0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.11 % Command : do_CVC4 %s %d 0.10/0.32 % Computer : n007.cluster.edu 0.10/0.32 % Model : x86_64 x86_64 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.32 % Memory : 8042.1875MB 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.32 % CPULimit : 960 0.10/0.32 % WCLimit : 120 0.10/0.32 % DateTime : Thu Jul 2 07:48:39 EDT 2020 0.10/0.32 % CPUTime : 1.00/1.18 %----Proving TF0_NAR, FOF, or CNF 1.00/1.18 ------- cvc4-fof casc j10 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 960... 1.00/1.18 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 6.35/6.56 % SZS status Theorem for theBenchmark 6.35/6.56 % SZS output start Proof for theBenchmark 6.35/6.56 (skolem (forall ((V_F_2 $$unsorted) (V_fa_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (not (c_Finite__Set_Ofolding T_b T_c V_fa_2 V_F_2)) ) 6.35/6.56 ( skv_1 skv_2 skv_3 skv_4 ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) V_n_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP _let_0 V_m_2)) (hAPP _let_0 V_n_2))))) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_w $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_w) V_w)) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_a $$unsorted)) (hBOOL (hAPP (c_List_Odistinct T_a) (c_List_Olist_ONil T_a))) ) 6.35/6.56 ( tc_Nat_Onat ) 6.35/6.56 ( tc_Int_Oint ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Nat_OSuc V_n))))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.56 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_m_2) V_n_2)) (c_Transitive__Closure_Ortrancl tc_Nat_Onat c_Wellfounded_Opred__nat))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_n_2))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_n) (hAPP c_Nat_OSuc V_n))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.56 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_k $$unsorted)) (not (= c_Int_OPls (c_Int_OBit1 V_k))) ) 6.35/6.56 ( c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.56 ( c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) V_A_2)) ) 6.35/6.56 ( v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_z_2 $$unsorted) (V_m_2 $$unsorted)) (= (and (= V_m_2 (hAPP c_Int_Onat V_z_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_2))) (= V_z_2 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_v_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) V_v_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v_2)))) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.56 ( c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.56 ( c_Int_OMin ) 6.35/6.56 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.56 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_w $$unsorted) (V_z $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (or (hBOOL (hAPP (hAPP _let_0 V_w) V_z)) (hBOOL (hAPP (hAPP _let_0 V_z) V_w)))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OPls, c_Int_OMin ) 6.35/6.56 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OMin, c_Int_OPls ) 6.35/6.56 ( c_Int_OMin, c_Int_OMin ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)))) ) 6.35/6.56 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ( c_FunDef_Opair__less, (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.56 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Orefl__on T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) ) 6.35/6.56 ( tc_Nat_Onat ) 6.35/6.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)))) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w_2) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_z_2) (c_Groups_Oone__class_Oone tc_Int_Oint)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_w_2) V_z_2))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OPls, c_Int_OMin ) 6.35/6.56 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OMin, c_Int_OMin ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit0 V_k_2)) (c_Int_OBit0 V_l_2))) (hBOOL (hAPP (hAPP _let_0 V_k_2) V_l_2)))) ) 6.35/6.56 ( c_Int_OPls, c_Int_OPls ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_l $$unsorted)) (not (= c_Int_OMin (c_Int_OBit0 V_l))) ) 6.35/6.56 ( c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.56 ( c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_z $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (= V_z (hAPP _let_0 (hAPP _let_0 V_z)))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) V_n_2)) (hBOOL (hAPP (hAPP (c_member (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_m_2) V_n_2)) (c_Transitive__Closure_Otrancl tc_Nat_Onat c_Wellfounded_Opred__nat)))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_k_2 $$unsorted)) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_k_2))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_a_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_B_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_B_2))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 V_k1_2) V_k2_2)) (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit0 V_k1_2)) (c_Int_OBit0 V_k2_2))))) ) 6.35/6.56 ( c_Int_OPls, c_Int_OPls ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit0 V_k_2)) c_Int_OMin)) (hBOOL (hAPP (hAPP _let_0 V_k_2) c_Int_OMin)))) ) 6.35/6.56 ( c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.56 ( c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_Opred V_k_2)) V_l_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_k_2) V_l_2))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OPls, c_Int_OMin ) 6.35/6.56 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OMin, c_Int_OPls ) 6.35/6.56 ( c_Int_OMin, c_Int_OMin ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Predicate_Oreflp T_b V_r_2) (c_Relation_Orefl__on T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_OCollect (tc_prod T_b T_b)) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_b tc_HOL_Obool) V_r_2)))) ) 6.35/6.56 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.56 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), tc_Int_Oint ) 6.35/6.56 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_OBit0 V_k_2)) c_Int_OMin)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_k_2) c_Int_OMin))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.56 ( c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_b $$unsorted)) (c_Wellfounded_Owf T_b (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) ) 6.35/6.56 ( tc_Nat_Onat ) 6.35/6.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_b $$unsorted)) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 6.35/6.56 ( tc_HOL_Obool ) 6.35/6.56 ( tc_Nat_Onat ) 6.35/6.56 ( tc_Int_Oint ) 6.35/6.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.56 ( tc_Product__Type_Ounit ) 6.35/6.56 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_k_2) V_l_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_OBit0 V_k_2)) (c_Int_OBit1 V_l_2)))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OPls, c_Int_OMin ) 6.35/6.56 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OMin, c_Int_OPls ) 6.35/6.56 ( c_Int_OMin, c_Int_OMin ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP _let_0 V_n)) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP _let_0 V_m)))))) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit0 V_k_2)) (c_Int_OBit1 V_l_2))) (hBOOL (hAPP (hAPP _let_0 V_k_2) V_l_2)))) ) 6.35/6.56 ( c_Int_OMin, c_Int_OPls ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k_2)) c_Int_OMin)) (hBOOL (hAPP (hAPP _let_0 V_k_2) c_Int_OMin)))) ) 6.35/6.56 ( c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.56 ( c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Otrans (tc_fun T_b tc_HOL_Obool) (c_Wellfounded_Ofinite__psubset T_b)) ) 6.35/6.56 ( tc_HOL_Obool ) 6.35/6.56 ( tc_Nat_Onat ) 6.35/6.56 ( tc_Int_Oint ) 6.35/6.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.56 ( tc_Product__Type_Ounit ) 6.35/6.56 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_b $$unsorted)) (c_Wellfounded_Owf (tc_fun T_b tc_HOL_Obool) (c_Wellfounded_Ofinite__psubset T_b)) ) 6.35/6.56 ( tc_HOL_Obool ) 6.35/6.56 ( tc_Nat_Onat ) 6.35/6.56 ( tc_Int_Oint ) 6.35/6.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.56 ( tc_Product__Type_Ounit ) 6.35/6.56 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Oantisym T_b (c_Relation_OId T_b)) ) 6.35/6.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_x_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_x_2)) (c_Nat__Transfer_Ois__nat V_x_2)) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.56 ( c_Int_OMin ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_member (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_x_2) V_y_2)) c_Wellfounded_Oless__than))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_m $$unsorted)) (not (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP c_Nat_OSuc V_m))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.56 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_m $$unsorted) (V_i $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_i) (hAPP c_Nat_OSuc (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_i) V_m)))) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (c_Fun_Oinj__on T_b _let_0 (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (c_Set_Oinsert T_b)) (c_Orderings_Obot__class_Obot _let_0)) (c_Orderings_Otop__class_Otop _let_0))) ) 6.35/6.56 ( tc_HOL_Obool ) 6.35/6.56 ( tc_Nat_Onat ) 6.35/6.56 ( tc_Int_Oint ) 6.35/6.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.56 ( tc_Product__Type_Ounit ) 6.35/6.56 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (and (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2)) (not (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)))) ) 6.35/6.56 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.56 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.56 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 6.35/6.56 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_v_2 $$unsorted)) (= (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_v_2) c_Int_OPls))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.56 ( c_Int_OMin ) 6.35/6.56 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.56 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k_2)) (c_Int_OBit1 V_l_2))) (hBOOL (hAPP (hAPP _let_0 V_k_2) V_l_2)))) ) 6.35/6.56 ( c_Int_OMin, c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (hBOOL (hAPP (hAPP (c_member _let_0) V_A_2) (hAPP (c_Set_OPow T_b) V_B_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2)))) ) 6.35/6.56 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Relation_Otrans T_b (hAPP (c_Set_OCollect (tc_prod T_b T_b)) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_b tc_HOL_Obool) V_r_2))) (c_Predicate_Otransp T_b V_r_2)) ) 6.35/6.56 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.56 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), tc_Int_Oint ) 6.35/6.56 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Int_OBit1 V_k_2)) (c_Int_OBit0 V_l_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_k_2) V_l_2))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OPls, c_Int_OMin ) 6.35/6.56 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OMin, c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 V_k1_2) V_k2_2)) (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k1_2)) (c_Int_OBit1 V_k2_2))))) ) 6.35/6.56 ( c_Int_OMin, c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Otop__class_Otop _let_0))) (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) _let_1)))) ) 6.35/6.56 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.56 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_w_2 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_1 (c_Int_OBit0 V_w_2)) _let_0)) (hBOOL (hAPP (hAPP _let_1 V_w_2) _let_0))))) ) 6.35/6.56 ( c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.56 ( c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Relation_Oantisym T_b V_r_2) (c_Relation_Oantisym T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (c_Relation_OId T_b)))) ) 6.35/6.56 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.56 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 V_k_2) V_l_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_k_2)) (hAPP _let_1 V_l_2)))))) ) 6.35/6.56 ( c_Int_OPls, c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_b $$unsorted)) (c_Wellfounded_OwfP T_b (hAPP (c_COMBK (tc_fun T_b tc_HOL_Obool) T_b) (hAPP (c_COMBK tc_HOL_Obool T_b) c_fFalse))) ) 6.35/6.56 ( tc_HOL_Obool ) 6.35/6.56 ( tc_Nat_Onat ) 6.35/6.56 ( tc_Int_Oint ) 6.35/6.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.56 ( tc_Product__Type_Ounit ) 6.35/6.56 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) _let_0)) (= V_A_2 _let_0))) ) 6.35/6.56 ( v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (= (and (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_2)) (hBOOL (hAPP (hAPP _let_0 V_w_2) V_z_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP c_Int_Onat V_w_2)) (hAPP c_Int_Onat V_z_2))))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.56 ( c_Int_OMin, c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP _let_0 V_n))) (hAPP _let_0 V_m)))) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k_2)) (c_Int_OBit0 V_l_2))) (hBOOL (hAPP (hAPP _let_0 V_k_2) V_l_2)))) ) 6.35/6.56 ( c_Int_OPls, c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Osym T_b (c_Relation_OId T_b)) ) 6.35/6.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Osingle__valued T_b T_b (c_Relation_OId T_b)) ) 6.35/6.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_k $$unsorted)) (= V_k (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_k)) ) 6.35/6.56 ( c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.56 ( c_Int_OMin ) 6.35/6.56 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.56 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_c))) (= (hBOOL (hAPP (hAPP (c_Orderings_Obot__class_Obot (tc_fun T_b (tc_fun T_c tc_HOL_Obool))) V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_x_2) V_y_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))))) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.56 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.56 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.56 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Wellfounded_Owf T_b V_r_2) (forall ((B_x $$unsorted)) (hBOOL (hAPP (hAPP (c_member T_b) B_x) (c_Wellfounded_Oacc T_b V_r_2))) )) ) 6.35/6.56 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.56 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.35/6.56 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2)) (or (= V_B_2 V_A_2) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_A_2) V_B_2))))) ) 6.35/6.56 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (class_Nat_Osize (tc_prod T_2 T_1)) ) 6.35/6.56 ( tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Orefl__on T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) (c_Relation_OId T_b)) ) 6.35/6.56 ( tc_HOL_Obool ) 6.35/6.56 ( tc_Nat_Onat ) 6.35/6.56 ( tc_Int_Oint ) 6.35/6.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.56 ( tc_Product__Type_Ounit ) 6.35/6.56 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 c_Int_OPls))) (= (hBOOL (hAPP _let_1 (c_Int_OBit1 V_k_2))) (hBOOL (hAPP _let_1 V_k_2))))) ) 6.35/6.56 ( c_Int_OPls ) 6.35/6.56 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.56 ( c_Int_OMin ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_n $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 V_n))) (= _let_1 (hAPP (c_Int_Oring__1__class_Oof__int tc_Int_Oint) _let_1)))) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.56 ) 6.35/6.56 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_a_2)) (c_Relation_OId T_b))) ) 6.35/6.56 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.56 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.56 ( c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.56 ( c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.56 ) 6.35/6.57 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (c_Fun_Oid T_b))) (= _let_0 (c_Hilbert__Choice_Oinv__into T_b T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) _let_0))) ) 6.35/6.57 ( tc_HOL_Obool ) 6.35/6.57 ( tc_Nat_Onat ) 6.35/6.57 ( tc_Int_Oint ) 6.35/6.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.57 ( tc_Product__Type_Ounit ) 6.35/6.57 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (c_Relation_Orefl__on T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (c_Relation_OId T_b))) ) 6.35/6.57 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (= _let_1 (c_Transitive__Closure_Otrancl T_b _let_1)))) ) 6.35/6.57 ( tc_Nat_Onat ) 6.35/6.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_b_2)) (c_Relation_OId T_b))) (= V_b_2 V_a_2)) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.57 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 V_k_2) V_l_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_k_2)) (hAPP _let_1 V_l_2)))))) ) 6.35/6.57 ( c_Int_OPls, c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 V_k_2) c_Int_OMin)) (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k_2)) c_Int_OMin)))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (tc_fun _let_1 tc_HOL_Obool))) (let ((_let_4 (tc_fun T_b _let_3))) (= (c_Wellfounded_OwfP T_b (hAPP (hAPP (c_COMBC T_b _let_1 _let_2) (hAPP (hAPP (c_COMBB _let_4 (tc_fun _let_1 _let_2) T_b) (c_COMBC T_b _let_1 tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun T_b _let_0) _let_4 T_b) (hAPP (c_COMBB _let_0 _let_3 T_b) (c_member _let_0))) (c_Product__Type_OPair T_b T_b)))) V_r_2)) (c_Wellfounded_Owf T_b V_r_2))))))) ) 6.35/6.57 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.57 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.35/6.57 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_C_2 $$unsorted)) (c_Nat__Transfer_Onat__set (hAPP (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) V_C_2)) ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_z $$unsorted)) (c_Nat__Transfer_Ois__nat (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_z)) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) V_k_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) (c_Int_OBit1 V_k_2)))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k_2)) c_Int_OPls)) (hBOOL (hAPP (hAPP _let_0 V_k_2) c_Int_OPls)))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_P_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Product__Type_Ofst _let_1 _let_1))) (let ((_let_3 (hAPP _let_2 V_P_2))) (= (c_FunDef_Oreduction__pair T_b V_P_2) (and (c_Wellfounded_Owf T_b _let_3) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_1) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) _let_3) (hAPP (c_Product__Type_Osnd _let_1 _let_1) V_P_2))) _let_3)))))))) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omax__strict) c_FunDef_Omax__weak))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omin__strict) c_FunDef_Omin__weak))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (c_Finite__Set_Ofun__left__comm__idem T_b _let_0 (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_0 _let_0) T_b) (hAPP (c_COMBC _let_0 _let_0 _let_0) (c_Groups_Ominus__class_Ominus _let_0))) (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (c_Set_Oinsert T_b)) (c_Orderings_Obot__class_Obot _let_0))))) ) 6.35/6.57 ( tc_HOL_Obool ) 6.35/6.57 ( tc_Nat_Onat ) 6.35/6.57 ( tc_Int_Oint ) 6.35/6.