combs _let_3 bool bool) (hAPP _let_4 _let_7 (hAPP (fun bool _let_0) (fun _let_4 _let_7) (combb bool _let_0 _let_3) fconj) (hAPP _let_3 _let_4 (hAPP _let_8 _let_8 (combc _let_3 _let_3 bool) (fequal _let_3)) fa))) (hAPP _let_3 _let_4 (hoare_122391849derivs state) (hAPP _let_5 _let_3 (hAPP _let_6 (fun _let_5 _let_3) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_5 (dom pname com) body))))))))))))), skv_28 ) 14.25/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_2 (fun _let_2 bool)))) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_3 (fun (fun _let_2 bool) (fun _let_2 bool)) (combs _let_2 bool bool) (hAPP (fun _let_2 bool) _let_3 (hAPP (fun bool _let_0) (fun (fun _let_2 bool) _let_3) (combb bool _let_0 _let_2) fconj) (hAPP _let_2 (fun _let_2 bool) (hAPP _let_4 _let_4 (combc _let_2 _let_2 bool) (fequal _let_2)) fa))) (finite_finite _let_1))))))), skv_27 ) 14.25/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_4)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.25/12.49 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple 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_let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 14.25/12.50 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_7)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 14.25/12.50 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun _let_0 (fun _let_1 bool)))) (hAPP _let_0 (fun _let_1 bool) (hAPP _let_2 _let_3 (combc _let_1 _let_0 bool) (hAPP _let_3 _let_2 (combc _let_0 _let_1 bool) (member _let_0))) (hAPP com _let_0 hoare_Mirabelle_MGT y)))))), fa ) 14.25/12.50 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (let ((_let_2 (combc _let_0 _let_0 bool))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 _let_2 (hAPP _let_1 _let_1 _let_2 (ord_less_eq _let_0))) fa)))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 14.25/12.50 ( bool, (fun 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(hoare_122391849derivs state)) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.25/12.50 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (hoare_122391849derivs 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(hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 14.25/12.50 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 (fun _let_1 bool)))) (hAPP _let_1 (fun _let_1 bool) (hAPP _let_2 _let_2 (combc _let_1 _let_1 bool) (hoare_122391849derivs state)) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.25/12.50 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun _let_2 _let_2))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_0))) (hAPP _let_4 _let_3 (hAPP _let_3 (fun _let_4 _let_3) (combb _let_2 bool _let_2) (hAPP _let_2 _let_3 (hoare_122391849derivs state) (hAPP _let_5 _let_2 (hAPP _let_6 (fun _let_5 _let_2) (image pname _let_0) (hAPP _let_1 _let_6 (hAPP (fun com _let_0) (fun _let_1 _let_6) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP 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com) body)))) (collect _let_0))))))))), (let ((_let_0 (hoare_509422987triple state))) (hAPP bool (fun _let_0 bool) (combk bool _let_0) fFalse)) ) 14.25/12.50 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun (fun _let_0 bool) (fun _let_0 bool)))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (let ((_let_6 (fun _let_3 _let_2))) (let ((_let_7 (combb (fun _let_0 bool) bool (fun _let_0 bool)))) (hAPP _let_3 _let_2 (hAPP _let_2 _let_6 _let_7 (hAPP _let_3 _let_2 (hAPP _let_2 _let_6 _let_7 (hAPP (fun _let_0 bool) _let_2 (hoare_122391849derivs state) (hAPP _let_4 (fun _let_0 bool) (hAPP _let_5 (fun _let_4 (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))) (hAPP 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(finite_finite _let_0)) (collect _let_0)))))), (let ((_let_0 (hoare_509422987triple state))) (hAPP bool (fun _let_0 bool) (combk bool _let_0) fFalse)) ) 14.25/12.50 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun (fun _let_0 bool) bool))) (let ((_let_2 (fun (fun _let_0 bool) (fun _let_0 bool)))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb (fun _let_0 bool) bool (fun _let_0 bool)) (finite_finite _let_0)) (hAPP _let_0 _let_2 (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.25/12.50 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun (fun _let_0 bool) bool))) (let ((_let_2 (fun (fun _let_0 bool) (fun _let_0 bool)))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb (fun _let_0 bool) bool (fun _let_0 bool)) (hAPP (fun _let_0 bool) _let_1 (ord_less_eq (fun _let_0 bool)) (bot_bot (fun _let_0 bool)))) (hAPP _let_0 _let_2 (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.25/12.50 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun pname _let_1))) (let ((_let_8 (fun _let_4 _let_5))) (let ((_let_9 (fun _let_5 bool))) (hAPP _let_8 _let_5 (hAPP _let_9 (fun _let_8 _let_5) (combb _let_5 bool _let_4) (hAPP _let_4 _let_9 (member _let_4) (hAPP _let_6 _let_4 (hAPP _let_7 (fun _let_6 _let_4) (image pname _let_1) (hAPP _let_2 _let_7 (hAPP (fun com _let_1) (fun _let_2 _let_7) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_6 (dom pname com) body)))) (ord_less_eq _let_4)))))))))))), fa ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_1))) (let ((_let_3 (fun _let_1 bool))) (hAPP _let_2 _let_1 (hAPP _let_3 (fun _let_2 _let_1) (combb _let_1 bool _let_0) (hAPP _let_0 _let_3 (member _let_0) fa)) (hoare_122391849derivs state)))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let 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(let ((_let_1 (fun pname com))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun (fun _let_0 bool) (fun _let_0 bool)))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_2 (fun _let_3 _let_2) (combb (fun _let_0 bool) bool (fun _let_0 bool)) (hAPP (fun _let_0 bool) _let_2 (hoare_122391849derivs state) (hAPP _let_4 (fun _let_0 bool) (hAPP _let_5 (fun _let_4 (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))) (hAPP _let_0 _let_3 (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)))))))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (ord_less_eq _let_2) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (ord_less_eq _let_2) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), fa ) 14.25/12.51 ( bool, 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(insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1))))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (hAPP _let_2 _let_2 (hAPP _let_1 (fun _let_2 _let_2) (insert _let_1) (hAPP com _let_1 hoare_Mirabelle_MGT (hAPP _let_0 com (the com) (hAPP pname _let_0 body skv_3)))) (bot_bot _let_2))))) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com 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(fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 (fun _let_1 bool) (hoare_122391849derivs state) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 (fun _let_1 bool) (hoare_122391849derivs state) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1))))), fa ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 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_let_1 (hAPP (fun (fun _let_0 bool) _let_1) (fun _let_2 _let_1) (combs (fun _let_0 bool) (fun _let_0 bool) bool) (hoare_122391849derivs state)) (hAPP _let_0 _let_2 (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun (fun _let_0 bool) bool))) (let ((_let_2 (fun (fun _let_0 bool) (fun _let_0 bool)))) (hAPP _let_2 _let_1 (hAPP (fun (fun _let_0 bool) _let_1) (fun _let_2 _let_1) (combs (fun _let_0 bool) (fun _let_0 bool) bool) (ord_less_eq (fun _let_0 bool))) (hAPP (fun _let_0 _let_0) _let_2 (image _let_0 _let_0) (combi _let_0)))))), fa ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_11)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 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_let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_33)), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_34)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_39)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_39)), fa ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_41)), fa ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_41)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_58)), fa ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_58)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_59)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 14.25/12.51 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) skv_59)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 14.25/12.52 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 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(hAPP com _let_0 hoare_Mirabelle_MGT y))))))))) ) 14.25/12.55 ( bool, (fun (fun (hoare_509422987triple state) bool) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun (fun _let_2 bool) bool) (member _let_2) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)) ) 14.25/12.55 ( bool, (fun (fun (hoare_509422987triple state) bool) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP 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bool))) (let ((_let_7 (fun _let_6 bool))) (let ((_let_8 (fun pname _let_1))) (let ((_let_9 (fun _let_6 _let_4))) (hAPP _let_9 _let_7 (hAPP _let_5 (fun _let_9 _let_7) (combb _let_4 bool _let_6) (hAPP _let_4 _let_5 (ord_less_eq _let_4) fa)) (hAPP _let_8 _let_9 (image pname _let_1) (hAPP _let_2 _let_8 (hAPP (fun com _let_1) (fun _let_2 _let_8) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)))))))))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.55 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.55 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn), (bot_bot (fun pname bool)) ) 14.25/12.55 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn), skv_1 ) 14.25/12.55 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) pn), skv_2 ) 14.25/12.55 ( bool, (fun pname bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun pname bool))) (let ((_let_2 (fun _let_1 _let_0))) (let ((_let_3 (fun _let_1 (fun _let_1 bool)))) (hAPP (fun _let_1 bool) (fun _let_1 bool) (hAPP _let_2 (fun (fun _let_1 bool) (fun _let_1 bool)) (combs _let_1 bool bool) (hAPP (fun _let_1 bool) _let_2 (hAPP (fun bool _let_0) (fun (fun _let_1 bool) _let_2) (combb bool _let_0 _let_1) fconj) (hAPP _let_1 (fun _let_1 bool) (hAPP _let_3 _let_3 (combc _let_1 _let_1 bool) (fequal _let_1)) (hAPP (fun pname (option com)) _let_1 (dom pname com) body)))) (finite_finite pname)))))), skv_32 ) 14.25/12.55 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_1)), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.55 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_1)), (bot_bot (fun pname bool)) ) 14.25/12.55 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_1)), skv_1 ) 14.25/12.55 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_2)), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.55 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_2)), (bot_bot (fun pname bool)) ) 14.25/12.55 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_2)), skv_2 ) 14.25/12.55 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_3), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.55 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_3), (bot_bot (fun pname bool)) ) 14.25/12.55 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_3), skv_2 ) 14.25/12.55 ( bool, (fun pname bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname _let_0))) (let ((_let_7 (fun _let_4 _let_2))) (let ((_let_8 (fun _let_4 _let_3))) (hAPP _let_2 _let_5 (hAPP _let_8 (fun _let_2 _let_5) (combc _let_4 _let_2 bool) (hAPP _let_7 _let_8 (hAPP (fun _let_2 _let_3) (fun _let_7 _let_8) (combb _let_2 _let_3 _let_4) (hoare_122391849derivs state)) (hAPP _let_6 _let_7 (image pname _let_0) (hAPP _let_1 _let_6 (hAPP (fun com _let_0) (fun _let_1 _let_6) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2)))))))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.55 ( bool, (fun pname bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname _let_0))) (let ((_let_7 (fun _let_4 _let_2))) (let ((_let_8 (fun _let_4 _let_3))) (hAPP _let_2 _let_5 (hAPP _let_8 (fun _let_2 _let_5) (combc _let_4 _let_2 bool) (hAPP _let_7 _let_8 (hAPP (fun _let_2 _let_3) (fun _let_7 _let_8) (combb _let_2 _let_3 _let_4) (hoare_122391849derivs state)) (hAPP _let_6 _let_7 (image pname _let_0) (hAPP _let_1 _let_6 (hAPP (fun com _let_0) (fun _let_1 _let_6) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))) fa)))))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) (finite_finite pname)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (fun _let_4 (fun _let_1 bool)))) (hAPP _let_1 _let_5 (hAPP _let_7 (fun _let_1 _let_5) (combc _let_4 _let_1 bool) (hAPP _let_6 _let_7 (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)))) (hAPP com _let_1 hoare_Mirabelle_MGT y)))))))))), skv_2 ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (ord_less_eq _let_0)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))), skv_1 ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (ord_less_eq _let_0)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))), skv_2 ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (fun (fun pname bool) bool))) (let ((_let_1 (fun (fun pname bool) (fun pname bool)))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb (fun pname bool) bool (fun pname bool)) (finite_finite pname)) (hAPP pname _let_1 (insert pname) pn)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun _let_6 bool))) (let ((_let_8 (fun pname _let_1))) (let ((_let_9 (fun _let_6 _let_4))) (hAPP _let_9 _let_7 (hAPP _let_5 (fun _let_9 _let_7) (combb _let_4 bool _let_6) (hAPP _let_1 _let_5 (member _let_1) (hAPP com _let_1 hoare_Mirabelle_MGT y))) (hAPP _let_8 _let_9 (image pname _let_1) (hAPP _let_2 _let_8 (hAPP (fun com _let_1) (fun _let_2 _let_8) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)))))))))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun _let_6 bool))) (let ((_let_8 (fun pname _let_1))) (let ((_let_9 (fun _let_6 _let_4))) (hAPP _let_9 _let_7 (hAPP _let_5 (fun _let_9 _let_7) (combb _let_4 bool _let_6) (hAPP _let_1 _let_5 (member _let_1) (hAPP com _let_1 hoare_Mirabelle_MGT y))) (hAPP _let_8 _let_9 (image pname _let_1) (hAPP _let_2 _let_8 (hAPP (fun com _let_1) (fun _let_2 _let_8) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)))))))))))))), skv_2 ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun _let_5 bool))) (let ((_let_7 (fun pname _let_1))) (let ((_let_8 (fun _let_5 _let_4))) (hAPP _let_8 _let_6 (hAPP (fun _let_4 bool) (fun _let_8 _let_6) (combb _let_4 bool _let_5) (finite_finite _let_1)) (hAPP _let_7 _let_8 (image pname _let_1) (hAPP _let_2 _let_7 (hAPP (fun com _let_1) (fun _let_2 _let_7) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))))))))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun _let_5 bool))) (let ((_let_7 (fun pname _let_1))) (let ((_let_8 (fun _let_5 _let_4))) (hAPP _let_8 _let_6 (hAPP (fun _let_4 bool) (fun _let_8 _let_6) (combb _let_4 bool _let_5) (finite_finite _let_1)) (hAPP _let_7 _let_8 (image pname _let_1) (hAPP _let_2 _let_7 (hAPP (fun com _let_1) (fun _let_2 _let_7) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))))))))))))), skv_2 ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun (fun _let_1 bool) bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun _let_5 bool))) (let ((_let_7 (fun pname _let_1))) (let ((_let_8 (fun _let_5 (fun _let_1 bool)))) (let ((_let_9 (image pname _let_1))) (let ((_let_10 (hAPP (fun com _let_1) (fun _let_2 _let_7) (combb com _let_1 pname) hoare_Mirabelle_MGT))) (hAPP _let_8 _let_6 (hAPP _let_4 (fun _let_8 _let_6) (combb (fun _let_1 bool) bool _let_5) (hAPP (fun _let_1 bool) _let_4 (hoare_122391849derivs state) (hAPP _let_5 (fun _let_1 bool) (hAPP _let_7 _let_8 _let_9 (hAPP _let_2 _let_7 _let_10 body_1)) (hAPP _let_3 _let_5 (dom pname com) body)))) (hAPP _let_7 _let_8 _let_9 (hAPP _let_2 _let_7 _let_10 (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))))))))))))))), skv_2 ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (hAPP _let_6 (fun _let_4 (fun _let_1 bool)) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))))) (let ((_let_8 (fun (fun _let_1 bool) (fun (fun _let_1 bool) bool)))) (hAPP (fun _let_4 (fun _let_1 bool)) _let_5 (hAPP (fun (fun _let_1 bool) bool) (fun (fun _let_4 (fun _let_1 bool)) _let_5) (combb (fun _let_1 bool) bool _let_4) (hAPP (fun _let_1 bool) (fun (fun _let_1 bool) bool) (hAPP _let_8 _let_8 (combc (fun _let_1 bool) (fun _let_1 bool) bool) (ord_less_eq (fun _let_1 bool))) (hAPP _let_4 (fun _let_1 bool) _let_7 (hAPP _let_3 _let_4 (dom pname com) body)))) _let_7)))))))))), skv_2 ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname _let_0))) (let ((_let_6 (fun _let_3 _let_2))) (let ((_let_7 (fun _let_2 (fun _let_2 bool)))) (hAPP _let_6 _let_4 (hAPP (fun _let_2 bool) (fun _let_6 _let_4) (combb _let_2 bool _let_3) (hAPP _let_2 (fun _let_2 bool) (hAPP _let_7 _let_7 (combc _let_2 _let_2 bool) (hoare_122391849derivs state)) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2)))) (hAPP _let_5 _let_6 (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1))))))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname _let_0))) (let ((_let_6 (fun _let_3 _let_2))) (let ((_let_7 (fun _let_2 (fun _let_2 bool)))) (hAPP _let_6 _let_4 (hAPP (fun _let_2 bool) (fun _let_6 _let_4) (combb _let_2 bool _let_3) (hAPP _let_2 (fun _let_2 bool) (hAPP _let_7 _let_7 (combc _let_2 _let_2 bool) (hoare_122391849derivs state)) fa)) (hAPP _let_5 _let_6 (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1))))))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun (fun pname bool) bool))) (let ((_let_7 (fun pname _let_1))) (let ((_let_8 (fun (fun pname bool) _let_4))) (let ((_let_9 (fun (fun pname bool) (fun pname bool)))) (hAPP _let_9 _let_6 (hAPP _let_6 (fun _let_9 _let_6) (combb (fun pname bool) bool (fun pname bool)) (hAPP _let_8 _let_6 (hAPP _let_5 (fun _let_8 _let_6) (combb _let_4 bool (fun pname bool)) (hAPP _let_4 _let_5 (ord_less_eq _let_4) fa)) (hAPP _let_7 _let_8 (image pname _let_1) (hAPP _let_2 _let_7 (hAPP (fun com _let_1) (fun _let_2 _let_7) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))))) (hAPP pname _let_9 (insert pname) pn)))))))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname _let_0))) (let ((_let_6 (hAPP _let_5 (fun _let_3 (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))) (hAPP (fun _let_3 (fun _let_0 bool)) _let_4 (hAPP _let_2 (fun (fun _let_3 (fun _let_0 bool)) _let_4) (combb (fun _let_0 bool) bool _let_3) (hAPP (fun _let_0 bool) _let_2 (hoare_122391849derivs state) (hAPP _let_3 (fun _let_0 bool) _let_6 (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))) _let_6)))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun (fun _let_1 bool) bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun _let_5 bool))) (let ((_let_7 (fun pname _let_1))) (let ((_let_8 (hAPP _let_7 (fun _let_5 (fun _let_1 bool)) (image pname _let_1) (hAPP _let_2 _let_7 (hAPP (fun com _let_1) (fun _let_2 _let_7) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))))) (hAPP (fun _let_5 (fun _let_1 bool)) _let_6 (hAPP _let_4 (fun (fun _let_5 (fun _let_1 bool)) _let_6) (combb (fun _let_1 bool) bool _let_5) (hAPP (fun _let_1 bool) _let_4 (ord_less_eq (fun _let_1 bool)) (hAPP _let_5 (fun _let_1 bool) _let_8 (hAPP _let_3 _let_5 (dom pname com) body)))) _let_8)))))))))), skv_2 ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (fun (fun pname bool) bool))) (let ((_let_1 (fun (fun pname bool) (fun pname bool)))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb (fun pname bool) bool (fun pname bool)) (hAPP pname _let_0 (member pname) pn)) (hAPP pname _let_1 (insert pname) pn)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname _let_0))) (let ((_let_6 (fun _let_3 _let_2))) (hAPP _let_6 _let_4 (hAPP (fun _let_2 bool) (fun _let_6 _let_4) (combb _let_2 bool _let_3) (finite_finite _let_0)) (hAPP _let_5 _let_6 (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb _let_0 bool _let_0) (finite_finite pname)) (collect pname))))), (hAPP bool (fun pname bool) (combk bool pname) fFalse) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun (fun _let_1 bool) bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun _let_5 bool))) (let ((_let_7 (fun pname _let_1))) (let ((_let_8 (hAPP _let_7 (fun _let_5 (fun _let_1 bool)) (image pname _let_1) (hAPP _let_2 _let_7 (hAPP (fun com _let_1) (fun _let_2 _let_7) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))))) (hAPP (fun _let_5 (fun _let_1 bool)) _let_6 (hAPP _let_4 (fun (fun _let_5 (fun _let_1 bool)) _let_6) (combb (fun _let_1 bool) bool _let_5) (hAPP (fun _let_1 bool) _let_4 (hoare_122391849derivs state) (hAPP _let_5 (fun _let_1 bool) _let_8 (hAPP _let_3 _let_5 (dom pname com) body)))) _let_8)))))))))), skv_2 ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname _let_0))) (let ((_let_7 (fun _let_4 _let_2))) (hAPP _let_7 _let_5 (hAPP _let_3 (fun _let_7 _let_5) (combb _let_2 bool _let_4) (hAPP _let_2 _let_3 (ord_less_eq _let_2) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2)))) (hAPP _let_6 _let_7 (image pname _let_0) (hAPP _let_1 _let_6 (hAPP (fun com _let_0) (fun _let_1 _let_6) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1))))))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname _let_0))) (let ((_let_7 (fun _let_4 _let_2))) (hAPP _let_7 _let_5 (hAPP _let_3 (fun _let_7 _let_5) (combb _let_2 bool _let_4) (hAPP _let_2 _let_3 (ord_less_eq _let_2) fa)) (hAPP _let_6 _let_7 (image pname _let_0) (hAPP _let_1 _let_6 (hAPP (fun com _let_0) (fun _let_1 _let_6) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1))))))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (fun (fun pname bool) bool))) (let ((_let_1 (fun (fun pname bool) (fun pname bool)))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb (fun pname bool) bool (fun pname bool)) (hAPP (fun pname bool) _let_0 (ord_less_eq (fun pname bool)) skv_1)) (hAPP pname _let_1 (insert pname) pn)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (fun (fun pname bool) bool))) (let ((_let_1 (fun (fun pname bool) (fun pname bool)))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb (fun pname bool) bool (fun pname bool)) (hAPP (fun pname bool) _let_0 (ord_less_eq (fun pname bool)) skv_2)) (hAPP pname _let_1 (insert pname) pn)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (fun (fun pname bool) bool))) (let ((_let_1 (fun (fun pname bool) (fun pname bool)))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb (fun pname bool) bool (fun pname bool)) (hAPP pname _let_0 (member pname) skv_3)) (hAPP pname _let_1 (insert pname) pn)))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.56 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun _let_6 bool))) (let ((_let_8 (fun pname _let_1))) (let ((_let_9 (fun _let_6 _let_4))) (hAPP _let_9 _let_7 (hAPP _let_5 (fun _let_9 _let_7) (combb _let_4 bool _let_6) (hAPP _let_1 _let_5 (member _let_1) skv_4)) (hAPP _let_8 _let_9 (image pname _let_1) (hAPP _let_2 _let_8 (hAPP (fun com _let_1) (fun _let_2 _let_8) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)))))))))))))), skv_2 ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun _let_6 bool))) (let ((_let_8 (fun pname _let_1))) (let ((_let_9 (fun _let_6 _let_4))) (hAPP _let_9 _let_7 (hAPP _let_5 (fun _let_9 _let_7) (combb _let_4 bool _let_6) (hAPP _let_1 _let_5 (member _let_1) skv_7)) (hAPP _let_8 _let_9 (image pname _let_1) (hAPP _let_2 _let_8 (hAPP (fun com _let_1) (fun _let_2 _let_8) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)))))))))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun _let_6 bool))) (let ((_let_8 (fun pname _let_1))) (let ((_let_9 (fun _let_6 _let_4))) (hAPP _let_9 _let_7 (hAPP _let_5 (fun _let_9 _let_7) (combb _let_4 bool _let_6) (hAPP _let_1 _let_5 (member _let_1) skv_7)) (hAPP _let_8 _let_9 (image pname _let_1) (hAPP _let_2 _let_8 (hAPP (fun com _let_1) (fun _let_2 _let_8) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)))))))))))))), skv_2 ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (bot_bot (fun pname bool)) ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP pname (fun _let_0 _let_0) (insert pname) pn) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), skv_1 ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), skv_2 ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), (bot_bot (fun pname bool)) ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun (fun pname bool) bool))) (let ((_let_4 (fun pname _let_0))) (let ((_let_5 (hAPP _let_4 (fun (fun pname bool) (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)))) (let ((_let_6 (fun (fun pname bool) _let_2))) (hAPP (fun (fun pname bool) (fun _let_0 bool)) _let_3 (hAPP _let_6 (fun (fun (fun pname bool) (fun _let_0 bool)) _let_3) (combs (fun pname bool) (fun _let_0 bool) bool) (hAPP (fun (fun pname bool) (fun _let_0 bool)) _let_6 (hAPP (fun (fun _let_0 bool) _let_2) (fun (fun (fun pname bool) (fun _let_0 bool)) _let_6) (combb (fun _let_0 bool) _let_2 (fun pname bool)) (hoare_122391849derivs state)) _let_5)) _let_5)))))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.57 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_12), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_22)), skv_2 ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_23)), skv_2 ) 14.25/12.57 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_38), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.57 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_43), skv_2 ) 14.25/12.57 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_44), skv_2 ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_45)), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_46)), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_47)), skv_2 ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_48)), skv_2 ) 14.25/12.57 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_55), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.57 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_56), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.57 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_56), skv_2 ) 14.25/12.57 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_57), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.57 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_57), skv_1 ) 14.25/12.57 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_61), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.57 ( bool, (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_61), skv_62 ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_86)), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 14.25/12.57 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_87)), (bot_bot (fun pname bool)) ) 14.25/12.57 ( bool, (fun (fun pname bool) bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (finite_finite pname) ) 14.25/12.57 ( bool, (fun (fun pname bool) bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (bot_bot (fun (fun pname bool) bool)) ) 14.25/12.57 ( bool, (fun (fun pname bool) bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)) (bot_bot _let_1)))) ) 14.25/12.57 ( bool, (fun (fun pname bool) bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun _let_6 bool))) (let ((_let_8 (fun pname _let_1))) (let ((_let_9 (fun _let_6 _let_4))) (hAPP _let_9 _let_7 (hAPP _let_5 (fun _let_9 _let_7) (combb _let_4 bool _let_6) (hAPP _let_4 _let_5 (ord_less_eq _let_4) fa)) (hAPP _let_8 _let_9 (image pname _let_1) (hAPP _let_2 _let_8 (hAPP (fun com _let_1) (fun _let_2 _let_8) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)))))))))))))) ) 14.25/12.57 ( bool, (fun (fun pname bool) bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (hAPP pname (fun (fun pname bool) bool) (member pname) pn) ) 14.25/12.57 ( bool, (fun (fun pname bool) bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_1)) ) 14.25/12.57 ( bool, (fun (fun pname bool) bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq 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bool), (finite_finite com), skv_66 ) 14.25/12.57 ( bool, (fun com bool), (finite_finite com), (let ((_let_0 (fun com bool))) (hAPP _let_0 _let_0 (hAPP com (fun _let_0 _let_0) (insert com) skv_65) skv_66)) ) 14.25/12.57 ( bool, (fun com bool), (let ((_let_0 (fun com bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) wt)), wt ) 14.25/12.57 ( bool, (fun com bool), (let ((_let_0 (fun com bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) wt)), (bot_bot (fun com bool)) ) 14.25/12.57 ( bool, (fun com bool), (hAPP com (fun (fun com bool) bool) (member com) skv_5), wt ) 14.25/12.57 ( bool, (fun com bool), (hAPP com (fun (fun com bool) bool) (member com) skv_5), (bot_bot (fun com bool)) ) 14.25/12.57 ( bool, (fun com bool), (let ((_let_0 (fun (fun com bool) bool))) (let ((_let_1 (fun (fun com bool) (fun com bool)))) (hAPP com _let_0 (hAPP _let_1 (fun com _let_0) (combc (fun com bool) com bool) (hAPP (fun com com) _let_1 (image com com) (combi com))) y))), wt ) 14.25/12.57 ( 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((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun com bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun _let_3 _let_1))) (hAPP _let_5 _let_4 (hAPP _let_2 (fun _let_5 _let_4) (combb _let_1 bool _let_3) (hAPP _let_1 _let_2 (ord_less_eq _let_1) fa)) (hAPP (fun com _let_0) _let_5 (image com _let_0) hoare_Mirabelle_MGT)))))))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 14.25/12.57 ( bool, (fun com bool), (let ((_let_0 (fun com bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb 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com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 14.25/12.58 ( bool, (fun com bool), (hAPP com (fun (fun com bool) bool) (member com) skv_35), wt ) 14.25/12.58 ( bool, (fun com bool), (hAPP com (fun (fun com bool) bool) (member com) skv_35), (bot_bot (fun com bool)) ) 14.25/12.58 ( bool, (fun com bool), (hAPP com (fun (fun com bool) bool) (member com) skv_37), wt ) 14.25/12.58 ( bool, (fun com bool), (hAPP com (fun (fun com bool) bool) (member com) skv_65), (bot_bot (fun com bool)) ) 14.25/12.58 ( bool, (fun com bool), (hAPP com (fun (fun com bool) bool) (member com) skv_65), skv_66 ) 14.25/12.58 ( bool, (fun (fun pname bool) (fun (hoare_509422987triple state) bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_3 (fun _let_2 bool)))) (let ((_let_5 (fun _let_3 bool))) (hAPP _let_2 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(let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (let ((_let_6 (fun _let_3 bool))) (hAPP _let_3 _let_6 (hAPP (fun _let_2 _let_3) (fun _let_3 _let_6) (image _let_2 _let_3) (ord_less_eq _let_2)) (hAPP _let_2 _let_3 (hoare_122391849derivs state) (hAPP _let_4 _let_2 (hAPP _let_5 (fun _let_4 _let_2) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body))))))))))) ) 14.25/12.58 ( bool, (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 (fun (fun _let_3 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pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 15.20/13.10 ( (let ((_let_0 (fun (fun (fun (hoare_509422987triple state) bool) bool) bool))) (fun _let_0 _let_0)), (fun (fun (hoare_509422987triple state) bool) bool), (insert (fun (fun (hoare_509422987triple state) bool) bool)), (finite_finite (hoare_509422987triple state)) ) 15.20/13.10 ( (let ((_let_0 (fun (fun (fun (hoare_509422987triple state) bool) bool) bool))) (fun _let_0 _let_0)), (fun (fun (hoare_509422987triple state) bool) bool), (insert (fun (fun (hoare_509422987triple state) bool) bool)), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 15.20/13.10 ( (let ((_let_0 (fun (fun (fun (hoare_509422987triple state) bool) bool) bool))) (fun _let_0 _let_0)), (fun (fun (fun (hoare_509422987triple state) bool) bool) (fun bool bool)), (combs (fun (fun (hoare_509422987triple state) bool) bool) bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 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(hoare_509422987triple state), com, hoare_Mirabelle_MGT, y, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 15.39/13.26 ( (hoare_509422987triple state), com, hoare_Mirabelle_MGT, (hAPP pname com body_1 skv_3), (bot_bot (fun com bool)) ) 15.39/13.26 ( (hoare_509422987triple state), com, hoare_Mirabelle_MGT, (let ((_let_0 (option com))) (hAPP _let_0 com (the com) (hAPP pname _let_0 body skv_3))), (bot_bot (fun com bool)) ) 15.39/13.26 ( (hoare_509422987triple state), com, hoare_Mirabelle_MGT, (hAPP pname com body_1 skv_55), (bot_bot (fun com bool)) ) 15.39/13.26 ( (hoare_509422987triple state), pname, (let ((_let_0 (option com))) (let ((_let_1 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(hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (finite_finite pname) ) 15.39/13.27 ) 15.39/13.27 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (ord_less_eq _let_0))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 A_1) B))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 _let_1 _let_2 B) A_1))) (= (ti _let_0 B) (ti _let_0 A_1))) )))) 15.39/13.27 ( bool, fNot, fNot ) 15.39/13.27 ( bool, fNot, (bot_bot (fun bool bool)) ) 15.39/13.27 ( bool, (combi bool), (bot_bot (fun bool bool)) ) 15.39/13.27 ( bool, (bot_bot (fun bool bool)), fNot ) 15.39/13.27 ( bool, (bot_bot (fun bool bool)), (combi bool) ) 15.39/13.27 ( bool, (bot_bot (fun bool bool)), (bot_bot (fun bool bool)) ) 15.39/13.27 ( com, wt, wt ) 15.39/13.27 ( com, wt, (bot_bot (fun com bool)) ) 15.39/13.27 ( com, (bot_bot (fun com bool)), wt ) 15.39/13.27 ( com, (bot_bot (fun com bool)), (bot_bot (fun com bool)) ) 15.39/13.27 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))), skv_24 ) 15.39/13.27 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))), skv_25 ) 15.39/13.27 ( com, skv_24, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname 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_let_0 _let_0 (hAPP pname (fun _let_0 _let_0) (insert pname) pn) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 15.39/13.27 ( pname, skv_1, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 15.39/13.27 ( pname, skv_1, (bot_bot (fun pname bool)) ) 15.39/13.27 ( pname, skv_1, skv_1 ) 15.39/13.27 ( pname, skv_2, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 15.39/13.27 ( pname, skv_2, (bot_bot (fun pname bool)) ) 15.39/13.27 ( pname, skv_2, skv_2 ) 15.39/13.27 ( pname, skv_2, skv_22 ) 15.39/13.27 ( pname, skv_2, skv_23 ) 15.39/13.27 ( pname, skv_2, skv_47 ) 15.39/13.27 ( pname, skv_2, skv_48 ) 15.39/13.27 ( pname, skv_22, skv_2 ) 15.39/13.27 ( pname, skv_23, skv_2 ) 15.39/13.27 ( pname, skv_45, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 15.39/13.27 ( pname, skv_46, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 15.39/13.27 ( pname, skv_47, skv_2 ) 15.39/13.27 ( pname, skv_48, skv_2 ) 15.39/13.27 ( pname, skv_86, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 15.39/13.27 ( pname, skv_87, (bot_bot (fun pname bool)) ) 15.39/13.27 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.39/13.27 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), fa ) 15.39/13.27 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) 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com (fun pname com)) ) 15.39/13.30 ( (let ((_let_0 (option com))) (fun _let_0 (fun pname _let_0))) ) 15.39/13.30 ( (let ((_let_0 (hoare_509422987triple state))) (fun _let_0 (fun pname _let_0))) ) 15.39/13.30 ( (fun bool (fun (hoare_509422987triple state) bool)) ) 15.39/13.30 ( (let ((_let_0 (fun pname (hoare_509422987triple state)))) (fun _let_0 (fun (fun pname com) _let_0))) ) 15.39/13.30 ( (let ((_let_0 (fun pname com))) (fun _let_0 (fun (fun pname (option com)) _let_0))) ) 15.39/13.30 ( (fun bool (fun (fun (hoare_509422987triple state) bool) bool)) ) 15.39/13.30 ( (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun _let_0 (fun _let_0 _let_0))) ) 15.39/13.30 ( (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun _let_0 (fun (fun pname bool) _let_0))) ) 15.39/13.30 ( (let ((_let_0 (fun bool bool))) (fun _let_0 _let_0)) ) 15.39/13.30 ( (let ((_let_0 (fun bool bool))) (fun bool (fun _let_0 _let_0))) ) 15.39/13.30 ( (let ((_let_0 (fun com bool))) (fun _let_0 _let_0)) ) 15.39/13.30 ( (let ((_let_0 (fun com bool))) (fun com (fun _let_0 _let_0))) ) 15.39/13.30 ( (let ((_let_0 (fun pname bool))) (fun _let_0 _let_0)) ) 15.39/13.30 ( (let ((_let_0 (fun pname bool))) (fun pname (fun _let_0 _let_0))) ) 15.39/13.30 ( (let ((_let_0 (fun (fun (hoare_509422987triple state) bool) bool))) (fun (fun (hoare_509422987triple state) bool) (fun _let_0 _let_0))) ) 15.39/13.30 ( (fun com com) ) 15.39/13.30 ( (let ((_let_0 (fun pname bool))) (fun _let_0 (fun _let_0 bool))) ) 15.39/13.30 ( (let ((_let_0 (fun bool (fun bool bool)))) (fun _let_0 _let_0)) ) 15.39/13.30 ( (let ((_let_0 (fun pname (option com)))) (fun (fun pname (fun _let_0 com)) (fun _let_0 (fun pname com)))) ) 15.39/13.30 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (fun (fun pname (fun _let_1 _let_0)) (fun _let_1 (fun pname _let_0))))) ) 15.39/13.30 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname bool))) (fun (fun _let_0 (fun _let_1 bool)) (fun _let_1 (fun _let_0 bool))))) ) 15.39/13.30 ( (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun (fun (hoare_509422987triple state) (fun _let_0 bool)) (fun _let_0 _let_0))) ) 15.39/13.30 ( (let ((_let_0 (fun pname (option com)))) (fun _let_0 _let_0)) ) 15.39/13.30 ( (let ((_let_0 (fun com (hoare_509422987triple state)))) (fun _let_0 _let_0)) ) 15.39/13.30 ( (let ((_let_0 (fun pname com))) (fun _let_0 _let_0)) ) 15.39/13.30 ( (fun pname pname) ) 15.39/13.30 ( (let ((_let_0 (fun (option com) com))) (fun _let_0 _let_0)) ) 15.39/13.30 ) 15.39/13.30 (instantiation (let ((_let_0 (fun (hoare_509422987triple X_a) bool))) (let ((_let_1 (hAPP _let_0 (fun _let_0 bool) (hoare_122391849derivs X_a) G))) (let ((_let_2 (hAPP (hoare_509422987triple X_a) (fun _let_0 _let_0) (insert (hoare_509422987triple X_a)) T_3))) (forall ((X_a $$unsorted) (G $$unsorted) (T_3 $$unsorted) (Ts $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 _let_2 Ts)))) (and (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 _let_2 (bot_bot _let_0)))) (hBOOL (hAPP _let_0 bool _let_1 Ts)))) )))) 15.39/13.30 ( state, (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.39/13.30 ( state, (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 15.39/13.30 ( state, (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.39/13.30 ( state, (bot_bot (fun (hoare_509422987triple state) bool)), skv_7, fa ) 15.39/13.30 ( state, (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 15.39/13.30 ( state, (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_55)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.39/13.30 ( state, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), skv_7, fa ) 15.39/13.30 ( state, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 15.39/13.30 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.39/13.31 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 15.39/13.31 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.39/13.31 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), skv_7, fa ) 15.39/13.31 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 15.39/13.31 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), skv_69, skv_70 ) 15.39/13.31 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.39/13.31 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), skv_7, fa ) 15.39/13.31 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))), (let ((_let_0 (option com))) (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP _let_0 com (the com) (hAPP pname _let_0 body skv_3)))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.39/13.31 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (let ((_let_0 (option com))) (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP _let_0 com (the com) (hAPP pname _let_0 body skv_3)))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.39/13.31 ) 15.39/13.31 (instantiation (let ((_let_0 (fun X_c bool))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (fun X_c X_a))) (let ((_let_3 (fun X_c X_b))) (let ((_let_4 (fun X_b X_a))) (let ((_let_5 (fun X_b bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_c $$unsorted) (F $$unsorted) (G_1 $$unsorted) (A_1 $$unsorted)) (= (hAPP _let_5 _let_1 (hAPP _let_4 (fun _let_5 _let_1) (image X_b X_a) F) (hAPP _let_0 _let_5 (hAPP _let_3 (fun _let_0 _let_5) (image X_c X_b) G_1) A_1)) (hAPP _let_0 _let_1 (hAPP _let_2 (fun _let_0 _let_1) (image X_c X_a) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (combb X_b X_a X_c) F) G_1)) A_1)) ))))))) 15.39/13.31 ( bool, bool, bool, (combi bool), (combi bool), fNot ) 15.39/13.31 ( bool, bool, bool, (combi bool), (combi bool), (combi bool) ) 15.39/13.31 ( bool, bool, bool, (combi bool), (combi bool), (bot_bot (fun bool bool)) ) 15.39/13.31 ( bool, bool, bool, (combi bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fNot ) 15.39/13.31 ( bool, bool, bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fNot ) 15.39/13.31 ( com, com, com, (combi com), (combi com), wt ) 15.39/13.31 ( com, com, com, (combi com), (combi com), (bot_bot (fun com bool)) ) 15.39/13.31 ( com, com, com, (combi com), (let ((_let_0 (combi com))) (let ((_let_1 (fun com com))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb com com com) _let_0) _let_0))), wt ) 15.39/13.31 ( com, com, com, (let ((_let_0 (combi com))) (let ((_let_1 (fun com com))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb com com com) _let_0) _let_0))), (let ((_let_0 (combi com))) (let ((_let_1 (fun com com))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb com com com) _let_0) _let_0))), wt ) 15.39/13.31 ( com, (hoare_509422987triple state), com, hoare_Mirabelle_MGT, (combi com), (bot_bot (fun com bool)) ) 15.39/13.31 ( com, (hoare_509422987triple state), (option com), hoare_Mirabelle_MGT, (the com), (let ((_let_0 (option com))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun _let_0 bool))) (hAPP _let_2 _let_3 (hAPP _let_1 (fun _let_2 _let_3) (image pname _let_0) body) (hAPP _let_1 _let_2 (dom pname com) body)))))) ) 15.39/13.31 ( com, (hoare_509422987triple state), pname, hoare_Mirabelle_MGT, body_1, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 15.39/13.31 ( com, (hoare_509422987triple state), pname, hoare_Mirabelle_MGT, body_1, (bot_bot (fun pname bool)) ) 15.39/13.31 ( com, (hoare_509422987triple state), pname, hoare_Mirabelle_MGT, body_1, skv_45 ) 15.39/13.31 ( com, (hoare_509422987triple state), pname, hoare_Mirabelle_MGT, body_1, skv_46 ) 15.39/13.31 ( com, (hoare_509422987triple state), pname, hoare_Mirabelle_MGT, body_1, skv_80 ) 15.39/13.31 ( com, (hoare_509422987triple state), pname, 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(let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 15.54/13.35 ( com, y, (hAPP (fun com (option com)) (fun com bool) (dom com com) (some com)) ) 15.54/13.35 ( com, skv_5, wt ) 15.54/13.35 ( com, skv_5, (bot_bot (fun com bool)) ) 15.54/13.35 ( com, skv_35, wt ) 15.54/13.35 ( com, skv_35, (bot_bot (fun com bool)) ) 15.54/13.35 ( com, skv_37, wt ) 15.54/13.35 ( com, skv_65, (bot_bot (fun com bool)) ) 15.54/13.35 ( com, skv_65, skv_66 ) 15.54/13.35 ( (option com), (hAPP com (option com) (some com) y), (let ((_let_0 (option com))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun _let_0 bool))) (hAPP _let_2 _let_3 (hAPP 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(hAPP _let_3 (fun _let_2 _let_2) (combs _let_1 bool bool) (hAPP _let_2 _let_3 (hAPP (fun bool _let_0) (fun _let_2 _let_3) (combb bool _let_0 _let_1) fconj) (hAPP _let_1 _let_2 (fequal _let_1) (hAPP (fun pname (option com)) _let_1 (dom pname com) body)))) (finite_finite pname)))))) ) 15.54/13.38 ( (fun pname bool), (bot_bot (fun (fun pname bool) bool)) ) 15.54/13.38 ( (fun pname bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun _let_4 bool))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun _let_6 bool))) (let ((_let_8 (fun pname _let_1))) (let ((_let_9 (fun _let_6 _let_4))) (hAPP _let_9 _let_7 (hAPP _let_5 (fun _let_9 _let_7) (combb _let_4 bool _let_6) (hAPP _let_4 _let_5 (ord_less_eq _let_4) fa)) (hAPP _let_8 _let_9 (image pname _let_1) (hAPP _let_2 _let_8 (hAPP (fun com _let_1) (fun _let_2 _let_8) (combb com _let_1 pname) 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pname (option com)) _let_0 (dom pname com) body))) ) 15.54/13.38 ( (fun (fun pname bool) bool), (finite_finite (fun pname bool)) ) 15.54/13.38 ( (fun (fun pname bool) bool), (bot_bot (fun (fun (fun pname bool) bool) bool)) ) 15.54/13.38 ( (fun com bool), (finite_finite com) ) 15.54/13.38 ( (fun com bool), (let ((_let_0 (fun com bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) wt)) ) 15.54/13.38 ( (fun com bool), (hAPP com (fun (fun com bool) bool) (member com) skv_5) ) 15.54/13.38 ( (fun com bool), (bot_bot (fun (fun com bool) bool)) ) 15.54/13.38 ) 15.54/13.38 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) A_1))) (forall ((X_a $$unsorted) (B $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (or (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) X_2) A_1)) (= (hBOOL (hAPP _let_0 bool _let_1 B)) (hBOOL (hAPP _let_0 bool _let_1 (hAPP _let_0 _let_0 (hAPP X_a (fun _let_0 _let_0) (insert X_a) X_2) B))))) ))) 15.54/13.38 ( bool, fNot, skv_6, fNot ) 15.54/13.38 ( bool, fNot, skv_6, (bot_bot (fun bool bool)) ) 15.54/13.38 ( com, wt, skv_5, wt ) 15.54/13.38 ( com, wt, skv_5, (bot_bot (fun com bool)) ) 15.54/13.38 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), skv_24 ) 15.54/13.38 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), skv_25 ) 15.54/13.38 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn, skv_1 ) 15.54/13.38 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn, skv_2 ) 15.54/13.38 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 15.54/13.38 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3, skv_1 ) 15.54/13.38 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3, skv_2 ) 15.54/13.38 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3, skv_45 ) 15.54/13.38 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3, skv_46 ) 15.54/13.38 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3, skv_86 ) 15.54/13.38 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.54/13.38 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), fa ) 15.54/13.38 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun 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15.54/13.38 ( (hoare_509422987triple state), fa, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), fa ) 15.54/13.38 ( (hoare_509422987triple state), fa, skv_7, (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.54/13.38 ( (hoare_509422987triple state), fa, skv_7, fa ) 15.54/13.38 ( (hoare_509422987triple state), fa, skv_7, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 15.54/13.38 ( (hoare_509422987triple state), fa, skv_7, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 15.54/13.38 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.54/13.38 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), fa ) 15.54/13.38 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) 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(fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 15.54/13.38 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP 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(hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.54/13.38 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), fa ) 15.54/13.38 ( (hoare_509422987triple state), skv_64, skv_63, fa ) 15.54/13.38 ( (fun (hoare_509422987triple state) bool), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), fa, (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 15.54/13.38 ( (fun (hoare_509422987triple state) bool), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) 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$$unsorted)) (or (not (hBOOL (hAPP _let_0 bool _let_1 F_1))) (not (hBOOL (hAPP _let_0 bool _let_2 A_1))) (hBOOL (hAPP _let_0 bool _let_2 F_1)) (not (hBOOL (hAPP _let_0 bool P_1 F_1))) (hBOOL (hAPP _let_0 bool P_1 (hAPP _let_0 _let_0 (hAPP X_a (fun _let_0 _let_0) (insert X_a) A_2) F_1)))) )) (hBOOL (hAPP _let_0 bool P_1 Fa))) )))) 15.54/13.38 ( bool, (finite_finite bool), fNot, (bot_bot (fun bool bool)) ) 15.54/13.38 ( bool, (finite_finite bool), (bot_bot (fun bool bool)), fNot ) 15.54/13.38 ( bool, (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), (bot_bot (fun bool bool)), fNot ) 15.54/13.38 ( bool, (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6), (bot_bot (fun bool bool)), (combi bool) ) 15.54/13.38 ( bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb _let_0 bool _let_0) (finite_finite bool)) (collect bool))))), (bot_bot (fun bool bool)), (bot_bot (fun bool bool)) ) 15.54/13.38 ( bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb _let_0 bool _let_0) (hAPP _let_0 _let_1 (ord_less_eq _let_0) fNot)) (collect bool))))), fNot, fNot ) 15.54/13.38 ( com, (finite_finite com), wt, (bot_bot (fun com bool)) ) 15.54/13.38 ( com, (finite_finite com), (bot_bot (fun com bool)), wt ) 15.54/13.38 ( com, (let ((_let_0 (fun com bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) wt)), (bot_bot (fun com bool)), wt ) 15.54/13.39 ( com, (hAPP com (fun (fun com bool) bool) (member com) skv_5), (bot_bot (fun com bool)), (bot_bot (fun com bool)) ) 15.54/13.39 ( com, (let ((_let_0 (fun com bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb _let_0 bool _let_0) (finite_finite com)) (collect com))))), wt, wt ) 15.54/13.39 ( com, (let ((_let_0 (fun com bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb _let_0 bool _let_0) (hAPP _let_0 _let_1 (ord_less_eq _let_0) wt)) (collect com))))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))), skv_24 ) 15.54/13.39 ( com, (let ((_let_0 (fun com bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))), skv_25 ) 15.54/13.39 ( pname, (finite_finite pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_1 ) 15.54/13.39 ( pname, (finite_finite pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_2 ) 15.54/13.39 ( pname, (hAPP pname (fun (fun pname bool) bool) (member pname) pn), skv_2, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 15.54/13.39 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_1)), (bot_bot (fun pname bool)), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 15.54/13.39 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_2)), skv_1, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 15.54/13.39 ( pname, (hAPP pname (fun (fun pname bool) bool) (member pname) skv_3), (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP pname (fun _let_0 _let_0) (insert pname) pn) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 15.54/13.39 ( pname, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb _let_0 bool _let_0) (finite_finite pname)) (collect pname))))), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_1 ) 15.54/13.39 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (bot_bot (fun pname bool)), skv_2 ) 15.54/13.39 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), skv_2, skv_2 ) 15.54/13.39 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_87)), (bot_bot (fun pname bool)), (bot_bot (fun pname bool)) ) 15.54/13.39 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), fa, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 15.66/13.39 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), fa ) 15.66/13.39 ( (hoare_509422987triple state), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (bot_bot (fun (hoare_509422987triple state) bool)), fa ) 15.66/13.39 ( (hoare_509422987triple state), 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_let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (bot_bot (fun (hoare_509422987triple state) bool)), fa ) 15.66/13.39 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), fa ) 15.66/13.39 ( (hoare_509422987triple state), (finite_finite (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.66/13.39 ( (hoare_509422987triple state), (finite_finite (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), fa ) 15.66/13.39 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 (fun _let_1 bool)))) (hAPP _let_1 (fun _let_1 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(hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.66/13.40 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), fa ) 15.66/13.40 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))), (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 15.66/13.40 ( state, skv_82, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), fa ) 15.66/13.40 ( state, skv_90, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 15.66/13.41 ) 15.66/13.41 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (finite_finite X_a))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B 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15.84/13.52 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.84/13.52 ( state, (let ((_let_0 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_let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 15.84/13.52 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 15.84/13.52 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 15.84/13.52 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))), (bot_bot (fun (hoare_509422987triple state) bool)), fa ) 15.84/13.52 ) 15.84/13.52 (instantiation (let ((_let_0 (fun X_b bool))) (let ((_let_1 (hAPP (fun X_b (option X_a)) _let_0 (dom X_b X_a) F))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (X_2 $$unsorted) (Y_3 $$unsorted)) (let ((_let_0 (option X_a))) (or (not (= (hAPP X_a _let_0 (some X_a) Y_3) (hAPP X_b _let_0 F X_2))) (= _let_1 (hAPP _let_0 _let_0 (hAPP X_b (fun _let_0 _let_0) (insert X_b) X_2) _let_1)))) ))) 15.84/13.52 ( com, com, (some com), y, y ) 15.84/13.52 ( (option com), com, (combi (option com)), (hAPP com (option com) (some com) y), y ) 15.84/13.52 ( pname, com, body, pn, y ) 15.84/13.52 ( pname, com, body, pn, skv_77 ) 15.84/13.52 ) 15.84/13.52 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (collect X_a))) (forall ((X_a $$unsorted)) (= _let_1 (ti (fun _let_0 _let_0) _let_1)) ))) 15.84/13.52 ( bool ) 15.84/13.52 ( com ) 15.84/13.52 ( (option com) ) 15.84/13.52 ( (fun bool bool) ) 15.84/13.52 ( pname ) 15.84/13.52 ( (hoare_509422987triple state) ) 15.84/13.52 ( (fun pname (option com)) ) 15.84/13.52 ( (fun (hoare_509422987triple state) bool) ) 15.84/13.52 ( (fun (fun (hoare_509422987triple state) bool) bool) ) 15.84/13.52 ( (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun _let_0 _let_0)) ) 15.84/13.52 ( (fun pname bool) ) 15.84/13.52 ( (fun (fun pname bool) bool) ) 15.84/13.52 ( (fun com bool) ) 15.84/13.52 ( (fun pname (hoare_509422987triple state)) ) 15.84/13.52 ( (fun (fun pname bool) (fun (hoare_509422987triple state) bool)) ) 15.84/13.52 ( (fun (fun pname (option com)) (fun pname bool)) ) 15.84/13.52 ( (fun (fun pname (option com)) bool) ) 15.88/13.52 ( (fun (fun bool bool) bool) ) 15.88/13.52 ( (fun (fun com bool) bool) ) 15.88/13.52 ( (fun (fun (fun (hoare_509422987triple state) bool) bool) bool) ) 15.88/13.52 ( (fun (fun (fun pname bool) bool) bool) ) 15.88/13.52 ( (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun (fun _let_0 _let_0) bool)) ) 15.88/13.52 ( (fun (option com) bool) ) 15.88/13.52 ) 15.88/13.52 (instantiation (forall ((T_1 $$unsorted)) (or (not (finite_finite_1 T_1)) (finite_finite_1 (option T_1))) ) 15.88/13.52 ( com ) 15.88/13.53 ) 15.88/13.53 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_b bool))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_2 $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) X_2) A_1))) (not (= (hAPP X_a X_b F 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(hAPP pname (fun _let_0 bool) (member pname) pn) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), (let ((_let_0 (fun com bool))) (hAPP _let_0 _let_0 (hAPP (fun com (fun _let_0 bool)) (fun _let_0 _let_0) (combc com _let_0 bool) (member com)) wt)), skv_5, (bot_bot (fun com bool)) ) 15.88/13.53 ( bool, (fun bool bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 bool))) (hAPP _let_2 bool (hAPP _let_1 (fun _let_2 bool) (member _let_1) fa) (finite_finite _let_0))))), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), (bot_bot (fun bool bool)), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)) ) 15.88/13.53 ( bool, (fun bool bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) skv_7) fa))), (finite_finite bool), (bot_bot (fun bool bool)), (finite_finite bool) ) 15.88/13.53 ( bool, pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 bool (finite_finite pname) (bot_bot _let_0))), (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), skv_3, (bot_bot (fun pname bool)) ) 15.88/13.53 ( bool, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))) (hAPP _let_2 _let_2 (hAPP _let_0 (fun 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bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) fa))), skv_7, (bot_bot (fun (hoare_509422987triple state) bool)) ) 15.88/13.53 ( bool, (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) skv_4) fa))), fa, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), skv_54 ) 15.88/13.53 ( bool, (fun (hoare_509422987triple state) bool), fTrue, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))) ) 15.88/13.53 ( bool, (fun (hoare_509422987triple state) bool), fFalse, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 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((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (let ((_let_5 (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) _let_5) _let_5))))))), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (hoare_122391849derivs state)) fa))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_1 (fun _let_1 bool)))) (hAPP _let_1 (fun _let_1 bool) (hAPP _let_2 _let_2 (combc _let_1 _let_1 bool) (hoare_122391849derivs state)) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))))) ) 15.88/13.53 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 bool (finite_finite _let_0) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (hoare_122391849derivs state)) fa))) ) 15.88/13.53 ( bool, (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 bool (finite_finite _let_0) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun (fun _let_0 bool) (fun _let_0 bool)))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_2 (fun _let_3 _let_2) (combb (fun _let_0 bool) bool (fun _let_0 bool)) (hAPP (fun _let_0 bool) _let_2 (hoare_122391849derivs state) (hAPP _let_4 (fun _let_0 bool) (hAPP _let_5 (fun _let_4 (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun 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pname (option com)) (fun pname bool) (dom pname com) body), (finite_finite pname) ) 15.88/13.55 ( bool, (fun pname bool), fFalse, (finite_finite pname), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (finite_finite pname) ) 15.88/13.55 ( bool, (fun pname bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 bool (hAPP _let_2 (fun _let_3 bool) (member _let_2) fa) (hAPP _let_2 _let_3 (hoare_122391849derivs state) (hAPP _let_4 _let_2 (hAPP _let_5 (fun _let_4 _let_2) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))))))))), (finite_finite pname), (bot_bot (fun pname bool)), (finite_finite pname) ) 15.88/13.55 ( bool, (fun pname bool), (let 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(let ((_let_5 (fun pname _let_1))) (let ((_let_6 (hAPP _let_3 (fun _let_3 bool) (hoare_122391849derivs state) (hAPP _let_4 _let_3 (hAPP _let_5 (fun _let_4 _let_3) (image pname _let_1) (hAPP _let_2 _let_5 (hAPP (fun com _let_1) (fun _let_2 _let_5) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body))))) (hAPP (fun _let_3 bool) _let_0 (hAPP (fun _let_3 bool) (fun (fun _let_3 bool) _let_0) (image _let_3 bool) _let_6) _let_6)))))))), fTrue, (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_1))) (let ((_let_6 (hAPP _let_3 (fun _let_3 bool) (hoare_122391849derivs state) (hAPP _let_4 _let_3 (hAPP _let_5 (fun _let_4 _let_3) (image pname _let_1) (hAPP _let_2 _let_5 (hAPP (fun com _let_1) (fun _let_2 _let_5) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body))))) (hAPP (fun _let_3 bool) _let_0 (hAPP (fun _let_3 bool) (fun (fun _let_3 bool) _let_0) (image _let_3 bool) _let_6) _let_6)))))))) ) 15.88/13.61 ( bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_1))) (let ((_let_6 (hAPP _let_3 (fun _let_3 bool) (hoare_122391849derivs state) (hAPP _let_4 _let_3 (hAPP _let_5 (fun _let_4 _let_3) (image pname _let_1) (hAPP _let_2 _let_5 (hAPP (fun com _let_1) (fun _let_2 _let_5) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body))))) (hAPP (fun _let_3 bool) _let_0 (hAPP (fun _let_3 bool) (fun (fun _let_3 bool) _let_0) (image _let_3 bool) _let_6) _let_6)))))))), fTrue, (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun (hoare_509422987triple state) bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (finite_finite (hoare_509422987triple state)))) (hAPP _let_2 _let_0 (hAPP _let_2 (fun _let_2 _let_0) (image _let_1 bool) _let_3) _let_3))))) ) 15.88/13.61 ( bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun (hoare_509422987triple state) bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (finite_finite (hoare_509422987triple state)))) (hAPP _let_2 _let_0 (hAPP _let_2 (fun _let_2 _let_0) (image _let_1 bool) _let_3) _let_3))))), fTrue, (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_1))) (let ((_let_6 (hAPP _let_3 (fun _let_3 bool) (hoare_122391849derivs state) (hAPP _let_4 _let_3 (hAPP _let_5 (fun _let_4 _let_3) (image pname _let_1) (hAPP _let_2 _let_5 (hAPP (fun com _let_1) (fun _let_2 _let_5) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body))))) (hAPP (fun _let_3 bool) _let_0 (hAPP (fun _let_3 bool) (fun (fun _let_3 bool) _let_0) (image _let_3 bool) _let_6) _let_6)))))))) ) 15.88/13.61 ( bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (hAPP _let_2 _let_0 (hAPP _let_2 (fun _let_2 _let_0) (image _let_1 bool) (hAPP _let_2 _let_2 (hAPP (fun _let_1 (fun _let_2 bool)) (fun _let_2 _let_2) (combc _let_1 _let_2 bool) (member _let_1)) fa)) (bot_bot _let_2))))), fFalse, (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun (hoare_509422987triple state) bool))) (let ((_let_2 (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) fa))) (hAPP (fun _let_1 bool) _let_0 (hAPP (fun _let_1 bool) (fun (fun _let_1 bool) _let_0) (image _let_1 bool) _let_2) _let_2)))) ) 15.88/13.62 ( bool, skv_68, skv_67, (bot_bot (fun bool bool)) ) 15.88/13.62 ( com, wt, y, wt ) 15.88/13.62 ( com, wt, skv_5, wt ) 15.88/13.62 ( com, wt, skv_5, (bot_bot (fun com bool)) ) 15.88/13.62 ( com, wt, skv_35, wt ) 15.88/13.62 ( com, wt, skv_35, (bot_bot (fun