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.57 ( tc_Product__Type_Ounit ) 6.35/6.57 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_v_2 $$unsorted) (V_u_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (let ((_let_1 (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat))) (let ((_let_2 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_3 (c_Relation_OImage _let_2 _let_2 c_Int_Ointrel))) (let ((_let_4 (c_Set_Oinsert _let_2))) (let ((_let_5 (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP (hAPP _let_0 V_x_2) V_v_2)) (hAPP (hAPP _let_0 V_u_2) V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP c_Int_OAbs__Integ (hAPP _let_3 (hAPP (hAPP _let_4 (hAPP (hAPP _let_1 V_x_2) V_y_2)) _let_5)))) (hAPP c_Int_OAbs__Integ (hAPP _let_3 (hAPP (hAPP _let_4 (hAPP (hAPP _let_1 V_u_2) V_v_2)) _let_5)))))))))))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 c_Int_OMin))) (= (hBOOL (hAPP _let_1 V_k_2)) (hBOOL (hAPP _let_1 (c_Int_OBit0 V_k_2)))))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_X_2 $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hBOOL (hAPP (hAPP (c_member (tc_prod _let_1 _let_1)) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) V_X_2) (c_Orderings_Obot__class_Obot _let_1))) c_FunDef_Omin__weak)))) ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Relation_OField T_b))) (let ((_let_1 (hAPP _let_0 V_r_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) (c_Transitive__Closure_Otrancl T_b V_r_2)) (hAPP (hAPP (c_Product__Type_OSigma T_b T_b) _let_1) (hAPP (c_COMBK (tc_fun T_b tc_HOL_Obool) T_b) _let_1)))))) ) 6.35/6.57 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_m $$unsorted)) (= V_m (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_A_2 $$unsorted)) (= V_A_2 (hAPP (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) (hAPP (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) V_A_2))) ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (and (not (= V_B_2 V_A_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_A_2) V_B_2)))) ) 6.35/6.57 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_w_2) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_z_2) (c_Groups_Oone__class_Oone tc_Int_Oint)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w_2) V_z_2))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OMin, c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 c_Int_OMin))) (= (hBOOL (hAPP _let_1 (c_Int_OBit1 V_k_2))) (hBOOL (hAPP _let_1 V_k_2))))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) V_k_2))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n))) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_x_2) V_y_2)) (c_List_Omeasures T_b (c_List_Olist_ONil (tc_fun T_b tc_Nat_Onat)))))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.57 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_n $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Nat_OSuc V_n)))))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.57 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (c_List_Olist_ONil T_a))) (= _let_0 (c_List_Obutlast T_a _let_0))) ) 6.35/6.57 ( tc_Nat_Onat ) 6.35/6.57 ( tc_Int_Oint ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_x_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_x_2)) (not (hBOOL (hAPP c_Nat__Numeral_Oneg V_x_2)))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (= V_m (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) V_m)) V_n)) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_f_2 $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= V_f_2 (c_Product__Type_Ocurry T_b T_c T_d (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c T_d) V_f_2))) ) 6.35/6.57 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_HOL_Obool, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.57 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), tc_HOL_Obool, tc_Int_Oint, tc_Int_Oint ) 6.35/6.57 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_HOL_Obool, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_u_2 $$unsorted)) (= V_u_2 (hAPP (c_Finite__Set_Ocard tc_Nat_Onat) (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) V_u_2))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (c_Fun_Obij__betw T_b T_b (c_Fun_Oid T_b) _let_0 _let_0)) ) 6.35/6.57 ( tc_HOL_Obool ) 6.35/6.57 ( tc_Nat_Onat ) 6.35/6.57 ( tc_Int_Oint ) 6.35/6.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.57 ( tc_Product__Type_Ounit ) 6.35/6.57 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_z_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP c_Int_Onat V_z_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_z_2))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) (c_Orderings_Otop__class_Otop _let_0)))) ) 6.35/6.57 ( v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_i_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_i_2) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP c_Int_Onat V_i_2))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Wellfounded_OwfP T_b V_r_2) (c_Wellfounded_Owf T_b (hAPP (c_Set_OCollect (tc_prod T_b T_b)) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_b tc_HOL_Obool) V_r_2)))) ) 6.35/6.57 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.57 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), tc_Int_Oint ) 6.35/6.57 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (= (c_Wellfounded_Oacyclic T_b (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP _let_1 V_y_2) V_x_2)) V_r_2)) (and (c_Wellfounded_Oacyclic T_b V_r_2) (not (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP _let_1 V_x_2) V_y_2)) (c_Transitive__Closure_Ortrancl T_b V_r_2)))))))) ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (= V_m (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_n)) V_n)) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) (c_Int_OBit0 V_k_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) V_k_2))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_1 $$unsorted)) (class_Nat_Osize (tc_Hoare__Mirabelle_Otriple T_1)) ) 6.35/6.57 ( t_a ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_n $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Nat_OSuc V_n)) V_n))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.57 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 V_k_2) c_Int_OPls)) (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit0 V_k_2)) c_Int_OPls)))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_z_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) (hAPP c_Int_Onat V_z_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2)) V_z_2))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b T_c))) (let ((_let_1 (tc_prod T_b T_c))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (let ((_let_3 (tc_fun T_c tc_HOL_Obool))) (c_Fun_Oinj__on _let_0 _let_2 (hAPP (hAPP (c_COMBB _let_2 _let_2 _let_0) (c_Set_OCollect _let_1)) (hAPP (hAPP (c_COMBB (tc_fun T_b _let_3) _let_2 _let_0) (c_Product__Type_Oprod_Oprod__case T_b T_c tc_HOL_Obool)) (hAPP (c_COMBB T_c _let_3 T_b) (hAPP (c_COMBC T_c T_c tc_HOL_Obool) c_fequal)))) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))))))) ) 6.35/6.57 ( tc_HOL_Obool, tc_Int_Oint ) 6.35/6.57 ( tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.57 ( tc_Int_Oint, tc_Int_Oint ) 6.35/6.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP _let_0 V_x_2)) (hAPP _let_0 V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_x_2) V_y_2)))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Oantisym T_b (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) ) 6.35/6.57 ( tc_Nat_Onat ) 6.35/6.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_z_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_z_2))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 c_Int_OPls))) (= (hBOOL (hAPP _let_1 V_k_2)) (hBOOL (hAPP _let_1 (c_Int_OBit0 V_k_2)))))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 c_Int_OPls))) (= (hBOOL (hAPP _let_1 (c_Int_OBit0 V_k_2))) (hBOOL (hAPP _let_1 V_k_2))))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (or (hBOOL (hAPP (hAPP _let_0 V_x) V_y)) (hBOOL (hAPP (hAPP _let_0 V_y) V_x)) (= V_y V_x))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OMin, c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_m $$unsorted) (V_i $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_i) (hAPP c_Nat_OSuc (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_i)))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_n_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_n_2))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_j) V_i)) V_i))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_v_2 $$unsorted) (V_u_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (let ((_let_1 (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat))) (let ((_let_2 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_3 (c_Relation_OImage _let_2 _let_2 c_Int_Ointrel))) (let ((_let_4 (c_Set_Oinsert _let_2))) (let ((_let_5 (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool)))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP (hAPP _let_0 V_x_2) V_v_2)) (hAPP (hAPP _let_0 V_u_2) V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP c_Int_OAbs__Integ (hAPP _let_3 (hAPP (hAPP _let_4 (hAPP (hAPP _let_1 V_x_2) V_y_2)) _let_5)))) (hAPP c_Int_OAbs__Integ (hAPP _let_3 (hAPP (hAPP _let_4 (hAPP (hAPP _let_1 V_u_2) V_v_2)) _let_5)))))))))))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (and (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_A_2) V_B_2))) (hBOOL (hAPP (hAPP (c_member (tc_prod _let_0 _let_0)) (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) V_A_2) V_B_2)) (c_Wellfounded_Ofinite__psubset T_b))))) ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (tc_fun _let_1 tc_HOL_Obool))) (let ((_let_4 (tc_fun T_b _let_3))) (= (c_Equiv__Relations_Oequivp T_b (hAPP (hAPP (c_COMBC T_b _let_1 _let_2) (hAPP (hAPP (c_COMBB _let_4 (tc_fun _let_1 _let_2) T_b) (c_COMBC T_b _let_1 tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun T_b _let_0) _let_4 T_b) (hAPP (c_COMBB _let_0 _let_3 T_b) (c_member _let_0))) (c_Product__Type_OPair T_b T_b)))) V_A_2)) (c_Equiv__Relations_Oequiv T_b (c_Orderings_Otop__class_Otop _let_2) V_A_2))))))) ) 6.35/6.57 ( c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_G_2 $$unsorted) (V_F_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (= (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_F_2) V_G_2))) (and (hBOOL (hAPP _let_0 V_G_2)) (hBOOL (hAPP _let_0 V_F_2))))) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (= (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2))) (hBOOL (hAPP _let_0 V_A_2)))) ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_n $$unsorted)) (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n)))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_k)) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2) (and (c_Relation_Orefl__on T_b V_A_2 V_r_2) (c_Relation_Osym T_b V_r_2) (c_Relation_Otrans T_b V_r_2))) ) 6.35/6.57 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_n))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_i) V_j)) V_i))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit0 V_k_2)) c_Int_OPls)) (hBOOL (hAPP (hAPP _let_0 V_k_2) c_Int_OPls)))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_m $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 V_m))) (= _let_1 (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) _let_1)))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (= (c_Wellfounded_Owf T_b (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP _let_1 V_y_2) V_x_2)) V_r_2)) (and (not (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP _let_1 V_x_2) V_y_2)) (c_Transitive__Closure_Ortrancl T_b V_r_2)))) (c_Wellfounded_Owf T_b V_r_2))))) ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_w_2 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (= (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP _let_0 (c_Int_OBit1 V_w_2)))) (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP _let_0 V_w_2))))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP c_Nat_OSuc V_n))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.57 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) V_m))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite (tc_prod T_b T_b)))) (= (hBOOL (hAPP _let_0 (c_Transitive__Closure_Otrancl T_b V_r_2))) (hBOOL (hAPP _let_0 V_r_2)))) ) 6.35/6.57 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Relation_Osym T_b (hAPP (c_Set_OCollect (tc_prod T_b T_b)) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_b tc_HOL_Obool) V_r_2))) (c_Predicate_Osymp T_b V_r_2)) ) 6.35/6.57 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.57 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), tc_Int_Oint ) 6.35/6.57 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_x $$unsorted)) (= V_x (c_Int_Osucc (c_Int_Opred V_x))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_b $$unsorted)) (c_Finite__Set_Ofun__left__comm__idem T_b (tc_fun T_b tc_HOL_Obool) (c_Set_Oinsert T_b)) ) 6.35/6.57 ( tc_HOL_Obool ) 6.35/6.57 ( tc_Nat_Onat ) 6.35/6.57 ( tc_Int_Oint ) 6.35/6.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.57 ( tc_Product__Type_Ounit ) 6.35/6.57 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Otrans T_b (c_Relation_OId T_b)) ) 6.35/6.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_a $$unsorted)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Nat_Osize__class_Osize (tc_List_Olist T_a)) (c_List_Olist_ONil T_a))) ) 6.35/6.57 ( tc_Nat_Onat ) 6.35/6.57 ( tc_Int_Oint ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_P_2 $$unsorted) (T_b $$unsorted)) (= V_P_2 (hAPP (c_Set_OCollect T_b) V_P_2)) ) 6.35/6.57 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (c_Relation_Osym T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (hAPP (c_Relation_Oconverse T_b T_b) V_r_2))) ) 6.35/6.57 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Nat_Onat))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_2 (hAPP _let_0 _let_1))) (= (hBOOL (hAPP _let_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m_2) V_n_2))) (or (hBOOL (hAPP _let_2 V_m_2)) (hBOOL (hAPP _let_2 V_n_2))))))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (c_Relation_OId T_b))) (= _let_0 (hAPP (c_Relation_Oconverse T_b T_b) _let_0))) ) 6.35/6.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_w_2) (c_Groups_Oone__class_Oone tc_Int_Oint))) V_z_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w_2) V_z_2))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OMin, c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_A_2 $$unsorted)) (= (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) V_A_2)) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Int_Oint) (hAPP (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) V_A_2)))) ) 6.35/6.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (= (and (= V_B_2 _let_1) (= V_A_2 _let_1)) (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2))))) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_w_2 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (= (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP _let_0 (c_Int_OBit0 V_w_2)))) (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP _let_0 V_w_2))))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_w_2 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (= (hBOOL (hAPP (hAPP _let_1 (c_Int_OBit1 V_w_2)) _let_0)) (hBOOL (hAPP (hAPP _let_1 V_w_2) _let_0))))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_v_2 $$unsorted)) (= (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v_2)) (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred V_v_2))))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.57 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (c_List_Olist_ONil T_a))) (= _let_0 (c_List_Oremdups T_a _let_0))) ) 6.35/6.57 ( tc_Nat_Onat ) 6.35/6.57 ( tc_Int_Oint ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_z_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP c_Int_Onat V_z_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_2))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_w_2 $$unsorted) (V_z_2 $$unsorted)) (= (and (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_z_2) V_w_2)) (not (= V_w_2 V_z_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_z_2) V_w_2))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OPls, c_Int_OMin ) 6.35/6.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OMin, c_Int_OMin ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (= V_x_2 (c_Set_Othe__elem T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Nat_OSuc V_n)))) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.57 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP _let_0 (hAPP c_Nat_OSuc V_n)))) (hAPP _let_0 V_m)))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_n $$unsorted)) (= V_n (hAPP c_Code__Numeral_Onat__of (hAPP c_Code__Numeral_Oof__nat V_n))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_Z_2 $$unsorted)) (= (hBOOL (hAPP c_Nat__Numeral_Oneg V_Z_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_Z_2) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_k_2) c_Int_OPls)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Int_OBit1 V_k_2)) c_Int_OPls))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 c_Int_OMin))) (= (hBOOL (hAPP _let_1 V_k_2)) (hBOOL (hAPP _let_1 (c_Int_OBit1 V_k_2)))))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (c_Relation_Otrans T_b (c_Transitive__Closure_Otrancl T_b V_r_2)) ) 6.35/6.57 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (and (c_Relation_Orefl__on T_b V_A_2 V_r_2) (c_Relation_Osym T_b V_r_2) (c_Relation_Otrans T_b V_r_2))) ) 6.35/6.57 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (c_Orderings_Otop__class_Otop T_a)) (c_Orderings_Obot__class_Obot T_a))) ) 6.35/6.57 ( tc_HOL_Obool ) 6.35/6.57 ( tc_Nat_Onat ) 6.35/6.57 ( tc_Int_Oint ) 6.35/6.57 ( (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 6.35/6.57 ( (tc_fun tc_HOL_Obool tc_HOL_Obool) ) 6.35/6.57 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ( (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.57 ( (tc_fun tc_Product__Type_Ounit tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_member (tc_prod T_b T_b)))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (let ((_let_2 (hAPP _let_1 V_a_2))) (or (not (c_Relation_Otrans T_b V_r_2)) (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_b_2)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_b_2) V_c_2)) V_r_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) V_r_2)))))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (let ((_let_1 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (hAPP _let_0 V_w))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP _let_1 (hAPP (hAPP _let_1 (c_Groups_Ozero__class_Ozero T_a)) _let_2)) _let_2) (hAPP _let_0 (c_Int_OBit0 V_w))))))) ) 6.35/6.57 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.57 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.57 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_b))) (or (not (class_Nat_Osemiring__char__0 T_b)) (= (= V_n_2 V_m_2) (= (hAPP _let_0 V_m_2) (hAPP _let_0 V_n_2))))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_List_Oupto V_i_2 V_j_2))) (let ((_let_2 (hAPP _let_0 V_i_2))) (let ((_let_3 (hBOOL (hAPP _let_2 V_j_2)))) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_List_Oupto__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) V_i_2) V_j_2)))) (and (or _let_3 (= _let_1 (c_List_Olist_ONil tc_Int_Oint))) (or (not _let_3) (= _let_1 (hAPP (hAPP (c_List_Olist_OCons tc_Int_Oint) V_i_2) (c_List_Oupto (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_i_2) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_j_2)))))))))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OPls, c_Int_OMin ) 6.35/6.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( c_Int_OMin, c_Int_OMin ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Osym T_b V_r_2)) (not (c_Relation_Otrans T_b V_r_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) (hAPP (c_Relation_Oconverse T_b T_b) V_r_2)) V_r_2)) V_r_2))) ) 6.35/6.57 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 6.35/6.57 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.57 ( v_G, v_Ga, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_x_2) (c_Int_OBit1 c_Int_OPls))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_x_2)) (c_Groups_Oone__class_Oone T_b))))) ) 6.35/6.57 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.57 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.57 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.35/6.57 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.57 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.57 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.57 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.57 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) V_B_2))) (= (not (forall ((B_f $$unsorted)) (not (c_Fun_Obij__betw T_b T_c B_f V_A_2 V_B_2)) )) (= (hAPP (c_Finite__Set_Ocard T_c) V_B_2) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)))) ) 6.35/6.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint, (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_x) V_y)))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_A_2 $$unsorted) (V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (c_Set_Oimage T_c T_b V_f_2) (hAPP (c_Set_Oimage T_d T_c V_g_2) V_A_2)) (hAPP (c_Set_Oimage T_d T_b (hAPP (hAPP (c_COMBB T_c T_b T_d) V_f_2) V_g_2)) V_A_2)) ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.35/6.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Obounded__lattice T_1)) (class_Lattices_Obounded__lattice__bot (tc_fun T_2 T_1))) ) 6.35/6.57 ( tc_HOL_Obool, tc_HOL_Obool ) 6.35/6.57 ( tc_Nat_Onat, tc_HOL_Obool ) 6.35/6.57 ( tc_Int_Oint, tc_HOL_Obool ) 6.35/6.57 ( tc_Int_Oint, tc_Int_Oint ) 6.35/6.57 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.35/6.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.35/6.57 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.35/6.57 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Transitive__Closure_Otrancl T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (c_Relation_OId T_b))) (c_Transitive__Closure_Ortrancl T_b V_r_2)) ) 6.35/6.57 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ocard T_b))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 V_A_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2))))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.57 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Lattices_Oboolean__algebra T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_x_2)) (hAPP _let_1 V_y_2))) (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2)))))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (hAPP _let_0 V_x))) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP _let_1 V_y))) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_z))) (hBOOL (hAPP _let_1 V_z))))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.57 ( c_Int_OMin, c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x)) V_x) (c_Orderings_Otop__class_Otop T_a))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_w $$unsorted)) (let ((_let_0 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (let ((_let_2 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_3 (hAPP _let_2 V_w))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_3) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (= (c_Divides_Odiv__class_Omod tc_Int_Oint _let_0 _let_3) (hAPP (c_Product__Type_Osnd tc_Int_Oint tc_Int_Oint) (hAPP c_Divides_OnegateSnd (c_Divides_OnegDivAlg (hAPP _let_1 _let_0) (hAPP _let_1 _let_3)))))))))) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.57 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_N_2 $$unsorted)) (= (not (forall ((B_m $$unsorted)) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_x) V_N_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_x) B_m))) )) )) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) V_N_2))) ) 6.35/6.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_x) V_y)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (hAPP _let_0 V_x)) (hAPP _let_0 V_y)))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_b $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)))) (= (and (hBOOL (hAPP (hAPP _let_0 V_B_2) V_A_2)) (hBOOL (hAPP (hAPP _let_0 V_A_2) V_B_2))) (= V_B_2 V_A_2))) ) 6.35/6.57 ( (tc_Hoare__Mirabelle_Otriple t_a), v_Ga, v_G ) 6.35/6.57 ( (tc_Hoare__Mirabelle_Otriple t_a), v_G, v_Ga ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((T_b $$unsorted)) (= (c_Relation_OId T_b) (c_Transitive__Closure_Ortrancl T_b (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)))) ) 6.35/6.57 ( tc_Nat_Onat ) 6.35/6.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.57 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Nat_Osemiring__1__class_Oof__nat T_b))) (or (not (class_Rings_Oring__1 T_b)) (= (hAPP (c_Int_Oring__1__class_Oof__int T_b) (hAPP c_Int_OAbs__Integ (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_i_2) V_j_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) (hAPP _let_1 V_i_2)) (hAPP _let_1 V_j_2)))))) ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_l_2 $$unsorted)) (= (= c_Int_OPls (c_Int_OBit0 V_l_2)) (= c_Int_OPls V_l_2)) ) 6.35/6.57 ( c_Int_OPls ) 6.35/6.57 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.57 ( c_Int_OMin ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_x_2 $$unsorted) (V_P_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (not (forall ((B_y $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (or (not (hBOOL (hAPP (hAPP (c_member T_c) B_y) (hAPP (c_Set_Oimage T_b T_c V_f_2) _let_0)))) (hBOOL (hAPP V_P_2 (hAPP (c_Hilbert__Choice_Oinv__into T_b T_c _let_0 V_f_2) B_y))))) )) (hBOOL (hAPP V_P_2 V_x_2))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.35/6.57 ) 6.35/6.57 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (or (not (class_Orderings_Olinorder T_a)) (hBOOL (hAPP (hAPP _let_0 V_y) V_x)) (= V_y V_x) (hBOOL (hAPP (hAPP _let_0 V_x) V_y)))) ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.57 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.57 ) 6.35/6.58 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (not (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2))) ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_v $$unsorted) (V_u $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of T_b))) (let ((_let_2 (hAPP _let_1 V_u))) (let ((_let_3 (hAPP _let_0 _let_2))) (let ((_let_4 (hAPP _let_1 V_v))) (let ((_let_5 (hAPP _let_3 _let_4))) (let ((_let_6 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_7 (hAPP _let_6 _let_2))) (let ((_let_8 (hBOOL (hAPP _let_7 _let_4)))) (or (not (class_Orderings_Oord T_b)) (not (class_Int_Onumber T_b)) (and (or (not _let_8) (= _let_4 _let_5)) (or _let_8 (= _let_2 _let_5))))))))))))) ) 6.35/6.58 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 6.35/6.58 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Int_Oint ) 6.35/6.58 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 6.35/6.58 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_f_2 $$unsorted) (V_X_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (hAPP _let_0 V_X_2))) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP _let_1 (hAPP V_f_2 V_X_2)))) (hBOOL (hAPP _let_1 (c_Inductive_Ocomplete__lattice__class_Ogfp T_b V_f_2)))))) ) 6.35/6.58 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (= (c_Fun_Obij__betw T_b T_c V_f_2 _let_0 _let_1) (and (c_Fun_Oinj__on T_b T_c V_f_2 _let_0) (= _let_1 (hAPP (c_Set_Oimage T_b T_c V_f_2) _let_0)))))) ) 6.35/6.58 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.35/6.58 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_c) B_x) V_A_2))) (= (c_Orderings_Otop__class_Otop _let_0) (hAPP V_B_2 B_x))) ) (= (c_Orderings_Otop__class_Otop _let_0) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) V_B_2)))) ) 6.35/6.58 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_k) V_k) (c_Int_OBit0 V_k)) ) 6.35/6.58 ( c_Int_OPls ) 6.35/6.58 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.58 ( c_Int_OMin ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_b_2) V_a_2))) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_a_2 V_b_2))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_z $$unsorted)) (= (c_Groups_Ozero__class_Ozero tc_Int_Oint) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_z)) V_z)) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (hAPP _let_0 V_a_2))) (or (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP _let_1 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2))) (hBOOL (hAPP _let_1 (c_Groups_Ozero__class_Ozero T_b))))))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= V_x_2 (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.58 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (c_Int_Oiszero T_a (c_Groups_Ozero__class_Ozero T_a))) ) 6.35/6.58 ( tc_Nat_Onat ) 6.35/6.58 ( tc_Int_Oint ) 6.35/6.58 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Orderings_Oord T_c)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b T_c)) V_f_2) V_g_2)) (forall ((B_x $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_c) (hAPP V_f_2 B_x)) (hAPP V_g_2 B_x))) ))) ) 6.35/6.58 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (c_Relation_ORange T_c T_b))) (= (hAPP (hAPP (c_Set_Oinsert T_b) V_b_2) (hAPP _let_0 V_r_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert (tc_prod T_c T_b)) (hAPP (hAPP (c_Product__Type_OPair T_c T_b) V_a_2) V_b_2)) V_r_2)))) ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) (= V_B_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)))) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.58 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.58 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (or (not (class_Rings_Olinordered__idom T_b)) (not (class_Int_Onumber__ring T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (hAPP _let_0 V_x_2)) (hAPP _let_0 V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_x_2) V_y_2))))) ) 6.35/6.58 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 6.35/6.58 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_y) V_x))) (= (c_Nat__Transfer_Otsub V_x V_y) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_x) V_y))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( c_Int_OPls, c_Int_OMin ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin, c_Int_OMin ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) (= V_y (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= V_a_2 (c_Complete__Lattice_OInf__class_OInf T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.58 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (= (c_Groups_Ozero__class_Ozero T_a) (hAPP (c_Int_Oring__1__class_Oof__int T_a) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 6.35/6.58 ( tc_Nat_Onat ) 6.35/6.58 ( tc_Int_Oint ) 6.35/6.58 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)) V_a))) (= (c_Groups_Oone__class_Oone T_a) (c_Groups_Osgn__class_Osgn T_a V_a))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_l $$unsorted) (V_k $$unsorted)) (not (= (c_Int_OBit1 V_l) (c_Int_OBit0 V_k))) ) 6.35/6.58 ( c_Int_OPls, (c_Int_OBit1 c_Int_OPls) ) 6.35/6.58 ( (c_Int_OBit1 c_Int_OPls), c_Int_OMin ) 6.35/6.58 ( c_Int_OMin, c_Int_OPls ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_nat $$unsorted)) (let ((_let_0 (c_Nat_Osize__class_Osize tc_Nat_Onat))) (= (hAPP _let_0 (hAPP c_Nat_OSuc V_nat)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP _let_0 V_nat)) (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.58 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.58 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Inductive_Ocomplete__lattice__class_Ogfp T_b V_f_2))) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (c_Orderings_Oorder__class_Omono T_b T_b V_f_2)) (= _let_0 (hAPP V_f_2 _let_0)))) ) 6.35/6.58 ( c_Nat_OSuc, tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (c_Orderings_Otop__class_Otop _let_0) (hAPP (c_Groups_Ouminus__class_Ouminus _let_0) (c_Orderings_Obot__class_Obot _let_0)))) ) 6.35/6.58 ( tc_HOL_Obool ) 6.35/6.58 ( tc_Nat_Onat ) 6.35/6.58 ( tc_Int_Oint ) 6.35/6.58 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.58 ( tc_Product__Type_Ounit ) 6.35/6.58 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2)) (not (forall ((B_n $$unsorted) (B_f $$unsorted)) (not (= V_A_2 (hAPP (c_Set_Oimage tc_Nat_Onat T_b B_f) (hAPP (c_Set_OCollect tc_Nat_Onat) (hAPP (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat)) B_n))))) ))) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.58 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_x) V_y))) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_x))))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= V_a (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) V_b)) V_b))) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (= V_r_2 (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) (hAPP (c_Relation_Oconverse T_b T_b) V_r_2)) V_r_2))) ) 6.35/6.58 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_k) (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) c_Int_OMin) V_k)) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_a) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 V_b) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_1))))) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_a))) (or (not (class_Groups_Oordered__ab__group__add T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) V_b))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_b)) (hAPP _let_1 V_a)))))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_M_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_M_2))) (not (forall ((B_h $$unsorted)) (not (c_Fun_Obij__betw tc_Nat_Onat T_b B_h (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Finite__Set_Ocard T_b) V_M_2)) V_M_2)) ))) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_n $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (hAPP _let_0 _let_1))) (let ((_let_3 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (or (not (hBOOL (hAPP _let_2 (hAPP _let_3 V_n)))) (and (hBOOL (hAPP _let_2 (hAPP _let_3 (c_Int_OBit1 V_n)))) (hBOOL (hAPP _let_2 (hAPP _let_3 (c_Int_OBit0 V_n)))))))))) ) 6.35/6.58 ( c_Int_OPls ) 6.35/6.58 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.58 ( c_Int_OMin ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (= (= V_n_2 V_m_2) (= (hAPP (hAPP _let_0 V_n_2) V_k_2) (hAPP (hAPP _let_0 V_m_2) V_k_2)))) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (let ((_let_1 (c_Groups_Oone__class_Oone T_a))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) _let_1) _let_1)) (hAPP _let_0 V_w)) (hAPP _let_0 (c_Int_OBit0 V_w)))))) ) 6.35/6.58 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.58 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.58 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.58 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.58 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 _let_0)) (= V_A_2 (hAPP (c_Set_Oimage T_c T_b (c_Hilbert__Choice_Oinv__into T_b T_c _let_0 V_f_2)) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2))))) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_b) V_a))) (= V_a V_b) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_b) V_a))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (c_Fun_Oid (tc_prod T_b T_c)) (c_Product__Type_Omap__pair T_b T_b T_c T_c (c_Fun_Oid T_b) (c_Fun_Oid T_c))) ) 6.35/6.58 ( tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Owellorder T_b)) (not (hBOOL (hAPP V_P_2 V_k_2))) (hBOOL (hAPP V_P_2 (c_Orderings_Oord__class_OLeast T_b V_P_2)))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Relation_ORange T_b T_b))) (= (hAPP _let_0 V_r_2) (hAPP _let_0 (c_Transitive__Closure_Otrancl T_b V_r_2)))) ) 6.35/6.58 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_1)) (class_Lattices_Oboolean__algebra (tc_fun T_2 T_1))) ) 6.35/6.58 ( tc_HOL_Obool, tc_HOL_Obool ) 6.35/6.58 ( tc_Nat_Onat, tc_HOL_Obool ) 6.35/6.58 ( tc_Int_Oint, tc_HOL_Obool ) 6.35/6.58 ( tc_Int_Oint, tc_Int_Oint ) 6.35/6.58 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.35/6.58 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.35/6.58 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.35/6.58 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_x_2 $$unsorted) (V_P_2 $$unsorted)) (or (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP V_P_2 (hAPP c_Code__Numeral_Oof__nat B_y)))) )) (hBOOL (hAPP V_P_2 V_x_2))) ) 6.35/6.58 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.35/6.58 ( c_Nat_OSuc, (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Nat__Numeral_Oneg ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert tc_Nat_Onat) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat__Numeral_Oneg ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_Onat ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))))) ) 6.35/6.58 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.35/6.58 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.35/6.58 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 6.35/6.58 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 6.35/6.58 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 6.35/6.58 ( c_fequal, (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.35/6.58 ( c_fequal, (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) ) 6.35/6.58 ( (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))) ) 6.35/6.58 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Nat_Onat) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Set_Oimage tc_Nat_Onat tc_Nat_Onat c_Nat_OSuc) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.58 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) ) 6.35/6.58 ( c_fconj, (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Oint__of ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral) ) 6.35/6.58 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.35/6.58 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.35/6.58 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 6.35/6.58 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.35/6.58 ( c_Int_Ointrel, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool)))) ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Product__Type_OPair _let_1 _let_1))) ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_1 _let_1) (c_Orderings_Obot__class_Obot _let_1)))) ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0))) ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.58 ( c_Int_OMin, (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin, (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 6.35/6.58 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 6.35/6.58 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 6.35/6.58 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) ) 6.35/6.58 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.35/6.58 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.35/6.58 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Nat_OSuc ) 6.35/6.58 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.58 ( c_Int_Onat, (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat) ) 6.35/6.58 ( c_Code__Numeral_Onat__of, (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.58 ( c_Nitpick_Oint__gcd, (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal))) ) 6.35/6.58 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.35/6.58 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.35/6.58 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.58 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (c_Set_Oinsert (tc_prod (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1)))) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 c_FunDef_Opair__leq)))) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 c_FunDef_Opair__leq)))) ) 6.35/6.58 ( c_FunDef_Omax__weak, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omax__strict))))) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral)) ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin), c_Nat__Numeral_Oneg ) 6.35/6.58 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))) ) 6.35/6.58 ( c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))) ) 6.35/6.58 ( c_fFalse, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.35/6.58 ( v_Ga, (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) v_G) ) 6.35/6.58 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.35/6.58 ( c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 6.35/6.58 ( c_fTrue, (c_COMBK tc_HOL_Obool tc_Nat_Onat) ) 6.35/6.58 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) c_FunDef_Opair__less)) ) 6.35/6.58 ( (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) ) 6.35/6.58 ( (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)) ) 6.35/6.58 ( (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal), (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) tc_Int_Oint) ) 6.35/6.58 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)))) ) 6.35/6.58 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))), (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.35/6.58 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 6.35/6.58 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), (c_Product__Type_Oprod_Oprod__case tc_Int_Oint tc_Int_Oint tc_HOL_Obool) ) 6.35/6.58 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))) ) 6.35/6.58 ( c_FunDef_Omin__weak, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omin__strict))))) ) 6.35/6.58 ( c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Int_Oint) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Finite__Set_Ocard tc_Product__Type_Ounit) ) 6.35/6.58 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat)), (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.35/6.58 ( (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal), (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) ) 6.35/6.58 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.35/6.58 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)), (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.35/6.58 ( v_G, (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), (c_Finite__Set_Ocard tc_HOL_Obool) ) 6.35/6.58 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.35/6.58 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)) ) 6.35/6.58 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))), c_Int_OAbs__Integ ) 6.35/6.58 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), c_Int_OAbs__Integ ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_l_2 $$unsorted)) (= (hAPP (hAPP (c_List_Omap tc_Int_Oint tc_Nat_Onat) c_Int_Onat) V_l_2) (c_List_Oreturn__list V_l_2)) ) 6.35/6.58 ( (c_List_Olist_ONil tc_Int_Oint) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (or (not (class_Groups_Oordered__ab__group__add__abs T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_b) V_a_2)) V_b_2)) (and (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) V_b_2)))))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_n_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) V_n_2) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_n_2)) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_u_2 $$unsorted)) (= (hAPP (c_Finite__Set_Ocard tc_Int_Oint) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Int_Oint (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_u_2)) (hAPP c_Int_Onat V_u_2)) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2)) (c_Fun_Oinj__on T_c T_b (c_Fun_Othe__inv__into T_b T_c V_A_2 V_f_2) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2))) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (c_Set_Oimage T_c T_b V_f_2))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d _let_2) V_A_2) (hAPP (hAPP (c_COMBB _let_1 _let_2 T_d) _let_0) V_B_2)) (hAPP _let_0 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d _let_1) V_A_2) V_B_2)))))) ) 6.35/6.58 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (c_Groups_Oone__class_Oone T_a))) (or (not (class_Fields_Olinordered__field T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) V_b))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Rings_Oinverse__class_Odivide T_a) (hAPP (hAPP _let_1 V_a) V_b)) (hAPP (hAPP _let_1 _let_2) _let_2))) V_b)))))) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (hAPP _let_0 (hAPP V_f_2 V_A_2)) V_A_2))) (hBOOL (hAPP (hAPP _let_0 (c_Inductive_Ocomplete__lattice__class_Olfp T_b V_f_2)) V_A_2)))) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))), c_Int_OAbs__Integ, tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Set_Oimage T_b T_b V_f_2))) (let ((_let_1 (hAPP _let_0 V_A_2))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) _let_1) V_A_2))) (not (c_Fun_Oinj__on T_b T_b V_f_2 V_A_2)) (= V_A_2 _let_1)))) ) 6.35/6.58 ( c_Nat_OSuc, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_d $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0))) (let ((_let_2 (tc_fun T_c tc_HOL_Obool))) (let ((_let_3 (tc_fun T_c _let_0))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_d _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_d _let_3 _let_0) (hAPP (hAPP (c_COMBB _let_2 (tc_fun _let_3 _let_0) T_d) _let_1) V_B_2)) V_C_2)) (hAPP (hAPP _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d _let_2) V_A_2) V_B_2)) V_C_2)))))) ) 6.35/6.58 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (let ((_let_2 (tc_fun T_c _let_0))) (= (c_Complete__Lattice_OSup__class_OSup _let_0 (hAPP (c_Set_OCollect _let_0) (hAPP (hAPP (c_COMBB _let_1 tc_HOL_Obool _let_0) (c_HOL_OEx T_c)) (hAPP (hAPP (c_COMBB _let_1 _let_1 _let_0) (hAPP (c_COMBS T_c tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_c) c_fconj) (hAPP (hAPP (c_COMBC T_c _let_1 tc_HOL_Obool) (c_member T_c)) V_A_2)))) (hAPP (hAPP (c_COMBC _let_0 _let_2 _let_1) (hAPP (hAPP (c_COMBB (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_2 _let_1) _let_0) (c_COMBB _let_0 tc_HOL_Obool T_c)) c_fequal)) V_B_2))))) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) V_B_2))))) ) 6.35/6.58 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (hAPP _let_0 V_z))) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) (not (hBOOL (hAPP _let_1 V_y))) (hBOOL (hAPP _let_1 V_x))))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (or (not (class_Rings_Osemiring__1 T_a)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_n)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP _let_0 V_m)) (hAPP _let_0 V_n))))) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) _let_0))) (not (= (hAPP _let_1 _let_0) (hAPP _let_1 V_A_2))) (= V_A_2 _let_0)))) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) V_b))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) V_b))) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a)) V_b)))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_R_2 $$unsorted) (T_b $$unsorted)) (= (c_Transitive__Closure_Ortrancl T_b (c_Transitive__Closure_Otrancl T_b V_R_2)) (c_Transitive__Closure_Ortrancl T_b V_R_2)) ) 6.35/6.58 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ogroup__add T_b)) (= (= V_a_2 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_b_2)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_b_2) (c_Groups_Ozero__class_Ozero T_b)))) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) B_x) B_y)) (hAPP (hAPP _let_0 B_x) (hAPP (hAPP _let_0 B_y) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))))) )) (hBOOL (hAPP (hAPP (c_member T_b) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)) V_A_2))) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (let ((_let_2 (tc_fun T_c _let_0))) (= (c_Complete__Lattice_OInf__class_OInf _let_0 (hAPP (c_Set_OCollect _let_0) (hAPP (hAPP (c_COMBB _let_1 tc_HOL_Obool _let_0) (c_HOL_OEx T_c)) (hAPP (hAPP (c_COMBB _let_1 _let_1 _let_0) (hAPP (c_COMBS T_c tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_c) c_fconj) (hAPP (hAPP (c_COMBC T_c _let_1 tc_HOL_Obool) (c_member T_c)) V_A_2)))) (hAPP (hAPP (c_COMBC _let_0 _let_2 _let_1) (hAPP (hAPP (c_COMBB (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_2 _let_1) _let_0) (c_COMBB _let_0 tc_HOL_Obool T_c)) c_fequal)) V_B_2))))) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) V_B_2))))) ) 6.35/6.58 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_r_2)) (c_Wellfounded_Owf T_b (c_Transitive__Closure_Otrancl T_b V_r_2))) ) 6.35/6.58 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Complete__Lattice_OSup__class_OSup T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (c_Orderings_Obot__class_Obot T_b))) ) 6.35/6.58 ( tc_HOL_Obool ) 6.35/6.58 ( tc_Nat_Onat ) 6.35/6.58 ( tc_Int_Oint ) 6.35/6.58 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.58 ( tc_Product__Type_Ounit ) 6.35/6.58 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((T_f $$unsorted) (T_e $$unsorted) (T_d $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_x_H_2 $$unsorted) (V_g_H_2 $$unsorted) (V_f_H_2 $$unsorted) (V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted)) (or (not (= (hAPP V_f_2 (hAPP V_g_2 V_x_2)) (hAPP V_f_H_2 (hAPP V_g_H_2 V_x_H_2)))) (= (hAPP (hAPP (c_Fun_Ocomp T_c T_b T_d V_f_2) V_g_2) V_x_2) (hAPP (hAPP (c_Fun_Ocomp T_e T_b T_f V_f_H_2) V_g_H_2) V_x_H_2))) ) 6.35/6.58 ( tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Oof__nat, c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool), c_Code__Numeral_Oof__nat ) 6.35/6.58 ( tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool), c_Code__Numeral_Oof__nat, c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool), c_Code__Numeral_Oof__nat ) 6.35/6.58 ( tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_Onat, (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_Onat ) 6.35/6.58 ( tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), c_Int_Onat, (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_Onat ) 6.35/6.58 ( tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral, tc_Int_Oint, tc_Nat_Onat, (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.58 ( tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral, tc_Int_Oint, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Finite__Set_Ocard tc_Product__Type_Ounit), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Oord__class_Omax T_b))) (let ((_let_2 (c_Big__Operators_Olattice_OSup__fin T_b _let_1 V_A_2))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_B_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= _let_2 (hAPP (hAPP _let_1 (c_Big__Operators_Olattice_OSup__fin T_b _let_1 V_B_2)) _let_2)))))) ) 6.35/6.58 ( v_G, v_Ga, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (let ((_let_1 (hAPP _let_0 V_x_2))) (let ((_let_2 (hAPP _let_1 V_A_2))) (let ((_let_3 (c_Big__Operators_Olinorder__class_OMax T_b _let_2))) (let ((_let_4 (tc_fun T_b tc_HOL_Obool))) (let ((_let_5 (c_Groups_Ominus__class_Ominus _let_4))) (let ((_let_6 (hAPP _let_5 V_A_2))) (let ((_let_7 (c_Orderings_Obot__class_Obot _let_4))) (let ((_let_8 (hAPP _let_1 _let_7))) (let ((_let_9 (hAPP _let_6 _let_8))) (let ((_let_10 (= _let_7 _let_9))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or (not _let_10) (= V_x_2 _let_3)) (or _let_10 (= _let_3 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMax T_b _let_9))))))))))))))))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.58 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_w_2))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w_2) V_z_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP c_Int_Onat V_w_2)) (hAPP c_Int_Onat V_z_2))))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin, c_Int_OMin ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (= (c_Groups_Oone__class_Oone T_a) (hAPP (c_Int_Oring__1__class_Oof__int T_a) (c_Groups_Oone__class_Oone tc_Int_Oint)))) ) 6.35/6.58 ( tc_Nat_Onat ) 6.35/6.58 ( tc_Int_Oint ) 6.35/6.58 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_z $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z))) (= V_z (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Int_Onat V_z)))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)))) (or (not (hBOOL (hAPP (hAPP _let_0 V_A_2) V_B_2))) (not (hBOOL (hAPP (hAPP _let_0 V_B_2) V_A_2))) (= V_B_2 V_A_2))) ) 6.35/6.58 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.58 ( v_G, v_Ga, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (c_SetInterval_Oord__class_OatLeastAtMost T_b V_l_2 V_u_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_l_2) V_u_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_u_2) (c_Orderings_Obot__class_Obot _let_0)))))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Olattice T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)))) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.58 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Transitive__Closure_Otrancl T_b V_r_2))) (= _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) _let_0) V_r_2)))) ) 6.35/6.58 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.58 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.58 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olinorder__class_OMax T_b V_A_2) (hAPP (c_Finite__Set_Ofold1 T_b (c_Orderings_Oord__class_Omax T_b)) V_A_2))) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Rings_Oring__1 T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (c_Groups_Ozero__class_Ozero T_b)) (c_Int_Oring__1__class_OInts T_b)))) ) 6.35/6.58 ( tc_Nat_Onat ) 6.35/6.58 ( tc_Int_Oint ) 6.35/6.58 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_v) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_w))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (hAPP _let_0 V_v)) (hAPP _let_0 V_w))))) ) 6.35/6.58 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= V_x_2 (c_Big__Operators_Olattice_OInf__fin T_b (c_Orderings_Oord__class_Omin T_b) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.58 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (not (forall ((B_n $$unsorted)) (not (= V_z_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_w_2) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Nat_OSuc B_n))))) )) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w_2) V_z_2))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin, c_Int_OMin ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_A_2 $$unsorted)) (or (not (c_Nat__Transfer_Onat__set V_A_2)) (= (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) (hAPP (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) V_A_2))) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Int_Oint) V_A_2)))) ) 6.35/6.58 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.35/6.