com bool)) ) 15.88/13.62 ( com, wt, skv_37, wt ) 15.88/13.62 ( com, (bot_bot (fun com bool)), skv_5, wt ) 15.88/13.62 ( com, (bot_bot (fun com bool)), skv_35, wt ) 15.88/13.62 ( com, (bot_bot (fun com bool)), skv_65, (bot_bot (fun com bool)) ) 15.88/13.62 ( com, (bot_bot (fun com bool)), skv_65, skv_66 ) 15.88/13.62 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))), y, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 15.88/13.62 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))), y, (hAPP (fun com (option com)) (fun com bool) (dom com com) (some com)) ) 15.88/13.62 ( com, (hAPP (fun com (option com)) (fun com bool) (dom com com) (some com)), y, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun com bool))) (hAPP _let_3 _let_4 (hAPP _let_1 (fun _let_3 _let_4) (image pname com) (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body)) (hAPP _let_2 _let_3 (dom pname com) body))))))) ) 16.01/13.62 ( com, skv_66, skv_65, (bot_bot (fun com bool)) ) 16.01/13.62 ( (option com), (let ((_let_0 (option com))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun _let_0 bool))) (hAPP _let_2 _let_3 (hAPP _let_1 (fun _let_2 _let_3) (image pname _let_0) body) (hAPP _let_1 _let_2 (dom pname com) body)))))), (hAPP com (option com) (some com) y), (let ((_let_0 (option com))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun _let_0 bool))) (hAPP _let_2 _let_3 (hAPP _let_1 (fun _let_2 _let_3) (image pname _let_0) body) (hAPP _let_1 _let_2 (dom pname com) body)))))) ) 16.01/13.62 ( (fun bool bool), (finite_finite bool), (bot_bot (fun bool bool)), (finite_finite bool) ) 16.01/13.62 ( (fun bool bool), (finite_finite bool), (bot_bot (fun bool bool)), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)) ) 16.01/13.62 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), (bot_bot (fun bool bool)), (finite_finite bool) ) 16.01/13.62 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6), fNot, (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6) ) 16.01/13.62 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.01/13.62 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn, skv_1 ) 16.01/13.62 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.01/13.62 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3, skv_2 ) 16.01/13.62 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_12, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.01/13.62 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_38, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.01/13.62 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_55, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.01/13.62 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_56, skv_2 ) 16.01/13.62 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_57, skv_1 ) 16.01/13.62 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_61, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.01/13.62 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_61, skv_62 ) 16.01/13.62 ( pname, (bot_bot (fun pname bool)), pn, skv_2 ) 16.01/13.62 ( pname, (bot_bot (fun pname bool)), skv_3, (bot_bot (fun pname bool)) ) 16.01/13.62 ( pname, skv_1, pn, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.01/13.62 ( pname, skv_1, skv_57, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.01/13.62 ( pname, skv_1, skv_57, skv_1 ) 16.01/13.62 ( pname, skv_2, pn, (bot_bot (fun pname bool)) ) 16.01/13.62 ( pname, skv_2, pn, skv_2 ) 16.01/13.62 ( pname, skv_2, skv_3, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.01/13.62 ( pname, skv_2, skv_43, skv_2 ) 16.01/13.62 ( pname, skv_2, skv_44, skv_2 ) 16.01/13.62 ( pname, skv_2, skv_56, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.01/13.62 ( pname, skv_2, skv_56, skv_2 ) 16.01/13.62 ( pname, skv_62, skv_61, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.01/13.62 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.01/13.62 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), fa ) 16.01/13.62 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 16.01/13.62 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.01/13.62 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) 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((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_4, (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_4, fa ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_7, (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_7, fa ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_7, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_39, (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_39, fa ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_41, fa ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_41, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_58, fa ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_58, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_73, fa ) 16.01/13.62 ( (hoare_509422987triple state), fa, skv_73, skv_74 ) 16.01/13.62 ( (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), fa ) 16.01/13.62 ( (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), skv_7, fa ) 16.01/13.62 ( (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), skv_33, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 16.01/13.62 ( (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), skv_60, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 16.01/13.62 ( (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), skv_75, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 16.01/13.62 ( (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), skv_75, skv_76 ) 16.01/13.62 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 16.01/13.62 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), skv_11, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 16.01/13.62 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), skv_34, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 16.01/13.63 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), skv_58, fa ) 16.01/13.63 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.01/13.63 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 16.01/13.63 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 16.01/13.63 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 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body))))))) ) 16.01/13.63 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), skv_11, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 16.01/13.63 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), skv_13, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 16.01/13.63 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), skv_41, fa ) 16.01/13.63 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), skv_59, (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.01/13.63 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), skv_69, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com 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) 16.01/13.64 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 16.01/13.64 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 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pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_1)) ) 16.01/13.67 ( (fun pname bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) skv_2)) ) 16.01/13.67 ( (fun pname bool), (hAPP pname (fun (fun pname bool) bool) (member pname) skv_3) ) 16.01/13.67 ( (fun (fun pname bool) bool), (let ((_let_0 (fun pname bool))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))) ) 16.01/13.67 ( (fun (fun pname bool) bool), (finite_finite (fun pname bool)) ) 16.01/13.67 ( (fun (fun pname bool) bool), (bot_bot (fun (fun (fun pname bool) bool) bool)) ) 16.01/13.67 ( (fun com bool), (finite_finite com) ) 16.01/13.67 ( (fun com bool), (let ((_let_0 (fun com bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) wt)) ) 16.01/13.67 ( (fun com bool), (hAPP com (fun (fun com bool) bool) (member com) skv_5) ) 16.01/13.67 ( (fun com bool), (bot_bot (fun (fun com bool) bool)) ) 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(bot_bot _let_1)))) ) 16.01/13.67 ( state, (bot_bot (fun (hoare_509422987triple state) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 16.01/13.67 ( state, fa, (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.01/13.67 ( state, fa, fa ) 16.01/13.67 ( state, fa, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 16.01/13.67 ( state, fa, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 16.01/13.67 ( state, fa, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 16.01/13.67 ( state, fa, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) fa))) ) 16.01/13.67 ( state, fa, skv_64 ) 16.01/13.67 ( state, fa, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) skv_63) skv_64))) ) 16.01/13.67 ( state, fa, skv_94 ) 16.01/13.67 ( state, (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), fa ) 16.01/13.67 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.01/13.68 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), fa ) 16.12/13.70 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))) ) 16.12/13.70 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 16.12/13.70 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 16.12/13.70 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.12/13.70 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), fa ) 16.12/13.70 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 16.12/13.70 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun 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com)) _let_3 (dom pname com) body))))))) ) 16.12/13.70 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_55))) (bot_bot _let_1)))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.12/13.70 ( state, skv_70, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 16.12/13.70 ( state, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) skv_69) skv_70))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 16.12/13.70 ( state, skv_95, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 16.12/13.70 ) 16.12/13.70 (instantiation (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 _let_0))) (let ((_let_2 (insert X_a))) (let ((_let_3 (bot_bot _let_0))) (let ((_let_4 (ti X_a A_3))) (let ((_let_5 (ti X_a D_1))) (let ((_let_6 (ti X_a C_1))) (let ((_let_7 (ti X_a B_1))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (= (= (hAPP _let_0 _let_0 (hAPP X_a _let_1 _let_2 A_3) (hAPP _let_0 _let_0 (hAPP X_a _let_1 _let_2 B_1) _let_3)) (hAPP _let_0 _let_0 (hAPP X_a _let_1 _let_2 C_1) (hAPP _let_0 _let_0 (hAPP X_a _let_1 _let_2 D_1) _let_3))) (or (and (= _let_4 _let_5) (= _let_6 _let_7)) (and (= _let_4 _let_6) (= _let_5 _let_7)))) ))))))))) 16.12/13.70 ( bool, fTrue, fTrue, fTrue, fTrue ) 16.12/13.70 ( bool, fTrue, fTrue, fTrue, fFalse ) 16.12/13.70 ( bool, fFalse, fFalse, fFalse, fTrue ) 16.12/13.70 ( bool, skv_6, skv_6, skv_6, skv_6 ) 16.12/13.70 ( bool, skv_6, skv_6, skv_6, skv_67 ) 16.12/13.70 ( bool, skv_67, skv_67, skv_67, skv_6 ) 16.12/13.70 ( com, y, y, y, y ) 16.12/13.70 ( com, y, y, y, skv_5 ) 16.12/13.70 ( com, (hAPP pname com body_1 pn), (hAPP pname com body_1 pn), (hAPP pname com body_1 pn), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))) ) 16.12/13.71 ( com, skv_5, skv_5, skv_5, y ) 16.12/13.71 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), (hAPP pname com body_1 pn) ) 16.12/13.71 ( com, (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname com (hAPP _let_2 _let_1 (hAPP (fun _let_0 com) (fun _let_2 _let_1) (combb _let_0 com pname) (the com)) body) pn)))) ) 16.12/13.71 ( com, skv_65, skv_65, skv_65, skv_65 ) 16.12/13.71 ( (fun bool bool), fNot, fNot, fNot, (bot_bot (fun bool bool)) ) 16.12/13.71 ( (fun bool bool), (bot_bot (fun bool bool)), (bot_bot (fun bool bool)), (bot_bot (fun bool bool)), fNot ) 16.12/13.71 ( (fun bool bool), (bot_bot (fun bool bool)), (bot_bot (fun bool bool)), (bot_bot (fun bool bool)), (bot_bot (fun bool bool)) ) 16.12/13.71 ( pname, pn, pn, pn, pn ) 16.12/13.71 ( pname, pn, pn, pn, skv_3 ) 16.12/13.71 ( pname, skv_3, skv_3, skv_3, pn ) 16.12/13.71 ( pname, skv_61, skv_61, skv_61, skv_61 ) 16.12/13.71 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 16.12/13.71 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)) ) 16.12/13.71 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (let ((_let_0 (option com))) (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP _let_0 com (the com) (hAPP pname _let_0 body skv_3)))) ) 16.12/13.71 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 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(hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 16.12/13.71 ( (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (hAPP pname _let_1 (hAPP _let_2 _let_4 (hAPP (fun com _let_1) (fun _let_2 _let_4) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) pn)))))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (hAPP pname _let_1 (hAPP _let_2 _let_4 (hAPP (fun com _let_1) (fun _let_2 _let_4) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) pn)))))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (hAPP pname _let_1 (hAPP _let_2 _let_4 (hAPP (fun com _let_1) (fun _let_2 _let_4) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) pn)))))), skv_7 ) 16.12/13.71 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let 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(hoare_509422987triple state), skv_63, skv_63, skv_63, skv_63 ) 16.12/13.71 ( (hoare_509422987triple state), skv_63, skv_63, skv_63, skv_69 ) 16.12/13.71 ( (hoare_509422987triple state), skv_69, skv_69, skv_69, skv_63 ) 16.12/13.71 ( (hoare_509422987triple state), skv_71, skv_71, skv_71, skv_71 ) 16.12/13.71 ( (hoare_509422987triple state), skv_71, skv_71, skv_71, skv_73 ) 16.12/13.71 ( (hoare_509422987triple state), skv_73, skv_73, skv_73, skv_71 ) 16.12/13.71 ( (hoare_509422987triple state), skv_75, skv_75, skv_75, skv_75 ) 16.12/13.71 ( (fun pname (option com)), body, body, body, body ) 16.12/13.71 ( (fun (hoare_509422987triple state) bool), (bot_bot (fun (hoare_509422987triple state) bool)), (bot_bot (fun (hoare_509422987triple state) bool)), (bot_bot (fun (hoare_509422987triple state) bool)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.12/13.71 ( (fun (hoare_509422987triple state) bool), (bot_bot (fun (hoare_509422987triple state) bool)), (bot_bot (fun 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bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.12/13.71 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) 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(hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 16.12/13.71 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 16.12/13.71 ( (fun (fun (hoare_509422987triple state) bool) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))) ) 16.12/13.71 ( (fun (fun (hoare_509422987triple state) bool) bool), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 16.12/13.72 ( (fun (fun (hoare_509422987triple state) bool) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)), (finite_finite (hoare_509422987triple state)) ) 16.12/13.72 ( (fun (fun (hoare_509422987triple state) bool) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 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(bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)), (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 16.12/13.72 ( (fun pname bool), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.12/13.72 ( (fun pname bool), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (bot_bot (fun pname bool)) ) 16.12/13.72 ( (fun pname bool), (bot_bot (fun pname