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a)) V_b))) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) V_b)))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2))) (not (hBOOL (hAPP _let_0 V_B_2))) (hBOOL (hAPP _let_0 V_A_2)))) ) 6.35/6.58 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (class_Lattices_Osemilattice__inf T_b)) (= (c_Orderings_Oord__class_Omin T_b) (c_Lattices_Osemilattice__inf__class_Oinf T_b))) ) 6.35/6.58 ( tc_HOL_Obool ) 6.35/6.58 ( tc_Nat_Onat ) 6.35/6.58 ( tc_Int_Oint ) 6.35/6.58 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_d $$unsorted)) (= (c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy tc_Int_Oint V_d) (c_Lazy__Sequence_Osmall__lazy_H V_d (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_d))) ) 6.35/6.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.58 ( c_Int_OMin ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)) (c_Groups_Oone__class_Oone T_a)))) ) 6.35/6.58 ( tc_Nat_Onat ) 6.35/6.58 ( tc_Int_Oint ) 6.35/6.58 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.58 ) 6.35/6.58 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Set_Oinsert _let_0))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2) (c_Complete__Lattice_OSup__class_OSup _let_0 (hAPP (hAPP _let_1 V_A_2) (hAPP (hAPP _let_1 V_B_2) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))))))) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.59 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_n $$unsorted)) (not (= V_n (hAPP c_Nat_OSuc V_n))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.59 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.59 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (or (not (class_Rings_Olinordered__idom T_a)) (= V_y V_x) (hBOOL (hAPP (hAPP _let_0 V_x) V_y)) (hBOOL (hAPP (hAPP _let_0 V_y) V_x)))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)))) V_n) (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_n)))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_v_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_d $$unsorted)) (= (hAPP V_a_2 (hAPP V_b_2 V_v_2)) (hAPP (hAPP (c_Fun_Ocomp T_d T_c T_b V_a_2) V_b_2) V_v_2)) ) 6.35/6.59 ( c_Int_OPls, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Onat__of, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Code__Numeral_Ocode__numeral, tc_Int_Oint, tc_Nat_Onat ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Orderings_Oord__class_Omin T_b)) V_x_2) V_A_2))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.59 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (not (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) V_A_2))) )) (not (= (c_Groups_Oone__class_Oone tc_Nat_Onat) _let_0))) (= _let_0 (hAPP (c_Finite__Set_Ocard T_b) V_A_2)))) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hBOOL (hAPP (hAPP (c_member T_b) (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) V_A_2))) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__sup__class_Osup T_b)) (c_Orderings_Obot__class_Obot T_b)) V_A_2) (c_Complete__Lattice_OSup__class_OSup T_b V_A_2))) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_m $$unsorted)) (= V_m (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_m)) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))))) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite (tc_prod T_b T_b)) V_r_2))) (= (c_Wellfounded_Owf T_b V_r_2) (c_Wellfounded_Oacyclic T_b V_r_2))) ) 6.35/6.59 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.59 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.35/6.59 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_m_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat V_m_2) (hAPP c_Nat_OSuc V_m_2)) (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) V_m_2) (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.59 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.59 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP c_Nat_OSuc V_n)) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.59 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.59 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_x_2)) (c_Groups_Oone__class_Oone T_b))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_x_2) (c_Int_OBit1 c_Int_OPls))))) ) 6.35/6.59 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.59 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2) (hAPP (c_Finite__Set_Ofold1 T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b)) V_A_2))) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_l $$unsorted)) (let ((_let_0 (c_Groups_Ominus__class_Ominus tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 c_Int_OMin))) (= (c_Int_OBit1 (hAPP _let_1 V_l)) (hAPP _let_1 (c_Int_OBit0 V_l))))) ) 6.35/6.59 ( c_Int_OPls ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.59 ( c_Int_OMin ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((BOUND_VARIABLE_101200 $$unsorted)) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) BOUND_VARIABLE_101200)))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 BOUND_VARIABLE_101200)))) ) 6.35/6.59 ( c_Int_OPls ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.59 ( c_Int_OMin ) 6.35/6.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((BOUND_VARIABLE_101211 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (or (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) BOUND_VARIABLE_101211))) (= (hAPP _let_0 (c_Int_OBit1 BOUND_VARIABLE_101211)) (hAPP (hAPP (c_HOL_OLet tc_Nat_Onat tc_Nat_Onat) (hAPP _let_0 BOUND_VARIABLE_101211)) (hAPP (hAPP (c_COMBB tc_Nat_Onat tc_Nat_Onat tc_Nat_Onat) c_Nat_OSuc) (hAPP (hAPP (c_COMBS tc_Nat_Onat tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oplus__class_Oplus tc_Nat_Onat)) (c_COMBI tc_Nat_Onat))))))) ) 6.35/6.59 ( c_Int_OPls ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.59 ( c_Int_OMin ) 6.35/6.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_z $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z))) (= (hAPP c_Nat_OSuc (hAPP c_Int_Onat V_z)) (hAPP c_Int_Onat (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_z)))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.59 ( c_Int_OMin ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (class_Lattices_Osemilattice__sup T_b)) (= (c_Orderings_Oord__class_Omax T_b) (c_Lattices_Osemilattice__sup__class_Osup T_b))) ) 6.35/6.59 ( tc_HOL_Obool ) 6.35/6.59 ( tc_Nat_Onat ) 6.35/6.59 ( tc_Int_Oint ) 6.35/6.59 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP _let_0 V_v)) (hAPP _let_0 V_w)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_v) V_w))))) ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_R2_2 $$unsorted) (T_c $$unsorted) (V_R1_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Otrans T_b V_R1_2)) (not (c_Relation_Otrans T_c V_R2_2)) (c_Relation_Otrans (tc_prod T_b T_c) (c_Wellfounded_Olex__prod T_b T_c V_R1_2 V_R2_2))) ) 6.35/6.59 ( c_Wellfounded_Oless__than, tc_Nat_Onat, c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Obounded__lattice__bot T_a)) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) (c_Orderings_Obot__class_Obot T_a)))) ) 6.35/6.59 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.59 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.35/6.59 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((BOUND_VARIABLE_101441 $$unsorted)) (let ((_let_0 (c_List_Olist_ONil BOUND_VARIABLE_101441))) (= _let_0 (hAPP (c_List_Orotate1 BOUND_VARIABLE_101441) _let_0))) ) 6.35/6.59 ( tc_Nat_Onat ) 6.35/6.59 ( tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_w $$unsorted)) (let ((_let_0 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_2 (hAPP _let_1 V_w))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) _let_2))) (= (c_Divides_Odiv__class_Omod tc_Int_Oint _let_0 _let_2) (hAPP (c_Product__Type_Osnd tc_Int_Oint tc_Int_Oint) (c_Divides_OposDivAlg _let_0 _let_2))))))) ) 6.35/6.59 ( c_Int_OPls ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.59 ( c_Int_OMin ) 6.35/6.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_Oimage T_c T_b V_f_2) (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool)))) ) 6.35/6.59 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.59 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.35/6.59 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__sup T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.59 ( c_FunDef_Opair__less, (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.35/6.59 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.59 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_A_2 $$unsorted) (V_Abs_2 $$unsorted) (V_Rep_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Typedef_Otype__definition T_b T_c V_Rep_2 V_Abs_2 V_A_2)) (= V_A_2 (hAPP (c_Set_Oimage T_b T_c V_Rep_2) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))))) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Code__Numeral_Oof__nat, c_Code__Numeral_Onat__of, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ( c_Int_OInteg, c_Int_OAbs__Integ, c_Int_ORep__Integ, (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_e $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_c))) (let ((_let_1 (tc_fun T_c T_d))) (= (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c T_d) (hAPP (hAPP (c_COMBB T_e _let_1 T_b) V_f_2) V_g_2)) (hAPP (hAPP (c_COMBS _let_0 T_c T_d) (hAPP (hAPP (c_COMBB T_e _let_1 _let_0) V_f_2) (hAPP (hAPP (c_COMBB T_b T_e _let_0) V_g_2) (c_Product__Type_Ofst T_b T_c)))) (c_Product__Type_Osnd T_b T_c))))) ) 6.35/6.59 ( c_Nat_OSuc, (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal), tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.59 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (tc_fun tc_Int_Oint tc_HOL_Obool), tc_HOL_Obool, tc_Int_Oint, tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_n_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_n_2) (c_SetInterval_Oord__class_OatLeastAtMost tc_Nat_Onat (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_n_2)) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of T_a))) (let ((_let_2 (hAPP _let_1 V_w))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP _let_1 (c_Int_OBit1 V_w)) (hAPP (hAPP _let_0 (hAPP (hAPP _let_0 (c_Groups_Oone__class_Oone T_a)) _let_2)) _let_2)))))) ) 6.35/6.59 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.59 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (c_Finite__Set_Ocard (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_OPow T_b) V_A_2)) (hAPP (hAPP (c_Power_Opower__class_Opower tc_Nat_Onat) (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)))) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_a_2)) V_b_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_b_2)) V_a_2)))))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (= (= (c_Groups_Osgn__class_Osgn T_b V_a_2) (hAPP (c_Groups_Ouminus__class_Ouminus T_b) (c_Groups_Oone__class_Oone T_b))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_a_2) (c_Groups_Ozero__class_Ozero T_b))))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_m_2 $$unsorted) (V_w_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (hAPP _let_0 _let_1))) (let ((_let_3 (hBOOL (hAPP _let_2 V_w_2)))) (= (and (or _let_3 (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_m_2)) (or (not _let_3) (= V_w_2 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2)))) (= V_m_2 (hAPP c_Int_Onat V_w_2))))))) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_OMin ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_w_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_w_2)) (c_Int_Oring__1__class_OInts T_b)))) ) 6.35/6.59 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.59 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted)) (or (hBOOL (hAPP V_P_2 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (not (hBOOL (hAPP V_P_2 V_n_2))) (not (forall ((B_k $$unsorted)) (or (not (hBOOL (hAPP V_P_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) B_k) (c_Groups_Oone__class_Oone tc_Nat_Onat))))) (not (forall ((B_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) B_i) B_k))) (not (hBOOL (hAPP V_P_2 B_i)))) )) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_k) V_n_2)))) ))) ) 6.35/6.59 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.35/6.59 ( c_Nat_OSuc, (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Nat__Numeral_Oneg ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat__Numeral_Oneg ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_Onat ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))))) ) 6.35/6.59 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.35/6.59 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.35/6.59 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 6.35/6.59 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 6.35/6.59 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 6.35/6.59 ( c_fequal, (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.35/6.59 ( c_fequal, (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) ) 6.35/6.59 ( (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))) ) 6.35/6.59 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Nat_Onat) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Set_Oimage tc_Nat_Onat tc_Nat_Onat c_Nat_OSuc) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.59 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) ) 6.35/6.59 ( c_fconj, (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Oint__of ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral) ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 6.35/6.59 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.35/6.59 ( c_Int_Ointrel, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool)))) ) 6.35/6.59 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Product__Type_OPair _let_1 _let_1))) ) 6.35/6.59 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_1 _let_1) (c_Orderings_Obot__class_Obot _let_1)))) ) 6.35/6.59 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0))) ) 6.35/6.59 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.59 ( c_Int_OMin, (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 6.35/6.59 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) ) 6.35/6.59 ( c_Int_OMin, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.35/6.59 ( c_Int_OMin, (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 6.35/6.59 ( c_Int_OMin, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.35/6.59 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 6.35/6.59 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 6.35/6.59 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 6.35/6.59 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.35/6.59 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) ) 6.35/6.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.35/6.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.35/6.59 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Nat_OSuc ) 6.35/6.59 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.59 ( c_Int_Onat, (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat) ) 6.35/6.59 ( c_Code__Numeral_Onat__of, (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 6.35/6.59 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) ) 6.35/6.59 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.59 ( c_Nitpick_Oint__gcd, (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal))) ) 6.35/6.59 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.35/6.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.35/6.