bool)), (bot_bot (fun pname bool)), (bot_bot (fun pname bool)), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 16.12/13.72 ( (fun pname bool), skv_1, skv_1, skv_1, skv_1 ) 16.12/13.72 ( (fun (fun pname bool) bool), (finite_finite pname), (finite_finite pname), (finite_finite pname), (finite_finite pname) ) 16.12/13.72 ( (fun com bool), wt, wt, wt, (bot_bot (fun com bool)) ) 16.12/13.72 ( (fun com bool), (bot_bot (fun com bool)), (bot_bot (fun com bool)), (bot_bot (fun com bool)), wt ) 16.12/13.72 ( (fun com bool), (bot_bot (fun com bool)), (bot_bot (fun com bool)), (bot_bot (fun com bool)), (bot_bot (fun com bool)) ) 16.12/13.72 ) 16.12/13.72 (instantiation (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun X_a bool))) (let ((_let_2 (fun _let_1 _let_1))) (let ((_let_3 (fun X_a _let_0))) (let ((_let_4 (fun X_a _let_1))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_3 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 A_3))) (= (hAPP _let_1 _let_1 (collect X_a) (hAPP _let_1 _let_1 (hAPP _let_3 _let_2 (combs X_a bool bool) (hAPP _let_1 _let_3 (hAPP (fun bool _let_0) (fun _let_1 _let_3) (combb bool _let_0 X_a) fconj) (hAPP X_a _let_1 (hAPP _let_4 _let_4 (combc X_a X_a bool) (fequal X_a)) A_3))) P_1)) (hAPP _let_1 _let_1 (hAPP X_a _let_2 (insert X_a) A_3) (bot_bot _let_1)))) )))))) 16.12/13.72 ( bool, fNot, skv_6 ) 16.12/13.72 ( bool, fNot, skv_50 ) 16.12/13.72 ( bool, fNot, skv_78 ) 16.12/13.72 ( bool, fNot, skv_84 ) 16.12/13.72 ( bool, (combi bool), fTrue ) 16.12/13.72 ( bool, (combi bool), fFalse ) 16.12/13.72 ( bool, (combi bool), skv_51 ) 16.12/13.72 ( bool, (combi bool), skv_78 ) 16.12/13.72 ( bool, (combi bool), skv_92 ) 16.12/13.72 ( bool, (bot_bot (fun bool bool)), skv_50 ) 16.12/13.72 ( bool, (bot_bot (fun bool bool)), skv_92 ) 16.12/13.72 ( bool, (let ((_let_0 (fun bool bool))) (hAPP _let_0 _let_0 (hAPP (fun bool (fun _let_0 bool)) (fun _let_0 _let_0) (combc bool _let_0 bool) (member bool)) fNot)), skv_6 ) 16.12/13.72 ( bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fTrue ) 16.12/13.72 ( bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fFalse ) 16.12/13.72 ( com, wt, y ) 16.12/13.72 ( com, wt, (hAPP pname com body_1 skv_3) ) 16.12/13.72 ( com, wt, skv_5 ) 16.12/13.72 ( com, wt, skv_36 ) 16.12/13.72 ( com, wt, skv_83 ) 16.12/13.72 ( com, (bot_bot (fun com bool)), skv_36 ) 16.12/13.72 ( com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun com bool))) (let ((_let_4 (fun com _let_2))) (hAPP (fun _let_0 bool) _let_3 (hAPP _let_4 (fun (fun _let_0 bool) _let_3) (combc com (fun _let_0 bool) bool) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_4) (combb _let_0 _let_2 com) (member _let_0)) hoare_Mirabelle_MGT)) fa)))))), y ) 16.12/13.72 ( com, (let ((_let_0 (fun com bool))) (hAPP _let_0 _let_0 (hAPP (fun com (fun _let_0 bool)) (fun _let_0 _let_0) (combc com _let_0 bool) (member com)) wt)), skv_5 ) 16.12/13.72 ( com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun com bool))) (hAPP _let_1 _let_3 (hAPP _let_2 (fun _let_1 _let_3) (combb _let_0 bool com) (hAPP _let_2 _let_2 (hAPP (fun _let_0 (fun _let_2 bool)) (fun _let_2 _let_2) (combc _let_0 _let_2 bool) (member _let_0)) fa)) hoare_Mirabelle_MGT))))), y ) 16.12/13.72 ( com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun com bool))) (hAPP _let_1 _let_2 (hAPP (fun _let_0 bool) (fun _let_1 _let_2) (combb _let_0 bool com) fa) hoare_Mirabelle_MGT)))), y ) 16.12/13.72 ( com, (let ((_let_0 (fun com bool))) (let ((_let_1 (fun com com))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb com bool com) wt) (combi com)))), y ) 16.12/13.72 ( (fun bool bool), (finite_finite bool), fNot ) 16.12/13.72 ( (fun bool bool), (finite_finite bool), (bot_bot (fun bool bool)) ) 16.12/13.72 ( (fun bool bool), (finite_finite bool), skv_68 ) 16.12/13.72 ( (fun bool bool), (finite_finite bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 _let_0 (hAPP bool (fun _let_0 _let_0) (insert bool) skv_67) skv_68)) ) 16.12/13.72 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), fNot ) 16.12/13.72 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), (bot_bot (fun bool bool)) ) 16.12/13.72 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6), fNot ) 16.12/13.72 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6), (bot_bot (fun bool bool)) ) 16.12/13.72 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (ord_less_eq _let_0)) (bot_bot _let_0)))), fNot ) 16.12/13.72 ( (fun bool 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(member bool) skv_67), skv_68 ) 16.12/13.72 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn ) 16.12/13.72 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3 ) 16.12/13.72 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_96 ) 16.12/13.72 ( pname, (bot_bot (fun pname bool)), skv_96 ) 16.12/13.72 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), pn ) 16.12/13.72 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), skv_3 ) 16.12/13.72 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple 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(let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun (fun _let_0 _let_0) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun (fun _let_0 bool) (fun _let_0 bool)))) (hAPP _let_1 (fun (fun _let_1 bool) bool) (member _let_1) (hAPP _let_0 _let_1 (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun _let_4 _let_4))) (let ((_let_6 (fun pname bool))) (let ((_let_7 (fun pname _let_1))) (let ((_let_8 (fun _let_5 bool))) (hAPP _let_4 _let_8 (hAPP (fun _let_1 _let_5) (fun _let_4 _let_8) (image _let_1 _let_5) (insert _let_1)) (hAPP _let_6 _let_4 (hAPP _let_7 (fun _let_6 _let_4) (image pname _let_1) (hAPP _let_2 _let_7 (hAPP (fun com _let_1) (fun _let_2 _let_7) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_6 (dom pname com) body)))))))))))) ) 16.34/13.84 ( (fun (option com) bool), (let ((_let_0 (option com))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 (some com) y))), (let ((_let_0 (option com))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun _let_0 bool))) (hAPP _let_2 _let_3 (hAPP _let_1 (fun _let_2 _let_3) (image pname _let_0) body) (hAPP _let_1 _let_2 (dom pname com) body)))))) ) 16.34/13.84 ) 16.34/13.84 (instantiation (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun X_a _let_0))) (let ((_let_2 (fun X_a (fun X_a bool)))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (hBOOL (hAPP X_a bool P_1 A_3)) (= (bot_bot _let_0) (hAPP _let_0 _let_0 (collect X_a) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs X_a bool bool) (hAPP _let_0 _let_1 (hAPP (fun bool _let_0) (fun _let_0 _let_1) (combb bool _let_0 X_a) fconj) (hAPP X_a _let_0 (hAPP _let_2 _let_2 (combc X_a X_a bool) (fequal X_a)) A_3))) P_1))))) )))) 16.34/13.84 ( bool, fNot, skv_6 ) 16.34/13.84 ( bool, fNot, skv_50 ) 16.34/13.84 ( bool, fNot, skv_78 ) 16.34/13.84 ( bool, fNot, skv_84 ) 16.34/13.84 ( bool, (combi bool), fTrue ) 16.34/13.84 ( bool, (combi bool), fFalse ) 16.34/13.84 ( bool, (combi bool), skv_51 ) 16.34/13.84 ( bool, (combi bool), skv_78 ) 16.34/13.84 ( bool, (combi bool), skv_92 ) 16.34/13.84 ( bool, (bot_bot (fun bool bool)), skv_50 ) 16.34/13.84 ( bool, (bot_bot (fun bool bool)), skv_92 ) 16.34/13.84 ( bool, (let ((_let_0 (fun bool bool))) (hAPP _let_0 _let_0 (hAPP (fun bool (fun _let_0 bool)) (fun _let_0 _let_0) (combc bool _let_0 bool) (member bool)) fNot)), skv_6 ) 16.34/13.84 ( bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fTrue ) 16.34/13.84 ( bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fFalse ) 16.34/13.84 ( com, wt, y ) 16.34/13.84 ( com, wt, (hAPP pname com body_1 skv_3) ) 16.34/13.84 ( com, wt, skv_5 ) 16.34/13.84 ( com, wt, skv_36 ) 16.34/13.84 ( com, wt, skv_83 ) 16.34/13.84 ( com, (bot_bot (fun com bool)), skv_36 ) 16.34/13.84 ( com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun com bool))) (let ((_let_4 (fun com _let_2))) (hAPP (fun _let_0 bool) _let_3 (hAPP _let_4 (fun (fun _let_0 bool) _let_3) (combc com (fun _let_0 bool) bool) (hAPP _let_1 _let_4 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_4) (combb _let_0 _let_2 com) (member _let_0)) hoare_Mirabelle_MGT)) fa)))))), y ) 16.34/13.85 ( com, (let ((_let_0 (fun com bool))) (hAPP _let_0 _let_0 (hAPP (fun com (fun _let_0 bool)) (fun _let_0 _let_0) (combc com _let_0 bool) (member com)) wt)), skv_5 ) 16.34/13.85 ( com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun com bool))) (hAPP _let_1 _let_3 (hAPP _let_2 (fun _let_1 _let_3) (combb _let_0 bool com) (hAPP _let_2 _let_2 (hAPP (fun _let_0 (fun _let_2 bool)) (fun _let_2 _let_2) (combc _let_0 _let_2 bool) (member _let_0)) fa)) hoare_Mirabelle_MGT))))), y ) 16.34/13.85 ( com, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun com _let_0))) (let ((_let_2 (fun com bool))) (hAPP _let_1 _let_2 (hAPP (fun _let_0 bool) (fun _let_1 _let_2) (combb _let_0 bool com) fa) hoare_Mirabelle_MGT)))), y ) 16.34/13.85 ( com, (let ((_let_0 (fun com bool))) (let ((_let_1 (fun com com))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb com bool com) wt) (combi com)))), y ) 16.34/13.85 ( (fun bool bool), (finite_finite bool), fNot ) 16.34/13.85 ( (fun bool bool), (finite_finite bool), (bot_bot (fun bool bool)) ) 16.34/13.85 ( (fun bool bool), (finite_finite bool), skv_68 ) 16.34/13.85 ( (fun bool bool), (finite_finite bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 _let_0 (hAPP bool (fun _let_0 _let_0) (insert bool) skv_67) skv_68)) ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), fNot ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fNot)), (bot_bot (fun bool bool)) ) 16.34/13.85 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6), fNot ) 16.34/13.85 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_6), (bot_bot (fun bool bool)) ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_0 (fun _let_0 bool) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (ord_less_eq _let_0)) (bot_bot _let_0)))), fNot ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb _let_0 bool _let_0) (finite_finite bool)) (collect bool))))), (hAPP bool (fun bool bool) (combk bool bool) fFalse) ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_0))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb _let_0 bool _let_0) (hAPP _let_0 _let_1 (ord_less_eq _let_0) fNot)) (collect bool))))), (hAPP bool (fun bool bool) (combk bool bool) fFalse) ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (fun (fun bool bool) bool))) (let ((_let_1 (fun (fun bool bool) (fun bool bool)))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb (fun bool bool) bool (fun bool bool)) (hAPP bool _let_0 (member bool) skv_6)) (hAPP (fun bool bool) _let_1 (image bool bool) (combi bool))))), fNot ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), fNot ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (bot_bot _let_0))), (bot_bot (fun bool bool)) ) 16.34/13.85 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) fTrue), (combi bool) ) 16.34/13.85 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) fTrue), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun pname bool))) (let ((_let_2 (finite_finite pname))) (let ((_let_3 (fun _let_1 bool))) (hAPP _let_3 _let_0 (hAPP _let_3 (fun _let_3 _let_0) (image _let_1 bool) _let_2) _let_2))))) ) 16.34/13.85 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) fFalse), (combi bool) ) 16.34/13.85 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) fFalse), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (hAPP _let_1 (fun (fun _let_1 bool) bool) (member _let_1) (hAPP com _let_1 hoare_Mirabelle_MGT y)))) (hAPP (fun (fun _let_1 bool) bool) _let_0 (hAPP (fun (fun _let_1 bool) bool) (fun (fun (fun _let_1 bool) bool) _let_0) (image (fun _let_1 bool) bool) _let_2) _let_2)))) ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP bool (fun (fun bool bool) bool) (member bool) (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) fa)))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun (hoare_509422987triple state) bool))) (let ((_let_2 (hAPP _let_1 (fun _let_1 bool) (ord_less_eq _let_1) fa))) (hAPP (fun _let_1 bool) _let_0 (hAPP (fun _let_1 bool) (fun (fun _let_1 bool) _let_0) (image _let_1 bool) _let_2) _let_2)))) ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP bool (fun (fun bool bool) bool) (member bool) (hAPP _let_4 bool (hAPP _let_4 (fun _let_4 bool) (ord_less_eq _let_4) fa) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_1))) (let ((_let_6 (hAPP _let_3 (fun _let_3 bool) (hoare_122391849derivs state) (hAPP _let_4 _let_3 (hAPP _let_5 (fun _let_4 _let_3) (image pname _let_1) (hAPP _let_2 _let_5 (hAPP (fun com _let_1) (fun _let_2 _let_5) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body))))) (hAPP (fun _let_3 bool) _let_0 (hAPP (fun _let_3 bool) (fun (fun _let_3 bool) _let_0) (image _let_3 bool) _let_6) _let_6)))))))) ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP bool (fun (fun bool bool) bool) (member bool) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))) fa))))))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun (hoare_509422987triple state) bool))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (finite_finite (hoare_509422987triple state)))) (hAPP _let_2 _let_0 (hAPP _let_2 (fun _let_2 _let_0) (image _let_1 bool) _let_3) _let_3))))) ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP bool (fun (fun bool bool) bool) (member bool) (hAPP _let_2 bool (hAPP _let_2 (fun _let_2 bool) (hoare_122391849derivs state) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))) (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2))))))))), (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (hAPP _let_2 _let_0 (hAPP _let_2 (fun _let_2 _let_0) (image _let_1 bool) (hAPP _let_2 _let_2 (hAPP (fun _let_1 (fun _let_2 bool)) (fun _let_2 _let_2) (combc _let_1 _let_2 bool) (member _let_1)) fa)) (bot_bot _let_2))))) ) 16.34/13.85 ( (fun bool bool), (let ((_let_0 (fun bool bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) (combi bool))), (bot_bot (fun bool bool)) ) 16.34/13.85 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_49), fNot ) 16.34/13.85 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_49), (bot_bot (fun bool bool)) ) 16.34/13.85 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_51), fNot ) 16.34/13.85 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_52), (combi bool) ) 16.34/13.85 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_67), (bot_bot (fun bool bool)) ) 16.34/13.85 ( (fun bool bool), (hAPP bool (fun (fun bool bool) bool) (member bool) skv_67), skv_68 ) 16.34/13.85 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), pn ) 16.34/13.85 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_3 ) 16.34/13.85 ( pname, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), skv_96 ) 16.34/13.85 ( pname, (bot_bot (fun pname bool)), skv_96 ) 16.34/13.85 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), pn ) 16.34/13.85 ( pname, (let ((_let_0 (fun pname bool))) (hAPP _let_0 _let_0 (hAPP (fun pname (fun _let_0 bool)) (fun _let_0 _let_0) (combc pname _let_0 bool) (member pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body))), skv_3 ) 16.34/13.85 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 16.34/13.85 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), skv_40 ) 16.34/13.85 ( (hoare_509422987triple state), (bot_bot (fun (hoare_509422987triple state) bool)), skv_100 ) 16.34/13.85 ( (hoare_509422987triple state), fa, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 16.34/13.85 ( (hoare_509422987triple state), fa, skv_4 ) 16.34/13.85 ( (hoare_509422987triple state), fa, skv_7 ) 16.34/13.85 ( (hoare_509422987triple state), fa, skv_40 ) 16.34/13.85 ( (hoare_509422987triple