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.59 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (c_Set_Oinsert (tc_prod (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1)))) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 c_FunDef_Opair__leq)))) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 c_FunDef_Opair__leq)))) ) 6.35/6.59 ( c_FunDef_Omax__weak, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omax__strict))))) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral)) ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin), c_Nat__Numeral_Oneg ) 6.35/6.59 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))) ) 6.35/6.59 ( c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))) ) 6.35/6.59 ( c_fFalse, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.35/6.59 ( v_Ga, (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) v_G) ) 6.35/6.59 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.35/6.59 ( c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 6.35/6.59 ( c_fTrue, (c_COMBK tc_HOL_Obool tc_Nat_Onat) ) 6.35/6.59 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) c_FunDef_Opair__less)) ) 6.35/6.59 ( (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) ) 6.35/6.59 ( (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)) ) 6.35/6.59 ( (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal), (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) tc_Int_Oint) ) 6.35/6.59 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)))) ) 6.35/6.59 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))), (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.35/6.59 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 6.35/6.59 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), (c_Product__Type_Oprod_Oprod__case tc_Int_Oint tc_Int_Oint tc_HOL_Obool) ) 6.35/6.59 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))) ) 6.35/6.59 ( c_FunDef_Omin__weak, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omin__strict))))) ) 6.35/6.59 ( c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Int_Oint) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Finite__Set_Ocard tc_Product__Type_Ounit) ) 6.35/6.59 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat)), (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.35/6.59 ( (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal), (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) ) 6.35/6.59 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.35/6.59 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)), (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.35/6.59 ( v_G, (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), (c_Finite__Set_Ocard tc_HOL_Obool) ) 6.35/6.59 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.35/6.59 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)) ) 6.35/6.59 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))), c_Int_OAbs__Integ ) 6.35/6.59 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), c_Int_OAbs__Integ ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_P_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (c_Relation_ORange T_c T_b) (hAPP (c_Set_OCollect (tc_prod T_c T_b)) (hAPP (c_Product__Type_Oprod_Oprod__case T_c T_b tc_HOL_Obool) V_P_2))) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBB (tc_fun T_c tc_HOL_Obool) tc_HOL_Obool T_b) (c_HOL_OEx T_c)) (hAPP (c_COMBC T_c T_b tc_HOL_Obool) V_P_2)))) ) 6.35/6.59 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.59 ( c_fequal, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.59 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), tc_Int_Oint, tc_Int_Oint ) 6.35/6.59 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Otrans T_b V_r_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) V_r_2) V_r_2)) V_r_2))) ) 6.35/6.59 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_l_2) V_u_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (c_SetInterval_Oord__class_OgreaterThanLessThan T_b V_l_2 V_u_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_u_2) (c_Orderings_Obot__class_Obot _let_0))) (c_SetInterval_Oord__class_OgreaterThanAtMost T_b V_l_2 V_u_2)))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Groups_Ominus__class_Ominus _let_0))) (let ((_let_2 (hAPP _let_1 V_A_2))) (let ((_let_3 (c_Set_Oinsert T_b))) (let ((_let_4 (hAPP _let_3 V_x_2))) (let ((_let_5 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_6 (hAPP _let_4 _let_5))) (let ((_let_7 (hAPP _let_2 _let_6))) (let ((_let_8 (hAPP _let_4 V_A_2))) (let ((_let_9 (c_Big__Operators_Olinorder__class_OMin T_b _let_8))) (let ((_let_10 (= _let_5 _let_7))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or _let_10 (= (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMin T_b _let_7)) _let_9)) (or (not _let_10) (= V_x_2 _let_9))))))))))))))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.59 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_w $$unsorted) (V_v $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_2 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_3 (hAPP _let_2 V_v))) (let ((_let_4 (hAPP _let_2 V_w))) (let ((_let_5 (c_Divides_OposDivAlg _let_4 _let_3))) (let ((_let_6 (hAPP _let_1 _let_4))) (let ((_let_7 (hBOOL (hAPP _let_6 _let_3)))) (or (not (hBOOL (hAPP (hAPP _let_1 _let_0) _let_3))) (and (or _let_7 (= (hAPP (c_Divides_Oadjust _let_3) (c_Divides_OposDivAlg _let_4 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP _let_2 (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) _let_3))) _let_5)) (or (not _let_7) (= _let_5 (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) _let_0) _let_4))))))))))))) ) 6.35/6.59 ( c_Int_OPls, c_Int_OPls ) 6.35/6.59 ( c_Int_OPls, (c_Int_OBit1 c_Int_OPls) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero T_b))) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (= V_a_2 _let_0) (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2))))) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (hAPP _let_0 V_w)) (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_w))))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, tc_Nat_Onat ) 6.35/6.59 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_a))) (or (not (class_Groups_Ogroup__add T_a)) (= V_a (hAPP _let_0 (hAPP _let_0 V_a))))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (or (not (= (hAPP (hAPP _let_0 V_a_2) _let_1) (hAPP (hAPP _let_0 V_b_2) _let_1))) (= V_b_2 V_a_2)))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.59 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_OCollect T_b) (hAPP (c_COMBK tc_HOL_Obool T_b) c_fFalse))) ) 6.35/6.59 ( tc_HOL_Obool ) 6.35/6.59 ( tc_Nat_Onat ) 6.35/6.59 ( tc_Int_Oint ) 6.35/6.59 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.59 ( tc_Product__Type_Ounit ) 6.35/6.59 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_k_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (not (forall ((B_b $$unsorted) (B_B $$unsorted)) (or (not (= V_k_2 (hAPP (c_Finite__Set_Ocard T_b) B_B))) (and (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_k_2) (not (= B_B (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_member T_b) B_b) B_B)) (not (= V_A_2 (hAPP (hAPP (c_Set_Oinsert T_b) B_b) B_B)))) )) (= (hAPP (c_Finite__Set_Ocard T_b) V_A_2) (hAPP c_Nat_OSuc V_k_2))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 6.35/6.59 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (or (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_b) V_a_2)) V_b_2)) (and (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) V_b_2)))))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) (= V_y (hAPP (hAPP (c_Orderings_Oord__class_Omin T_a) V_x) V_y))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (let ((_let_1 (hAPP _let_0 V_m))) (= (hAPP _let_1 (hAPP c_Nat_OSuc V_n)) (hAPP c_Nat_OSuc (hAPP _let_1 V_n))))) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (= (= (hAPP _let_0 V_x_2) (hAPP _let_0 V_y_2)) (= V_y_2 V_x_2))) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero T_b))) (or (not (class_Groups_Ogroup__add T_b)) (= (= (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2) _let_0) (= V_a_2 _let_0)))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_c tc_HOL_Obool))) (= (c_Orderings_Otop__class_Otop (tc_fun (tc_prod T_b T_c) tc_HOL_Obool)) (hAPP (hAPP (c_Product__Type_OSigma T_b T_c) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))) (hAPP (c_COMBK _let_0 T_b) (c_Orderings_Otop__class_Otop _let_0))))) ) 6.35/6.59 ( tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.59 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (= (hAPP (c_Finite__Set_Ocard T_b) V_A_2) (hAPP (c_Finite__Set_Ocard T_c) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2))) (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2))) ) 6.35/6.59 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.59 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.59 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.59 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Divides_Osemiring__div T_a)) (= (c_Divides_Odiv__class_Omod T_a (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_b) (c_Divides_Odiv__class_Omod T_a V_a V_b))) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (c_Orderings_Otop__class_Otop _let_0) (c_Complete__Lattice_OInf__class_OInf _let_0 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))) ) 6.35/6.59 ( tc_HOL_Obool ) 6.35/6.59 ( tc_Nat_Onat ) 6.35/6.59 ( tc_Int_Oint ) 6.35/6.59 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.59 ( tc_Product__Type_Ounit ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ocard T_b))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP _let_0 V_B_2)) (hAPP _let_0 V_A_2)))) (= V_A_2 V_B_2))) ) 6.35/6.59 ( v_G, v_Ga, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= V_x (hAPP (c_Product__Type_Ofst T_a T_b) (hAPP (hAPP (c_Product__Type_OPair T_a T_b) V_x) V_y))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.59 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.59 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.59 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_k_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (c_Groups_Ouminus__class_Ouminus (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_k_2)) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_k_2))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_x))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_n $$unsorted) (V_i $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP c_Int_Onat V_i)) V_n) (c_Int_Onat__aux V_i V_n)) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__sup T_a)) (= V_a (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_a) V_a))) ) 6.35/6.59 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.59 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.35/6.59 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (hBOOL (hAPP _let_2 V_x_2))) (not (hBOOL (hAPP _let_2 V_y_2))) (= (= V_y_2 V_x_2) (= (hAPP c_Int_Onat V_y_2) (hAPP c_Int_Onat V_x_2))))))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.59 ( c_Int_OMin, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_OMin ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_n $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) V_n) (hAPP (c_Int_Oring__1__class_Oof__int T_a) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n)))) ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (c_Int_Oiszero T_a (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OPls))) ) 6.35/6.59 ( tc_Nat_Onat ) 6.35/6.59 ( tc_Int_Oint ) 6.35/6.59 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_3 (hAPP _let_2 _let_1))) (or (not (hBOOL (hAPP (hAPP _let_0 _let_1) V_a_2))) (= (and (hBOOL (hAPP (hAPP _let_0 V_b_2) V_a_2)) (hBOOL (hAPP _let_3 V_b_2))) (hBOOL (hAPP _let_3 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_a_2) V_b_2))))))))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.59 ( c_Int_OMin, c_Int_OPls ) 6.35/6.59 ( c_Int_OMin, c_Int_OMin ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_k $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (c_Groups_Oone__class_Oone T_a)) (hAPP _let_0 V_k)) (hAPP _let_0 (c_Int_Osucc V_k))))) ) 6.35/6.59 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.59 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.59 ( c_Int_OMin, tc_Nat_Onat ) 6.35/6.59 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((BOUND_VARIABLE_102610 $$unsorted) (BOUND_VARIABLE_102611 $$unsorted)) (or (hBOOL (hAPP (c_Finite__Set_Ofinite BOUND_VARIABLE_102611) BOUND_VARIABLE_102610)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (c_Nitpick_Ocard_H BOUND_VARIABLE_102611 BOUND_VARIABLE_102610))) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((BOUND_VARIABLE_102620 $$unsorted) (BOUND_VARIABLE_102621 $$unsorted)) (let ((_let_0 (tc_List_Olist BOUND_VARIABLE_102621))) (let ((_let_1 (tc_fun BOUND_VARIABLE_102621 tc_HOL_Obool))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite BOUND_VARIABLE_102621) BOUND_VARIABLE_102620))) (= (c_Nitpick_Ocard_H BOUND_VARIABLE_102621 BOUND_VARIABLE_102620) (hAPP (c_Nat_Osize__class_Osize _let_0) (c_Hilbert__Choice_OEps _let_0 (hAPP (hAPP (c_COMBS _let_0 tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) _let_0) c_fconj) (hAPP (hAPP (c_COMBC _let_0 _let_1 tc_HOL_Obool) (hAPP (hAPP (c_COMBB _let_1 (tc_fun _let_1 tc_HOL_Obool) _let_0) c_fequal) (c_List_Oset BOUND_VARIABLE_102621))) BOUND_VARIABLE_102620))) (c_List_Odistinct BOUND_VARIABLE_102621)))))))) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)) (hBOOL (hAPP (hAPP _let_0 _let_1) (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2))))))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (or (not (class_Int_Onumber__ring T_b)) (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP _let_0 V_x_2)) (hAPP _let_0 V_y_2)))))) ) 6.35/6.59 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Int_Oint ) 6.35/6.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 6.35/6.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_P_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_c))) (= (c_HOL_OThe _let_0 (hAPP (hAPP (c_COMBS _let_0 T_c tc_HOL_Obool) (hAPP (hAPP (c_COMBB T_b (tc_fun T_c tc_HOL_Obool) _let_0) V_P_2) (c_Product__Type_Ofst T_b T_c))) (c_Product__Type_Osnd T_b T_c))) (c_HOL_OThe _let_0 (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c tc_HOL_Obool) V_P_2)))) ) 6.35/6.59 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.59 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), tc_Int_Oint, tc_Int_Oint ) 6.35/6.59 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (= V_l_2 V_k_2) (= (c_Int_OBit0 V_l_2) (c_Int_OBit0 V_k_2))) ) 6.35/6.59 ( c_Int_OPls, (c_Int_OBit1 c_Int_OPls) ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls) ) 6.35/6.59 ( (c_Int_OBit1 c_Int_OPls), c_Int_OMin ) 6.35/6.59 ( c_Int_OMin, c_Int_OPls ) 6.35/6.59 ( c_Int_OMin, (c_Int_OBit1 c_Int_OPls) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (= V_A_2 _let_2) (not (hBOOL (hAPP _let_0 V_B_2))) (= V_B_2 _let_2) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OSup__fin T_b V_B_2)) (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2))))))) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.59 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.59 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_v $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_v) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (c_Int_OBit1 c_Int_OPls)))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (hAPP _let_0 V_v)) (c_Groups_Oone__class_Oone T_a))))) ) 6.35/6.59 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__add__class_Osetsum T_b tc_Nat_Onat) (hAPP (c_COMBK tc_Nat_Onat T_b) (c_Groups_Oone__class_Oone tc_Nat_Onat))) V_A_2) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)) ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 6.35/6.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 6.35/6.59 ) 6.35/6.59 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)) (= V_y_2 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) V_y_2)))) ) 6.35/6.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.59 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.59 ) 6.35/6.60 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) _let_1) V_a))) (not (hBOOL (hAPP _let_2 V_b))) (hBOOL (hAPP _let_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b))))))) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 V_A_2)) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (c_Finite__Set_Ofold1 T_b _let_0) V_A_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 V_A_2)))) ) 6.35/6.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (= (c_SetInterval_Oord__class_OgreaterThanAtMost T_b V_k_2 V_l_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_k_2) V_l_2))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_X_2 $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (or (= _let_2 V_X_2) (hBOOL (hAPP (hAPP (c_member (tc_prod _let_1 _let_1)) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) V_X_2) _let_2)) c_FunDef_Omin__strict)))))) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_A_2 $$unsorted)) (= (hAPP (c_Finite__Set_Ocard tc_Int_Oint) (hAPP (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) V_A_2)) (hAPP (c_Finite__Set_Ocard tc_Nat_Onat) V_A_2)) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_N_2 $$unsorted) (V_M_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_M_2) V_N_2))) (= V_M_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Big__Operators_Olinorder__class_OMax T_b V_M_2)) (c_Big__Operators_Olinorder__class_OMax T_b V_N_2))))) ) 6.35/6.60 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_103130 $$unsorted) (BOUND_VARIABLE_103131 $$unsorted) (BOUND_VARIABLE_103132 $$unsorted)) (hBOOL (hAPP (hAPP (c_member BOUND_VARIABLE_103132) BOUND_VARIABLE_103131) (hAPP (hAPP (c_Set_Oinsert BOUND_VARIABLE_103132) BOUND_VARIABLE_103131) BOUND_VARIABLE_103130))) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (let ((_let_1 (c_Finite__Set_Ofinite T_b))) (let ((_let_2 (c_Finite__Set_Ocard T_b))) (let ((_let_3 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP _let_1 V_A_2))) (not (hBOOL (hAPP _let_1 V_B_2))) (= (hAPP (hAPP _let_0 (hAPP _let_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_3) V_A_2) V_B_2))) (hAPP _let_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_3) V_A_2) V_B_2))) (hAPP (hAPP _let_0 (hAPP _let_2 V_A_2)) (hAPP _let_2 V_B_2)))))))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Oone__class_Oone T_a)) (c_Groups_Ozero__class_Ozero T_a))))) ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.60 ( (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_103207 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 BOUND_VARIABLE_103207))) (or (hBOOL (hAPP c_Nat__Numeral_Oneg _let_1)) (= (hAPP c_Int_Onat (c_Divides_Odiv__class_Omod tc_Int_Oint (c_Groups_Oone__class_Oone tc_Int_Oint) _let_1)) (c_Divides_Odiv__class_Omod tc_Nat_Onat (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) BOUND_VARIABLE_103207)))))) ) 6.35/6.60 ( c_Int_OPls ) 6.35/6.60 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.60 ( c_Int_OMin ) 6.35/6.60 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.60 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_103219 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (hAPP c_Nat_OSuc _let_0))) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) BOUND_VARIABLE_103219)))) (= _let_1 (c_Divides_Odiv__class_Omod tc_Nat_Onat _let_1 (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) BOUND_VARIABLE_103219)))))) ) 6.35/6.60 ( c_Int_OPls ) 6.35/6.60 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.60 ( c_Int_OMin ) 6.35/6.60 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.60 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (let ((_let_1 (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat))) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) (hAPP _let_1 V_k_2)) (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) V_k_2) (c_Orderings_Obot__class_Obot _let_0))) (hAPP _let_1 (hAPP c_Nat_OSuc V_k_2))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.60 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.60 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_member (tc_prod T_b T_b)))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (let ((_let_2 (hAPP _let_1 V_a_2))) (let ((_let_3 (c_Transitive__Closure_Otrancl T_b V_r_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_b_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_b_2) V_c_2)) (c_Transitive__Closure_Ortrancl T_b V_r_2)))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Wellfounded_Opred__nat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_P_2 $$unsorted) (T_b $$unsorted)) (= (forall ((B_x $$unsorted)) (not (hBOOL (hAPP V_P_2 B_x))) ) (= (hAPP (c_Set_OCollect T_b) V_P_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 6.35/6.60 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hAPP (c_Set_OCollect T_b) (hAPP c_fequal V_a_2))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_y_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) V_y_2) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (= V_y_2 (hAPP c_Code__Numeral_Onat__of (hAPP c_Code__Numeral_Oof__nat V_y_2)))) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_c) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2))) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)))) ) 6.35/6.60 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.60 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.60 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_a_2) V_A_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Inductive_Ocomplete__lattice__class_Olfp T_b V_f_2))) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (c_Orderings_Oorder__class_Omono T_b T_b V_f_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) _let_0) (hAPP V_f_2 _let_0))))) ) 6.35/6.60 ( c_Nat_OSuc, tc_Nat_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Groups_Omonoid__add T_b)) (= (c_List_Omonoid__add__class_Olistsum T_b) (c_List_Ofoldl T_b T_b (c_Groups_Oplus__class_Oplus T_b) (c_Groups_Ozero__class_Ozero T_b)))) ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Complete__Lattice_OInf__class_OInf T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (c_Orderings_Otop__class_Otop T_b))) ) 6.35/6.60 ( tc_HOL_Obool ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 6.35/6.60 ( (tc_fun tc_HOL_Obool tc_HOL_Obool) ) 6.35/6.60 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.60 ( (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.60 ( tc_Product__Type_Ounit ) 6.35/6.60 ( (tc_fun tc_Product__Type_Ounit tc_HOL_Obool) ) 6.35/6.60 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_x) V_y))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (= _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) (hAPP (c_COMBK _let_0 T_c) _let_1))))) ) 6.35/6.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (or (not (hBOOL (hAPP _let_0 V_A_2))) (not (hBOOL (hAPP _let_0 V_B_2))) (and (not (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2)))) )) (not (= (c_Groups_Oone__class_Oone tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP _let_1 V_A_2)) (hAPP _let_1 V_B_2)) (hAPP _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2)))))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_103721 $$unsorted) (BOUND_VARIABLE_103722 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_103722) BOUND_VARIABLE_103721))) (= (c_Lazy__Sequence_Oempty tc_Int_Oint) (c_Lazy__Sequence_Osmall__lazy_H BOUND_VARIABLE_103722 BOUND_VARIABLE_103721))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, c_Int_OMin ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_103732 $$unsorted) (BOUND_VARIABLE_103733 $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_103733) BOUND_VARIABLE_103732)) (= (c_Lazy__Sequence_Osmall__lazy_H BOUND_VARIABLE_103733 BOUND_VARIABLE_103732) (c_Lazy__Sequence_Oappend tc_Int_Oint (hAPP (c_Lazy__Sequence_Osingle tc_Int_Oint) BOUND_VARIABLE_103732) (c_Lazy__Sequence_Osmall__lazy_H BOUND_VARIABLE_103733 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) BOUND_VARIABLE_103732) (c_Groups_Oone__class_Oone tc_Int_Oint)))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, c_Int_OMin ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_0 (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat))) (or (not (c_Nat__Transfer_Onat__set V_A_2)) (not (c_Nat__Transfer_Onat__set V_B_2)) (= (= (hAPP _let_0 V_A_2) (hAPP _let_0 V_B_2)) (= V_B_2 V_A_2)))) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_103813 $$unsorted) (BOUND_VARIABLE_103814 $$unsorted) (BOUND_VARIABLE_103815 $$unsorted) (BOUND_VARIABLE_103816 $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite BOUND_VARIABLE_103816) BOUND_VARIABLE_103815))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite BOUND_VARIABLE_103814) BOUND_VARIABLE_103813))) (= (hAPP (c_Finite__Set_Ocard (tc_sum BOUND_VARIABLE_103816 BOUND_VARIABLE_103814)) (c_Sum__Type_OPlus BOUND_VARIABLE_103816 BOUND_VARIABLE_103814 BOUND_VARIABLE_103815 BOUND_VARIABLE_103813)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard BOUND_VARIABLE_103816) BOUND_VARIABLE_103815)) (hAPP (c_Finite__Set_Ocard BOUND_VARIABLE_103814) BOUND_VARIABLE_103813)))) ) 6.35/6.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit, (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Orderings_Otop__class_Otop T_b) (c_Complete__Lattice_OSup__class_OSup T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))))) ) 6.35/6.60 ( tc_HOL_Obool ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.60 ( tc_Product__Type_Ounit ) 6.35/6.60 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (c_Orderings_Oord__class_Omin T_b) (c_Orderings_Oord_Omin T_b (c_Orderings_Oord__class_Oless__eq T_b)))) ) 6.35/6.60 ( tc_HOL_Obool ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.60 ( (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_w $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_2 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_3 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_4 (hAPP _let_2 _let_1))) (let ((_let_5 (hAPP _let_3 V_w))) (let ((_let_6 (hBOOL (hAPP _let_4 _let_5)))) (let ((_let_7 (c_Divides_OposDivAlg _let_1 _let_5))) (or (not (hBOOL (hAPP (hAPP _let_2 _let_0) _let_5))) (and (or (not _let_6) (= _let_7 (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) _let_0) _let_1))) (or _let_6 (= _let_7 (hAPP (c_Divides_Oadjust _let_5) (c_Divides_OposDivAlg _let_1 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP _let_3 (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) _let_5))))))))))))))) ) 6.35/6.60 ( c_Int_OPls ) 6.35/6.60 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.60 ( c_Int_OMin ) 6.35/6.60 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.60 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_v $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_1 (hAPP _let_0 V_v))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) _let_1))) (= _let_1 (hAPP c_Nat_OSuc (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) _let_1) (c_Groups_Oone__class_Oone tc_Nat_Onat))))))) ) 6.35/6.60 ( c_Int_OPls ) 6.35/6.60 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.60 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.60 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Ocomm__semiring__1 T_a)) (= V_a (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (= V_m (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_n))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_n)) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_a))) (or (not (class_Rings_Ocomm__ring__1 T_a)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (hAPP _let_0 (c_Groups_Oone__class_Oone T_a))) V_x) (hAPP _let_0 V_x)))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero T_b)) V_a_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) V_a_2))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Oone__class_Oone T_a)) (c_Groups_Ozero__class_Ozero T_a))))) ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus _let_0))) (= (hAPP _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) V_B_2)) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) (hAPP (hAPP (c_COMBB _let_0 _let_0 T_c) _let_1) V_B_2))))) ) 6.35/6.60 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (let ((_let_3 (tc_fun _let_1 _let_0))) (= (c_Wellfounded_Ofinite__psubset T_b) (hAPP (c_Set_OCollect (tc_prod _let_1 _let_1)) (hAPP (c_Product__Type_Oprod_Oprod__case _let_1 _let_1 tc_HOL_Obool) (hAPP (hAPP (c_COMBC _let_1 _let_2 _let_2) (hAPP (hAPP (c_COMBB _let_3 (tc_fun _let_2 _let_2) _let_1) (c_COMBS _let_1 tc_HOL_Obool tc_HOL_Obool)) (hAPP (hAPP (c_COMBB _let_2 _let_3 _let_1) (hAPP (c_COMBB tc_HOL_Obool _let_0 _let_1) c_fconj)) (c_Orderings_Oord__class_Oless _let_1)))) (c_Finite__Set_Ofinite T_b))))))))) ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_b)) (= (= V_b_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_b_2) V_a_2)) (= V_a_2 (c_Groups_Ozero__class_Ozero T_b)))) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_Oimage T_c T_b V_f_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool)))) ) 6.35/6.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_f_2 $$unsorted)) (or (not (hBOOL (hAPP V_f_2 (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_a_2) V_b_2)))) (hBOOL (hAPP (hAPP (c_Product__Type_Ocurry T_b T_c tc_HOL_Obool V_f_2) V_a_2) V_b_2))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat, (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat, (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_104334 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_104334) c_Int_OPls)) (= (hAPP _let_0 (c_Int_Osucc BOUND_VARIABLE_104334)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 BOUND_VARIABLE_104334))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls ) 6.35/6.60 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.60 ( c_Int_OMin ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_104346 $$unsorted)) (let ((_let_0 (c_Groups_Oone__class_Oone tc_Nat_Onat))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_104346) c_Int_OPls))) (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) _let_0) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) BOUND_VARIABLE_104346))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls ) 6.35/6.60 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.60 ( c_Int_OMin ) 6.35/6.60 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.60 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Set_OPow T_b))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (hAPP _let_1 V_a_2))) (let ((_let_3 (tc_fun T_b tc_HOL_Obool))) (let ((_let_4 (hAPP _let_0 V_A_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun _let_3 tc_HOL_Obool)) _let_4) (hAPP (c_Set_Oimage _let_3 _let_3 _let_2) _let_4)) (hAPP _let_0 (hAPP _let_2 V_A_2)))))))) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Rings_Osemiring__1 T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (c_Groups_Ozero__class_Ozero T_b)) (c_Nat_Osemiring__1__class_ONats T_b)))) ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (forall ((B_x $$unsorted) (B_y $$unsorted) (BOUND_VARIABLE_104494 $$unsorted)) (let ((_let_0 (c_member (tc_prod T_b T_b)))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (let ((_let_2 (hAPP _let_1 B_x))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 B_y)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_y) BOUND_VARIABLE_104494)) V_r_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 BOUND_VARIABLE_104494)) V_r_2)))))) ) (c_Relation_Otrans T_b V_r_2)) ) 6.35/6.60 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_S_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_S_2))) (= V_S_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (c_Set_Oimage T_b T_b _let_0) V_S_2)) (hAPP _let_0 (c_Big__Operators_Olinorder__class_OMax T_b V_S_2))))) ) 6.35/6.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_k $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (= (hAPP _let_0 (c_Int_OBit0 V_k)) (c_Int_OBit0 (hAPP _let_0 V_k)))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls ) 6.35/6.60 ( c_Int_OMin ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (= (hAPP c_Int_Onat (hAPP c_Int_OAbs__Integ (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_x_2) V_y_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_x_2) V_y_2))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (c_Complete__Lattice_OInf__class_OInf _let_0 (hAPP (c_Set_Oimage T_c _let_0 V_B_2) V_A_2)) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) V_B_2))) ) 6.35/6.60 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_104656 $$unsorted) (BOUND_VARIABLE_104657 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (or (and (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) BOUND_VARIABLE_104656) _let_0))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_104657) BOUND_VARIABLE_104656)))) (= (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) _let_0) BOUND_VARIABLE_104657) (c_Divides_OposDivAlg BOUND_VARIABLE_104657 BOUND_VARIABLE_104656)))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, c_Int_OMin ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_104673 $$unsorted) (BOUND_VARIABLE_104674 $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_104674) BOUND_VARIABLE_104673)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) BOUND_VARIABLE_104673) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (= (c_Divides_OposDivAlg BOUND_VARIABLE_104674 BOUND_VARIABLE_104673) (hAPP (c_Divides_Oadjust BOUND_VARIABLE_104673) (c_Divides_OposDivAlg BOUND_VARIABLE_104674 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) BOUND_VARIABLE_104673))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, c_Int_OMin ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_104832 $$unsorted) (BOUND_VARIABLE_104833 $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) BOUND_VARIABLE_104833) BOUND_VARIABLE_104832)) (= (c_List_Olist_ONil tc_Int_Oint) (c_List_Oupto BOUND_VARIABLE_104833 BOUND_VARIABLE_104832))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls, c_Int_OMin ) 6.35/6.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, c_Int_OMin ) 6.35/6.60 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_104842 $$unsorted) (BOUND_VARIABLE_104843 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) BOUND_VARIABLE_104843) BOUND_VARIABLE_104842))) (= (c_List_Oupto BOUND_VARIABLE_104843 BOUND_VARIABLE_104842) (hAPP (hAPP (c_List_Olist_OCons tc_Int_Oint) BOUND_VARIABLE_104843) (c_List_Oupto (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) BOUND_VARIABLE_104843) (c_Groups_Oone__class_Oone tc_Int_Oint)) BOUND_VARIABLE_104842)))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls, c_Int_OMin ) 6.35/6.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, c_Int_OMin ) 6.35/6.60 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (or (not (class_Orderings_Olinorder T_b)) (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2)) (= (not (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2))) (= V_x_2 V_y_2)))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_m $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (= (hAPP _let_0 (hAPP c_Nat_OSuc V_m)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) (hAPP _let_0 V_m)))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.60 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.60 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_104956 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) BOUND_VARIABLE_104956) c_Int_OPls)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP _let_0 BOUND_VARIABLE_104956)) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 (c_Int_Opred BOUND_VARIABLE_104956))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls ) 6.35/6.60 ( c_Int_OMin ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((BOUND_VARIABLE_104969 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) BOUND_VARIABLE_104969) c_Int_OPls))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) BOUND_VARIABLE_104969)) (c_Groups_Oone__class_Oone tc_Nat_Onat)))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls ) 6.35/6.60 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.60 ( c_Int_OMin ) 6.35/6.60 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.60 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_b $$unsorted)) (= (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Relation_ODomain T_b T_b) (c_Relation_OId T_b))) ) 6.35/6.60 ( tc_HOL_Obool ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.60 ( tc_Product__Type_Ounit ) 6.35/6.60 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (= (and (= _let_0 V_m_2) (= _let_0 V_n_2)) (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m_2) V_n_2)))) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_1)) (class_Complete__Lattice_Ocomplete__lattice (tc_fun T_2 T_1))) ) 6.35/6.60 ( tc_HOL_Obool, tc_HOL_Obool ) 6.35/6.60 ( tc_Nat_Onat, tc_HOL_Obool ) 6.35/6.60 ( tc_Int_Oint, tc_HOL_Obool ) 6.35/6.60 ( tc_Int_Oint, tc_Int_Oint ) 6.35/6.60 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.35/6.60 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.35/6.60 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.35/6.60 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Set_Oimage T_b T_c V_f_2))) (let ((_let_1 (hAPP _let_0 V_A_2))) (or (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= _let_1 (hAPP (hAPP (c_Set_Oinsert T_c) (hAPP V_f_2 V_x_2)) _let_1))))) ) 6.35/6.60 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (c_Groups_Oone__class_Oone T_a))) (or (not (class_Rings_Osemiring__1 T_a)) (= _let_0 (hAPP (hAPP (c_Power_Opower__class_Opower T_a) _let_0) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))))))) ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_COMBC T_b _let_0 tc_HOL_Obool))) (let ((_let_2 (c_member T_b))) (let ((_let_3 (hAPP _let_1 _let_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBS T_b tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_b) c_fdisj) (hAPP _let_3 V_A_2))) (hAPP _let_3 V_B_2)))))))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (= (or (and (hBOOL (hAPP (hAPP _let_2 V_i_2) V_k_2)) (hBOOL (hAPP (hAPP _let_0 _let_1) V_i_2))) (and (hBOOL (hAPP (hAPP _let_2 V_k_2) V_i_2)) (hBOOL (hAPP (hAPP _let_0 V_i_2) _let_1))) (= _let_1 V_k_2)) (= _let_1 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_i_2) V_k_2)))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, c_Int_OMin ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_a_2) (c_Complete__Lattice_OSup__class_OSup T_b V_A_2)) (c_Complete__Lattice_OSup__class_OSup T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)))) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) V_z) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_z) V_z))) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Ozero__neq__one T_a)) (not (= (c_Groups_Ozero__class_Ozero T_a) (c_Groups_Oone__class_Oone T_a)))) ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ocomm__monoid__add T_a)) (= V_a (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Obot__class_Obot T_b))) (or (not (class_Lattices_Obounded__lattice__bot T_b)) (= (= _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) V_y_2)) (and (= V_y_2 _let_0) (= V_x_2 _let_0))))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.60 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (hBOOL (hAPP (hAPP (c_member T_b) V_i_2) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_k_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_i_2) V_k_2)))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Relation_ODomain T_b T_b))) (= (hAPP _let_0 V_r_2) (hAPP _let_0 (c_Transitive__Closure_Otrancl T_b V_r_2)))) ) 6.35/6.60 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero T_a))) ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_B_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (c_Relation_OImage T_c T_b V_r_2))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (tc_fun T_c tc_HOL_Obool))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_1) V_B_2) (hAPP (hAPP (c_COMBB _let_2 _let_1 T_c) _let_0) (hAPP (hAPP (c_COMBC T_c _let_2 _let_2) (c_Set_Oinsert T_c)) (c_Orderings_Obot__class_Obot _let_2)))) (hAPP _let_0 V_B_2))))) ) 6.35/6.60 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_w $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Oring__char__0 T_a)) (not (class_Int_Onumber__ring T_a)) (not (c_Int_Oiszero T_a (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit1 V_w))))) ) 6.35/6.60 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.60 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.60 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.60 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.60 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_k) c_Int_OMin) (c_Int_Opred V_k)) ) 6.35/6.60 ( c_Int_OPls ) 6.35/6.60 ( c_Int_OMin ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit1 c_Int_OPls)) (c_Groups_Oone__class_Oone T_a))) ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (let ((_let_1 (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat))) (let ((_let_2 (hAPP c_Nat_OSuc V_k_2))) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) (hAPP _let_1 V_k_2)) (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) _let_2) (c_Orderings_Obot__class_Obot _let_0))) (hAPP _let_1 _let_2))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.60 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.60 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) B_x) B_y)) (hAPP (hAPP _let_0 B_x) (hAPP (hAPP _let_0 B_y) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))))) )) (hBOOL (hAPP (hAPP (c_member T_b) (c_Big__Operators_Olattice_OInf__fin T_b (c_Orderings_Oord__class_Omin T_b) V_A_2)) V_A_2))) ) 6.35/6.