state), fa, skv_42 ) 16.34/13.85 ( (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), skv_81 ) 16.34/13.85 ( (hoare_509422987triple state), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))))))), skv_100 ) 16.34/13.85 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let 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state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) fa))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 16.34/13.85 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) fa))), skv_4 ) 16.34/13.85 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) fa))), skv_7 ) 16.34/13.85 ( (hoare_509422987triple state), (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun _let_0 bool) (fequal _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))), skv_21 ) 16.34/13.85 ( (hoare_509422987triple state), (let 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(option com)) _let_4 (dom pname com) body)))) (hAPP _let_0 _let_3 (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))))))))), skv_76 ) 16.34/13.87 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun (fun _let_0 bool) bool))) (let ((_let_3 (fun (fun _let_0 bool) (fun _let_0 bool)))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_2 (fun _let_3 _let_2) (combb (fun _let_0 bool) bool (fun _let_0 bool)) (hAPP (fun _let_0 bool) _let_2 (hoare_122391849derivs state) (hAPP _let_4 (fun _let_0 bool) (hAPP _let_5 (fun _let_4 (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_5 (hAPP (fun com _let_0) (fun _let_1 _let_5) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_4 (dom pname com) body)))) (hAPP _let_0 _let_3 (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))))))))), (let ((_let_0 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body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 16.48/13.97 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), skv_73, skv_74 ) 16.48/13.97 ( (hoare_509422987triple state), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.48/13.97 ( (hoare_509422987triple state), skv_4, skv_7, fa ) 16.48/13.97 ( (hoare_509422987triple state), skv_7, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.48/13.97 ( (hoare_509422987triple state), skv_7, skv_4, fa ) 16.48/13.97 ( (hoare_509422987triple state), skv_7, skv_7, fa ) 16.48/13.97 ( (hoare_509422987triple state), skv_11, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple 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16.48/13.97 ( (hoare_509422987triple state), skv_34, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 16.48/13.98 ( (hoare_509422987triple state), skv_39, skv_7, fa ) 16.48/13.98 ( (hoare_509422987triple state), skv_41, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.48/13.98 ( (hoare_509422987triple state), skv_41, skv_7, fa ) 16.48/13.98 ( (hoare_509422987triple state), skv_58, skv_7, fa ) 16.48/13.98 ( (hoare_509422987triple state), skv_58, (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP pname _let_0 (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) pn)))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 16.48/13.98 ( (hoare_509422987triple state), skv_59, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.48/13.98 ( (hoare_509422987triple state), skv_60, skv_7, fa ) 16.48/13.98 ( (hoare_509422987triple state), skv_69, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.48/13.98 ( (hoare_509422987triple state), skv_71, (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y), (bot_bot (fun (hoare_509422987triple state) bool)) ) 16.48/13.98 ( (hoare_509422987triple state), skv_73, skv_7, fa ) 16.48/13.98 ( (hoare_509422987triple state), skv_75, skv_7, fa ) 16.48/13.98 ( (fun (hoare_509422987triple state) bool), (bot_bot (fun (hoare_509422987triple state) bool)), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))) ) 16.48/13.98 ( (fun (hoare_509422987triple state) bool), (bot_bot (fun (hoare_509422987triple state) bool)), fa, (let ((_let_0 (fun (hoare_509422987triple state) 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(hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))))))) ) 16.48/13.98 ( (fun (hoare_509422987triple state) bool), fa, fa, (finite_finite (hoare_509422987triple state)) ) 16.48/13.98 ( (fun (hoare_509422987triple state) bool), fa, fa, (bot_bot (fun (fun (hoare_509422987triple state) bool) bool)) ) 16.48/13.98 ( (fun (hoare_509422987triple state) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun 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(hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))), fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))) ) 16.48/13.98 ( (fun (hoare_509422987triple state) bool), skv_15, fa, (let ((_let_0 (fun (hoare_509422987triple state) bool))) (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) fa)) ) 16.48/13.98 ( (fun (hoare_509422987triple state) bool), skv_16, fa, (let ((_let_0 (hoare_509422987triple state))) (hAPP _let_0 (fun (fun _let_0 bool) bool) (member _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y))) ) 16.48/13.98 ( (fun (hoare_509422987triple state) bool), skv_17, fa, (finite_finite (hoare_509422987triple state)) ) 16.48/13.98 ( (fun pname bool), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (finite_finite pname) ) 16.48/13.98 ( (fun pname bool), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (bot_bot (fun (fun pname bool) bool)) ) 16.48/13.98 ( (fun pname bool), (bot_bot (fun pname bool)), (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (finite_finite pname) ) 16.48/13.98 ( (fun pname bool), skv_1, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (finite_finite pname) ) 16.48/13.98 ( (fun pname bool), skv_18, (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body), (finite_finite pname) ) 16.48/13.98 ) 16.48/13.98 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (hAPP X_a X_c B_1_1 (ti X_a B_2_1)) (hAPP X_a X_c B_1_1 B_2_1)) ) 16.48/13.98 ( bool, bool, (combi bool), fTrue ) 16.48/13.98 ( bool, bool, (combi bool), fFalse ) 16.48/13.98 ( bool, bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fTrue ) 16.58/13.98 ( bool, bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (combi bool))) (hAPP _let_0 _let_0 (hAPP _let_0 (fun _let_0 _let_0) (combb bool bool bool) _let_1) _let_1))), fFalse ) 16.58/13.98 ( bool, (fun bool bool), (fequal bool), fTrue ) 16.58/13.98 ( bool, (fun bool bool), (fequal bool), fFalse ) 16.58/13.98 ( bool, (fun bool bool), (combk bool bool), fFalse ) 16.58/13.98 ( bool, (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb bool _let_0 bool) (combk bool bool)) (combi bool)))), fFalse ) 16.58/13.98 ( bool, (fun bool bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun bool _let_0))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 _let_0) (fun _let_1 _let_1) (combb _let_0 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bool), (combk bool pname), fFalse ) 16.58/13.98 ( bool, (fun pname bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun pname bool))) (let ((_let_2 (fun bool _let_1))) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb bool _let_1 bool) (combk bool pname)) (combi bool))))), fFalse ) 16.58/13.98 ( bool, (fun pname bool), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun bool _let_0))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 _let_0) (fun _let_1 _let_1) (combb _let_0 _let_0 bool) (collect pname)) (combk bool pname)))), fFalse ) 16.58/13.98 ( bool, (fun (fun pname bool) bool), (combk bool (fun pname bool)), fFalse ) 16.58/13.98 ( bool, (fun com bool), (combk bool com), fFalse ) 16.58/13.98 ( bool, (fun com bool), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun com bool))) (let ((_let_2 (fun bool _let_1))) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb bool _let_1 bool) (combk bool com)) (combi bool))))), fFalse ) 16.58/13.98 ( bool, (fun com bool), (let 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(hAPP _let_4 (fun _let_2 _let_5) (combc _let_3 _let_2 bool) (hAPP _let_1 _let_4 (combb _let_0 bool _let_2) (hAPP _let_0 _let_1 (ord_less_eq _let_0) fa))) (hAPP (fun pname (option com)) _let_2 (dom pname com) body)))))))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (hAPP _let_4 (fun (fun pname bool) (fun _let_1 bool)) (image pname _let_1) (hAPP _let_2 _let_4 (hAPP (fun com _let_1) (fun _let_2 _let_4) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)))))))) ) 17.19/14.39 ( (fun (fun pname bool) (fun (hoare_509422987triple state) bool)), (fun (fun (hoare_509422987triple state) bool) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun _let_2 _let_0))) (let ((_let_4 (fun _let_3 (fun _let_2 _let_1)))) (let ((_let_5 (fun _let_3 _let_1))) (hAPP _let_2 _let_5 (hAPP _let_4 (fun _let_2 _let_5) (combc _let_3 _let_2 _let_1) (hAPP (fun _let_0 _let_1) _let_4 (combb _let_0 _let_1 _let_2) (hoare_122391849derivs state))) (hAPP (fun pname (option com)) _let_2 (dom pname com) body)))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_2 (fun (fun pname bool) (fun _let_0 bool)) (image pname _let_0) (hAPP _let_1 _let_2 (hAPP (fun com _let_0) (fun _let_1 _let_2) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1))))) ) 17.19/14.39 ( (fun (fun pname bool) (fun (hoare_509422987triple state) bool)), (fun (fun pname bool) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun pname bool))) (hAPP _let_1 (fun (fun _let_2 _let_0) (fun _let_2 bool)) (combb _let_0 bool _let_2) (hAPP _let_0 _let_1 (ord_less_eq _let_0) fa))))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (hAPP _let_4 (fun (fun pname bool) (fun _let_1 bool)) (image pname _let_1) (hAPP _let_2 _let_4 (hAPP (fun com _let_1) (fun _let_2 _let_4) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)))))))) ) 17.19/14.39 ( (fun (fun pname bool) (fun (hoare_509422987triple state) bool)), (fun (fun pname bool) bool), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun pname bool))) (hAPP _let_1 (fun (fun _let_2 _let_0) (fun _let_2 bool)) (combb _let_0 bool _let_2) (hAPP _let_0 _let_1 (ord_less_eq _let_0) fa))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname _let_0))) (hAPP _let_2 (fun (fun pname bool) (fun _let_0 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(combb _let_0 com pname) (the com)) body)))))))) ) 17.19/14.39 ( (fun (fun pname bool) (fun (hoare_509422987triple state) bool)), (fun (fun pname bool) bool), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun pname bool))) (hAPP (fun _let_1 bool) (fun (fun _let_2 _let_1) (fun _let_2 bool)) (combb _let_1 bool _let_2) (finite_finite _let_0))))), (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname _let_1))) (hAPP _let_4 (fun (fun pname bool) (fun _let_1 bool)) (image pname _let_1) (hAPP _let_2 _let_4 (hAPP (fun com _let_1) (fun _let_2 _let_4) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)))))))) ) 17.19/14.39 ( (fun (fun pname bool) (fun (hoare_509422987triple state) bool)), (fun (fun pname bool) bool), (let ((_let_0 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17.51/14.64 ( pname, bool, pname, (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun pname _let_0))) (hAPP _let_0 _let_1 (hAPP (fun pname (fun _let_0 _let_0)) (fun _let_0 _let_1) (combc pname _let_0 _let_0) (insert pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))), (let ((_let_0 (combi pname))) (let ((_let_1 (fun pname pname))) (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb pname pname pname) _let_0) _let_0))), pn ) 17.51/14.64 ( pname, bool, (fun pname bool), (let ((_let_0 (fun (fun pname bool) bool))) (let ((_let_1 (fun pname _let_0))) (let ((_let_2 (fun pname pname))) (hAPP _let_2 _let_1 (hAPP _let_1 (fun _let_2 _let_1) (combb pname _let_0 pname) (member pname)) (combi pname))))), (let ((_let_0 (fun pname bool))) (let ((_let_1 (fun pname _let_0))) (hAPP _let_0 _let_1 (hAPP (fun pname (fun _let_0 _let_0)) (fun _let_0 _let_1) (combc pname _let_0 _let_0) (insert pname)) (hAPP (fun pname (option com)) _let_0 (dom pname com) body)))), pn ) 17.51/14.64 ( 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(bot_bot _let_1)))), skv_14 ) 17.51/14.64 ( (hoare_509422987triple state), bool, bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 (fun _let_1 bool)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_1 bool) _let_3 (hAPP (fun bool _let_0) (fun (fun _let_1 bool) _let_3) (combb bool _let_0 _let_1) fdisj) (hAPP _let_1 (fun _let_1 bool) (hAPP _let_2 _let_2 (combc _let_1 _let_1 bool) (fequal _let_1)) (hAPP com _let_1 hoare_Mirabelle_MGT y))))))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP (fun _let_0 (fun _let_1 bool)) (fun _let_1 _let_1) (combc _let_0 _let_1 bool) (member _let_0)) (bot_bot _let_1)))), skv_19 ) 17.51/14.64 ( (hoare_509422987triple state), bool, bool, (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 (fun _let_1 bool)))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP (fun _let_1 bool) _let_3 (hAPP (fun 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(bot_bot _let_1))))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)) ) 17.51/14.67 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 (fun _let_0 bool)))) (hAPP _let_1 _let_1 (combc _let_0 _let_0 bool) (fequal _let_0)))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 17.51/14.67 ( (hoare_509422987triple state), bool, (fun (hoare_509422987triple state) bool), (member (hoare_509422987triple state)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun _let_0 _let_1))) (hAPP _let_1 _let_2 (hAPP (fun _let_0 (fun _let_1 _let_1)) (fun _let_1 _let_2) (combc _let_0 _let_1 _let_1) (insert _let_0)) fa)))), (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 17.51/14.67 ( (hoare_509422987triple state), (fun (hoare_509422987triple state) 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(fun (hoare_509422987triple state) bool) ) 17.69/14.74 ( (fun (fun pname (option com)) (fun pname bool)), (fun (fun pname bool) bool), (fun (fun pname (option com)) bool) ) 17.69/14.74 ( (fun (fun pname (option com)) (fun pname bool)), (fun pname (hoare_509422987triple state)), (fun (fun pname (option com)) (fun (hoare_509422987triple state) bool)) ) 17.69/14.74 ( (fun (fun pname (option com)) (fun pname bool)), (fun (fun pname bool) (fun (hoare_509422987triple state) bool)), (fun (fun pname (option com)) (fun (hoare_509422987triple state) bool)) ) 17.69/14.74 ( (fun (fun pname (option com)) (fun pname bool)), (fun (fun pname (option com)) bool), (fun (fun pname (option com)) bool) ) 17.69/14.74 ( (fun (fun pname (option com)) (fun pname bool)), (fun (fun pname (option com)) (fun (hoare_509422987triple state) bool)), (fun (fun pname (option com)) (fun (hoare_509422987triple state) bool)) ) 17.69/14.74 ( (fun (fun pname (option com)) (fun pname bool)), (let ((_let_0 (fun pname (option 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bool) bool), (fun com bool), (fun (fun com bool) bool) ) 17.69/14.74 ( (fun (hoare_509422987triple state) (fun bool bool)), (fun (hoare_509422987triple state) bool), (fun (hoare_509422987triple state) bool) ) 17.69/14.74 ( (fun (hoare_509422987triple state) (fun bool bool)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun _let_0 _let_0)), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun _let_0 _let_0)) ) 17.69/14.74 ( (fun (hoare_509422987triple state) (fun bool bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (fun _let_1 (fun (fun _let_0 (fun bool bool)) _let_1)))), (let ((_let_0 (fun (hoare_509422987triple state) bool))) (fun _let_0 _let_0)) ) 17.69/14.74 ( (fun pname (fun (option com) com)), (fun pname (option com)), (fun pname com) ) 17.69/14.74 ( (fun pname (fun (option com) com)), (fun (fun pname (option com)) (fun pname com)), (fun (fun pname (option com)) (fun pname com)) ) 17.69/14.74 ( (fun pname (fun (option com) com)), (let ((_let_0 (option com))) (fun (fun pname _let_0) (fun (fun pname (fun _let_0 com)) (fun pname com)))), (fun (fun pname (option com)) (fun pname com)) ) 17.69/14.74 ( (fun pname (fun com (hoare_509422987triple state))), (fun pname com), (fun pname (hoare_509422987triple state)) ) 17.69/14.74 ( (fun pname (fun com (hoare_509422987triple state))), (fun (fun pname com) (fun pname (hoare_509422987triple state))), (fun (fun pname com) (fun pname (hoare_509422987triple state))) ) 17.69/14.74 ( (fun pname (fun com (hoare_509422987triple state))), (let ((_let_0 (hoare_509422987triple state))) (fun (fun pname com) (fun (fun pname (fun com _let_0)) (fun pname _let_0)))), (fun (fun pname com) (fun pname (hoare_509422987triple state))) ) 17.69/14.74 ( (fun (fun (fun (hoare_509422987triple state) bool) bool) bool), (fun (fun (hoare_509422987triple state) bool) bool), (fun (fun (fun (hoare_509422987triple state) bool) bool) bool) ) 17.69/14.74 ( (fun (fun (fun pname bool) bool) bool), (fun (fun pname bool) bool), (fun (fun (fun pname bool) bool) bool) ) 17.69/14.74 ( (fun com com), (fun com bool), (fun com bool) ) 17.69/14.74 ( (let ((_let_0 (fun pname bool))) (fun _let_0 (fun _let_0 bool))), (fun pname bool), (fun (fun pname bool) bool) ) 17.69/14.74 ( (fun pname (fun (fun pname (option com)) com)), (fun pname (option com)), (fun pname com) ) 17.69/14.74 ( (fun pname (fun (fun pname (option com)) com)), (fun (fun pname (option com)) (fun pname com)), (fun (fun pname (option com)) (fun pname com)) ) 17.69/14.74 ( (fun pname (fun (fun pname (option com)) com)), (let ((_let_0 (fun pname (option com)))) (fun _let_0 (fun (fun pname (fun _let_0 com)) (fun pname com)))), (fun (fun pname (option com)) (fun pname com)) ) 17.69/14.74 ( (fun pname (fun (fun pname com) (hoare_509422987triple state))), (fun pname com), (fun pname (hoare_509422987triple state)) ) 17.69/14.74 ( (fun pname (fun (fun pname com) (hoare_509422987triple state))), (fun (fun pname com) (fun pname (hoare_509422987triple state))), (fun (fun pname com) (fun pname (hoare_509422987triple state))) ) 17.69/14.74 ( (fun pname (fun (fun pname com) (hoare_509422987triple state))), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (fun _let_1 (fun (fun pname (fun _let_1 _let_0)) (fun pname _let_0))))), (fun (fun pname com) (fun pname (hoare_509422987triple state))) ) 17.69/14.74 ( (fun (hoare_509422987triple state) (fun (fun pname bool) bool)), (fun pname bool), (fun (hoare_509422987triple state) bool) ) 17.69/14.74 ( (fun (hoare_509422987triple state) (fun (fun pname bool) bool)), (fun (fun pname bool) (fun (hoare_509422987triple state) bool)), (fun (fun pname bool) (fun (hoare_509422987triple state) bool)) ) 17.69/14.74 ( (fun (hoare_509422987triple state) (fun (fun pname bool) bool)), (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname bool))) (fun _let_1 (fun (fun _let_0 (fun _let_1 bool)) (fun _let_0 bool))))), (fun (fun pname bool) (fun (hoare_509422987triple state) bool)) ) 17.69/14.74 ) 17.69/14.74 (instantiation (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (hAPP _let_1 (fun _let_4 bool) (member _let_1) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_4 bool _let_7 fa))) (hBOOL (hAPP _let_4 bool _let_7 (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))) ))))))))) 17.69/14.74 ( (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 17.69/14.74 ( (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)) ) 17.69/14.74 ( skv_4 ) 17.69/14.74 ( skv_7 ) 17.69/14.74 ( skv_11 ) 17.69/14.74 ( skv_13 ) 17.69/14.74 ( skv_33 ) 17.69/14.74 ( skv_34 ) 17.69/14.74 ( skv_39 ) 17.69/14.74 ( skv_41 ) 17.69/14.74 ( skv_58 ) 17.69/14.74 ( skv_59 ) 17.69/14.74 ( skv_60 ) 17.69/14.74 ( skv_63 ) 17.69/14.74 ( skv_69 ) 17.69/14.74 ( skv_71 ) 17.69/14.74 ( skv_73 ) 17.69/14.74 ( skv_75 ) 17.69/14.74 ) 17.69/14.74 (instantiation (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (forall ((X_1 $$unsorted)) (= (hAPP _let_1 bool fa X_1) (hAPP _let_1 bool (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body)) X_1)) )))))))) 17.69/14.75 ( (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 17.69/14.75 ( skv_4 ) 17.69/14.75 ( skv_7 ) 17.69/14.75 ( skv_40 ) 17.69/14.75 ( skv_42 ) 17.69/14.75 ( skv_81 ) 17.69/14.75 ( skv_100 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun _let_2 _let_0))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_2 bool (hAPP _let_3 _let_3 (hAPP _let_4 (fun _let_3 _let_3) (combs _let_2 bool bool) (hAPP _let_3 _let_4 (hAPP (fun bool _let_0) (fun _let_3 _let_4) (combb bool _let_0 _let_2) fconj) (hAPP _let_2 _let_3 (fequal _let_2) fa))) (hAPP _let_1 _let_3 (member _let_1) (hAPP com _let_1 hoare_Mirabelle_MGT y))) X_1))) )))))) 17.69/14.75 ( skv_94 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (fun _let_3 _let_0))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_3 bool (hAPP _let_4 _let_4 (hAPP _let_7 (fun _let_4 _let_4) (combs _let_3 bool bool) (hAPP _let_4 _let_7 (hAPP (fun bool _let_0) (fun _let_4 _let_7) (combb bool _let_0 _let_3) fconj) (hAPP _let_3 _let_4 (fequal _let_3) (hAPP _let_3 _let_3 (hAPP _let_1 (fun _let_3 _let_3) (insert _let_1) (hAPP com _let_1 hoare_Mirabelle_MGT y)) (bot_bot _let_3))))) (hAPP _let_3 _let_4 (hoare_122391849derivs state) (hAPP _let_5 _let_3 (hAPP _let_6 (fun _let_5 _let_3) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_5 (dom pname com) body)))) X_1))) ))))))))) 17.69/14.75 ( skv_94 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (fun _let_2 _let_0))) (let ((_let_5 (fun _let_2 _let_3))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_2 bool (hAPP _let_3 _let_3 (hAPP _let_4 (fun _let_3 _let_3) (combs _let_2 bool bool) (hAPP _let_3 _let_4 (hAPP (fun bool _let_0) (fun _let_3 _let_4) (combb bool _let_0 _let_2) fconj) (hAPP _let_2 _let_3 (hAPP _let_5 _let_5 (combc _let_2 _let_2 bool) (fequal _let_2)) fa))) (hAPP _let_1 _let_3 (member _let_1) (hAPP com _let_1 hoare_Mirabelle_MGT y))) X_1))) ))))))) 17.69/14.75 ( skv_94 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (fun bool bool))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (fun _let_3 _let_0))) (let ((_let_8 (fun _let_3 _let_4))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_3 bool (hAPP _let_4 _let_4 (hAPP _let_7 (fun _let_4 _let_4) (combs _let_3 bool bool) (hAPP _let_4 _let_7 (hAPP (fun bool _let_0) (fun _let_4 _let_7) (combb bool _let_0 _let_3) fconj) (hAPP _let_3 _let_4 (hAPP _let_8 _let_8 (combc _let_3 _let_3 bool) (fequal _let_3)) (hAPP _let_3 _let_3 (hAPP _let_1 (fun _let_3 _let_3) (insert _let_1) (hAPP com _let_1 hoare_Mirabelle_MGT y)) (bot_bot _let_3))))) (hAPP _let_3 _let_4 (hoare_122391849derivs state) (hAPP _let_5 _let_3 (hAPP _let_6 (fun _let_5 _let_3) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_5 (dom pname com) body)))) X_1))) )))))))))) 17.69/14.75 ( skv_94 ) 17.69/14.75 ) 17.69/14.75 (instantiation (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP bool bool (hAPP bool (fun bool bool) (combk bool bool) fFalse) X_1))) ) 17.69/14.75 ( skv_50 ) 17.69/14.75 ( skv_92 ) 17.69/14.75 ) 17.69/14.75 (instantiation (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP com bool (hAPP bool (fun com bool) (combk bool com) fFalse) X_1))) ) 17.69/14.75 ( skv_36 ) 17.69/14.75 ) 17.69/14.75 (instantiation (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP pname bool (hAPP bool (fun pname bool) (combk bool pname) fFalse) X_1))) ) 17.69/14.75 ( skv_96 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (hoare_509422987triple state))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP bool (fun _let_0 bool) (combk bool _let_0) fFalse) X_1))) )) 17.69/14.75 ( (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 17.69/14.75 ( skv_40 ) 17.69/14.75 ( skv_100 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (fun (hoare_509422987triple state) bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP bool (fun _let_0 bool) (combk bool _let_0) fFalse) X_1))) )) 17.69/14.75 ( skv_94 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) X_1) (bot_bot _let_1)))) ))) 17.69/14.75 ( (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 17.69/14.75 ( (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)) ) 17.69/14.75 ( skv_4 ) 17.69/14.75 ( skv_7 ) 17.69/14.75 ( skv_11 ) 17.69/14.75 ( skv_13 ) 17.69/14.75 ( skv_33 ) 17.69/14.75 ( skv_34 ) 17.69/14.75 ( skv_39 ) 17.69/14.75 ( skv_41 ) 17.69/14.75 ( skv_58 ) 17.69/14.75 ( skv_59 ) 17.69/14.75 ( skv_60 ) 17.69/14.75 ( skv_63 ) 17.69/14.75 ( skv_69 ) 17.69/14.75 ( skv_71 ) 17.69/14.75 ( skv_73 ) 17.69/14.75 ( skv_75 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (fun bool bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP bool (fun _let_0 bool) (member bool) X_1) (bot_bot _let_0)))) )) 17.69/14.75 ( fTrue ) 17.69/14.75 ( fFalse ) 17.69/14.75 ( skv_6 ) 17.69/14.75 ( skv_49 ) 17.69/14.75 ( skv_51 ) 17.69/14.75 ( skv_52 ) 17.69/14.75 ( skv_67 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (fun com bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP com (fun _let_0 bool) (member com) X_1) (bot_bot _let_0)))) )) 17.69/14.75 ( y ) 17.69/14.75 ( skv_5 ) 17.69/14.75 ( skv_35 ) 17.69/14.75 ( skv_37 ) 17.69/14.75 ( skv_65 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (fun pname bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_0 bool (hAPP pname (fun _let_0 bool) (member pname) X_1) (bot_bot _let_0)))) )) 17.69/14.75 ( pn ) 17.69/14.75 ( skv_3 ) 17.69/14.75 ( skv_12 ) 17.69/14.75 ( skv_38 ) 17.69/14.75 ( skv_43 ) 17.69/14.75 ( skv_44 ) 17.69/14.75 ( skv_55 ) 17.69/14.75 ( skv_56 ) 17.69/14.75 ( skv_57 ) 17.69/14.75 ( skv_61 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (fun (hoare_509422987triple state) bool))) (let ((_let_1 (fun _let_0 bool))) (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_1 bool (hAPP _let_0 (fun _let_1 bool) (member _let_0) X_1) (bot_bot _let_1)))) ))) 17.69/14.75 ( (bot_bot (fun (hoare_509422987triple state) bool)) ) 17.69/14.75 ( fa ) 17.69/14.75 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) (hAPP (fun pname (option com)) _let_3 (dom pname com) body))))))) ) 17.69/14.75 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_1)))) ) 17.69/14.75 ( (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun _let_0 bool))) (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3))) (bot_bot _let_1)))) ) 17.69/14.75 ( skv_15 ) 17.69/14.75 ( skv_16 ) 17.69/14.75 ( skv_17 ) 17.69/14.75 ( skv_53 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_1))) (forall ((X_1 $$unsorted)) (or (not (= (ti _let_1 (hAPP com _let_1 hoare_Mirabelle_MGT y)) (hAPP pname _let_1 (hAPP _let_2 _let_5 (hAPP (fun com _let_1) (fun _let_2 _let_5) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) X_1))) (not (hBOOL (hAPP _let_4 bool (hAPP pname (fun _let_4 bool) (member pname) X_1) skv_2)))) ))))))) 17.69/14.75 ( pn ) 17.69/14.75 ( skv_3 ) 17.69/14.75 ( skv_12 ) 17.69/14.75 ( skv_38 ) 17.69/14.75 ( skv_43 ) 17.69/14.75 ( skv_44 ) 17.69/14.75 ( skv_55 ) 17.69/14.75 ( skv_56 ) 17.69/14.75 ( skv_57 ) 17.69/14.75 ( skv_61 ) 17.69/14.75 ( skv_97 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun pname bool))) (let ((_let_5 (fun pname _let_1))) (forall ((X_1 $$unsorted)) (or (not (= (ti _let_1 (hAPP com _let_1 hoare_Mirabelle_MGT y)) (hAPP pname _let_1 (hAPP _let_2 _let_5 (hAPP (fun com _let_1) (fun _let_2 _let_5) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body)) X_1))) (not (hBOOL (hAPP _let_4 bool (hAPP pname (fun _let_4 bool) (member pname) X_1) (hAPP _let_3 _let_4 (dom pname com) body))))) ))))))) 17.69/14.75 ( pn ) 17.69/14.75 ( skv_3 ) 17.69/14.75 ( skv_12 ) 17.69/14.75 ( skv_38 ) 17.69/14.75 ( skv_43 ) 17.69/14.75 ( skv_44 ) 17.69/14.75 ( skv_55 ) 17.69/14.75 ( skv_56 ) 17.69/14.75 ( skv_57 ) 17.69/14.75 ( skv_61 ) 17.69/14.75 ( skv_97 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun pname bool))) (let ((_let_3 (fun pname _let_0))) (forall ((X_1 $$unsorted)) (or (not (= (ti _let_0 (hAPP com _let_0 hoare_Mirabelle_MGT y)) (hAPP pname _let_0 (hAPP _let_1 _let_3 (hAPP (fun com _let_0) (fun _let_1 _let_3) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1) X_1))) (not (hBOOL (hAPP _let_2 bool (hAPP pname (fun _let_2 bool) (member pname) X_1) (bot_bot _let_2))))) ))))) 17.69/14.75 ( pn ) 17.69/14.75 ( skv_3 ) 17.69/14.75 ( skv_12 ) 17.69/14.75 ( skv_38 ) 17.69/14.75 ( skv_43 ) 17.69/14.75 ( skv_44 ) 17.69/14.75 ( skv_55 ) 17.69/14.75 ( skv_56 ) 17.69/14.75 ( skv_57 ) 17.69/14.75 ( skv_61 ) 17.69/14.75 ( skv_97 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (forall ((AA $$unsorted)) (or (not (hBOOL (hAPP _let_3 bool (hAPP _let_3 (fun _let_3 bool) (ord_less_eq _let_3) AA) (bot_bot _let_3)))) (not (= (ti _let_2 fa) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) AA)))) )))))) 17.69/14.75 ( (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 17.69/14.75 ( (bot_bot (fun pname bool)) ) 17.69/14.75 ( skv_1 ) 17.69/14.75 ( skv_2 ) 17.69/14.75 ( skv_22 ) 17.69/14.75 ( skv_23 ) 17.69/14.75 ( skv_45 ) 17.69/14.75 ( skv_46 ) 17.69/14.75 ( skv_47 ) 17.69/14.75 ( skv_48 ) 17.69/14.75 ( skv_80 ) 17.69/14.75 ( skv_86 ) 17.69/14.75 ( skv_87 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (hoare_509422987triple state))) (let ((_let_1 (fun pname com))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (fun pname bool))) (let ((_let_4 (fun pname _let_0))) (forall ((AA $$unsorted)) (or (not (hBOOL (hAPP _let_3 bool (hAPP _let_3 (fun _let_3 bool) (ord_less_eq _let_3) AA) (hAPP (fun pname (option com)) _let_3 (dom pname com) body)))) (not (= (ti _let_2 (hAPP _let_2 _let_2 (hAPP _let_0 (fun _let_2 _let_2) (insert _let_0) (hAPP com _let_0 hoare_Mirabelle_MGT y)) (bot_bot _let_2))) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (image pname _let_0) (hAPP _let_1 _let_4 (hAPP (fun com _let_0) (fun _let_1 _let_4) (combb com _let_0 pname) hoare_Mirabelle_MGT) body_1)) AA)))) )))))) 17.69/14.75 ( (hAPP (fun pname (option com)) (fun pname bool) (dom pname com) body) ) 17.69/14.75 ( (bot_bot (fun pname bool)) ) 17.69/14.75 ( skv_1 ) 17.69/14.75 ( skv_2 ) 17.69/14.75 ( skv_22 ) 17.69/14.75 ( skv_23 ) 17.69/14.75 ( skv_45 ) 17.69/14.75 ( skv_46 ) 17.69/14.75 ( skv_47 ) 17.69/14.75 ( skv_48 ) 17.69/14.75 ( skv_80 ) 17.69/14.75 ( skv_86 ) 17.69/14.75 ( skv_87 ) 17.69/14.75 ) 17.69/14.75 (instantiation (let ((_let_0 (option com))) (let ((_let_1 (hoare_509422987triple state))) (let ((_let_2 (fun pname com))) (let ((_let_3 (fun pname _let_0))) (let ((_let_4 (fun _let_1 bool))) (let ((_let_5 (fun pname bool))) (let ((_let_6 (fun pname _let_1))) (let ((_let_7 (hAPP _let_1 (fun _let_4 bool) (member _let_1) X_1))) (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP _let_4 bool _let_7 (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (image pname _let_1) (hAPP _let_2 _let_6 (hAPP (fun com _let_1) (fun _let_2 _let_6) (combb com _let_1 pname) hoare_Mirabelle_MGT) (hAPP _let_3 _let_2 (hAPP (fun _let_0 com) (fun _let_3 _let_2) (combb _let_0 com pname) (the com)) body))) (hAPP _let_3 _let_5 (dom pname com) body))))) (hBOOL (hAPP _let_4 bool _let_7 fa))) ))))))))) 17.69/14.75 ( (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT y) ) 17.69/14.75 ( (hAPP com (hoare_509422987triple state) hoare_Mirabelle_MGT (hAPP pname com body_1 skv_3)) ) 17.69/14.75 ( skv_4 ) 17.69/14.75 ( skv_7 ) 17.69/14.75 ( skv_11 ) 17.69/14.75 ( skv_13 ) 17.69/14.75 ( skv_33 ) 17.69/14.75 ( skv_34 ) 17.69/14.75 ( skv_39 ) 17.69/14.75 ( skv_41 ) 17.69/14.75 ( skv_58 ) 17.69/14.75 ( skv_59 ) 17.69/14.75 ( skv_60 ) 17.69/14.75 ( skv_63 ) 17.69/14.75 ( skv_69 ) 17.69/14.75 ( skv_71 ) 17.69/14.75 ( skv_73 ) 17.69/14.75 ( skv_75 ) 17.69/14.75 ) 17.69/14.75 % SZS output end Proof for theBenchmark 17.69/14.77 EOF