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_h_2 $$unsorted) (T_c $$unsorted) (V_F_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_F_2))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (hAPP (c_Set_Oimage T_b T_c V_h_2) V_F_2)))) ) 6.35/6.60 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.60 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.60 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_P_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Divides_OnegDivAlg__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) V_a0_2) V_a1_2)))) (not (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (hAPP V_P_2 B_a))) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Divides_OnegDivAlg__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) B_a) B_b)))) (and (not (hBOOL (hAPP (hAPP _let_0 B_b) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 _let_1) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) B_a) B_b)))) (not (hBOOL (hAPP _let_2 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) B_b))))) (hBOOL (hAPP _let_2 B_b)))))) )) (hBOOL (hAPP (hAPP V_P_2 V_a0_2) V_a1_2))) ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OPls, c_Int_OMin ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.35/6.60 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.60 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.60 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) ) 6.35/6.60 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.60 ( (c_Set_Oinsert tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.60 ( (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Product__Type_OPair _let_1 _let_1))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.35/6.60 ( (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 6.35/6.60 ( (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.35/6.60 ( (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_fconj ) 6.35/6.60 ( (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Onat__of ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less ) 6.35/6.60 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 6.35/6.60 ( (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Groups_Oone__class_Oone tc_Int_Oint), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))) ) 6.35/6.60 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool) ) 6.35/6.60 ( (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) tc_Int_Oint), c_Nitpick_Oint__gcd, (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal) ) 6.35/6.60 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.60 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.60 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.60 ( (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat), c_Nat_OSuc, (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal) ) 6.35/6.60 ( (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)), v_Ga, v_G ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omax__weak, c_FunDef_Omax__strict ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omin__weak, c_FunDef_Omin__strict ) 6.35/6.60 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), c_Int_OPls, c_Int_Onat ) 6.35/6.60 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), (c_Int_OBit1 c_Int_OPls), c_Int_Onat ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (let ((_let_2 (c_Orderings_Otop__class_Otop (tc_fun T_d tc_HOL_Obool)))) (or (not (c_Fun_Obij__betw T_b T_c V_f_2 _let_0 _let_1)) (not (c_Fun_Obij__betw T_c T_d V_g_2 _let_1 _let_2)) (c_Fun_Obij__betw T_b T_d (hAPP (c_Fun_Ocomp T_c T_d T_b V_g_2) V_f_2) _let_0 _let_2))))) ) 6.35/6.60 ( c_Code__Numeral_Oof__nat, tc_Code__Numeral_Ocode__numeral, c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.35/6.60 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, c_Code__Numeral_Onat__of, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral ) 6.35/6.60 ( c_Int_Onat, tc_Nat_Onat, (c_Groups_Oabs__class_Oabs tc_Int_Oint), tc_Int_Oint, tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (hBOOL (hAPP _let_2 V_x_2))) (not (hBOOL (hAPP _let_2 V_y_2))) (= (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Int_Onat V_x_2)) (hAPP c_Int_Onat V_y_2)))))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OPls, c_Int_OMin ) 6.35/6.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( c_Int_OMin, c_Int_OMin ) 6.35/6.60 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) (= (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ( v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_b_2)) (hAPP _let_1 V_a_2))) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2)))))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_n_2 $$unsorted)) (= (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_n_2) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n_2)) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.60 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.60 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (c_Orderings_Oord_Omax T_b (hAPP (c_COMBC T_b T_b tc_HOL_Obool) (c_Orderings_Oord__class_Oless__eq T_b))) (c_Orderings_Oord__class_Omin T_b))) ) 6.35/6.60 ( tc_Nat_Onat ) 6.35/6.60 ( tc_Int_Oint ) 6.35/6.60 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.60 ( (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (c_Groups_Ozero__class_Ozero T_b)) V_a_2)) (= (c_Groups_Osgn__class_Osgn T_b V_a_2) (c_Groups_Oone__class_Oone T_b)))) ) 6.35/6.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.60 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.60 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.60 ) 6.35/6.60 (instantiation (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Osym T_b V_r_2)) (not (c_Relation_Osym T_b V_s_2)) (c_Relation_Osym T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) V_s_2))) ) 6.35/6.60 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.61 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Big__Operators_Olinorder__class_OMax T_b V_A_2))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_B_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= _let_1 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) (c_Big__Operators_Olinorder__class_OMax T_b V_B_2)) _let_1))))) ) 6.35/6.61 ( v_G, v_Ga, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (= (hAPP (hAPP (c_Equiv__Relations_Oquotient T_b) V_A_2) V_r_2) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))) (= V_A_2 (c_Orderings_Obot__class_Obot _let_0)))) ) 6.35/6.61 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_member (tc_prod T_b T_b)))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (let ((_let_2 (hAPP _let_1 V_a_2))) (let ((_let_3 (c_Transitive__Closure_Otrancl T_b V_r_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_b_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_b_2) V_c_2)) V_r_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Wellfounded_Opred__nat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (tc_List_Olist T_b))) (= (hAPP (hAPP (c_Set_Oinsert _let_0) (c_List_Olist_ONil T_b)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))) (c_List_Olists T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 6.35/6.61 ( tc_Nat_Onat ) 6.35/6.61 ( tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (= V_x_2 (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_z_H_2 $$unsorted) (V_z_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (hBOOL (hAPP _let_2 V_z_2))) (not (hBOOL (hAPP _let_2 V_z_H_2))) (= (= (hAPP c_Int_Onat V_z_2) (hAPP c_Int_Onat V_z_H_2)) (= V_z_H_2 V_z_2)))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.61 ( c_Int_OMin, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_OMin ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (forall ((B_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) B_a) V_A_2))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (hAPP V_B_2 B_a)))) )) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tc_fun T_c tc_HOL_Obool)) V_A_2) V_B_2)))) ) 6.35/6.61 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.61 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.61 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_1 (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) (let ((_let_2 (hAPP _let_0 _let_1))) (let ((_let_3 (c_Power_Opower__class_Opower T_a))) (or (not (class_Rings_Oring__1 T_a)) (= (hAPP (hAPP _let_3 V_a) _let_2) (hAPP (hAPP _let_3 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) _let_2))))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (= (hAPP (hAPP _let_0 (hAPP c_Nat_OSuc V_m)) V_n) (hAPP (hAPP _let_0 V_m) (hAPP c_Nat_OSuc V_n)))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_c) B_x) V_A_2))) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP V_B_2 B_x))) ) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) V_B_2)))) ) 6.35/6.61 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_k_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (let ((_let_1 (hAPP _let_0 V_k_2))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (c_Orderings_Obot__class_Obot _let_2))) (let ((_let_4 (hAPP _let_1 _let_3))) (or (not (class_Orderings_Oorder T_b)) (= _let_4 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) _let_4) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_k_2))))))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Oabs__class_Oabs T_a))) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) V_b))) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP _let_0 V_a)) (hAPP _let_0 V_b)))))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_f_2 $$unsorted) (T_d $$unsorted) (V_g_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (hAPP (c_Set_Oimage T_c T_b V_g_2) _let_0)))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_d) (hAPP (c_Set_Oimage T_c T_d (hAPP (hAPP (c_COMBB T_b T_d T_c) V_f_2) V_g_2)) _let_0))))) ) 6.35/6.61 ( (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool), (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), tc_Int_Oint, (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.35/6.61 ( c_fconj, (tc_fun tc_HOL_Obool tc_HOL_Obool), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint, tc_HOL_Obool ) 6.35/6.61 ( (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (tc_fun tc_Int_Oint tc_HOL_Obool), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.35/6.61 ( (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal), (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Nitpick_Oint__gcd, tc_Int_Oint, (tc_fun tc_Int_Oint tc_Int_Oint) ) 6.35/6.61 ( (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal), (tc_fun tc_Nat_Onat tc_HOL_Obool), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Ocomm__ring__1 T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_x) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_y)) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_x) V_y))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_n_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (let ((_let_1 (c_Nat_Osemiring__1__class_Oof__nat T_b))) (let ((_let_2 (hAPP _let_1 V_n_2))) (let ((_let_3 (c_Groups_Oplus__class_Oplus T_b))) (let ((_let_4 (c_Groups_Oone__class_Oone T_b))) (or (not (class_Rings_Ocomm__semiring__1 T_b)) (= (hAPP (hAPP _let_0 (hAPP (hAPP _let_3 _let_4) _let_4)) (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__add__class_Osetsum tc_Nat_Onat T_b) _let_1) (c_SetInterval_Oord__class_OatLeastAtMost tc_Nat_Onat (c_Groups_Oone__class_Oone tc_Nat_Onat) V_n_2))) (hAPP (hAPP _let_0 _let_2) (hAPP (hAPP _let_3 _let_2) _let_4))))))))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((BOUND_VARIABLE_106491 $$unsorted) (BOUND_VARIABLE_106492 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_106492) BOUND_VARIABLE_106491))) (= (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) (c_SetInterval_Oord__class_OatLeastAtMost tc_Int_Oint BOUND_VARIABLE_106491 BOUND_VARIABLE_106492))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( c_Int_OMin, c_Int_OMin ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((BOUND_VARIABLE_106502 $$unsorted) (BOUND_VARIABLE_106503 $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_106503) BOUND_VARIABLE_106502)) (= (c_SetInterval_Oord__class_OatLeastAtMost tc_Int_Oint BOUND_VARIABLE_106502 BOUND_VARIABLE_106503) (hAPP (hAPP (c_Set_Oinsert tc_Int_Oint) BOUND_VARIABLE_106502) (c_SetInterval_Oord__class_OatLeastAtMost tc_Int_Oint (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) BOUND_VARIABLE_106502) (c_Groups_Oone__class_Oone tc_Int_Oint)) BOUND_VARIABLE_106503)))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( c_Int_OMin, c_Int_OMin ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (or (not (class_Orderings_Opreorder T_b)) (= (and (not (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2))) (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.61 ( v_G, v_Ga, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (hAPP _let_0 V_x))) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP _let_1 V_y))) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_z))) (hBOOL (hAPP _let_1 V_z))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OPls, c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (or (and (not (hBOOL (hAPP (hAPP _let_0 _let_1) V_z_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_1) V_w_2)))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Int_Onat V_w_2)) (hAPP c_Int_Onat V_z_2))) (hBOOL (hAPP (hAPP _let_0 V_w_2) V_z_2)))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( c_Int_OPls, c_Int_OMin ) 6.35/6.61 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( c_Int_OMin, c_Int_OMin ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (c_List_Olist_ONil T_a))) (= _let_0 (hAPP (c_List_Otl T_a) _let_0))) ) 6.35/6.61 ( tc_Nat_Onat ) 6.35/6.61 ( tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_A_2 $$unsorted) (V_Abs_2 $$unsorted) (V_Rep_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Typedef_Otype__definition T_b T_c V_Rep_2 V_Abs_2 V_A_2)) (= (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_Oimage T_c T_b V_Abs_2) V_A_2))) ) 6.35/6.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Code__Numeral_Oof__nat, c_Code__Numeral_Onat__of, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( c_Int_OInteg, c_Int_OAbs__Integ, c_Int_ORep__Integ, (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Enum_Oenum T_b)) (not (class_Orderings_Oorder T_c)) (= (hBOOL (hAPP (c_Enum_Oenum__class_Oenum__all T_b) (hAPP (hAPP (c_COMBS T_b T_c tc_HOL_Obool) (hAPP (hAPP (c_COMBB T_c (tc_fun T_c tc_HOL_Obool) T_b) (c_Orderings_Oord__class_Oless__eq T_c)) V_f_2)) V_g_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b T_c)) V_f_2) V_g_2)))) ) 6.35/6.61 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_l_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_l_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP (hAPP (c_Set_Oinsert T_b) V_l_2) (c_Orderings_Obot__class_Obot _let_0))) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_l_2))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Oorder T_1)) (class_Orderings_Oorder (tc_fun T_2 T_1))) ) 6.35/6.61 ( tc_HOL_Obool, tc_HOL_Obool ) 6.35/6.61 ( tc_Nat_Onat, tc_HOL_Obool ) 6.35/6.61 ( tc_Int_Oint, tc_HOL_Obool ) 6.35/6.61 ( tc_Int_Oint, tc_Int_Oint ) 6.35/6.61 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.35/6.61 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.35/6.61 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.35/6.61 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_N_2 $$unsorted) (V_h_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (= (hAPP (hAPP _let_0 (hAPP V_h_2 B_x)) (hAPP V_h_2 B_y)) (hAPP V_h_2 (hAPP (hAPP _let_0 B_x) B_y))) )) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (= V_N_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice_OInf__fin T_b _let_0 (hAPP (c_Set_Oimage T_b T_b V_h_2) V_N_2)) (hAPP V_h_2 (c_Big__Operators_Olattice_OInf__fin T_b _let_0 V_N_2))))) ) 6.35/6.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (or (not (c_Wellfounded_Owf T_b V_R_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_1) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) V_R_2) V_S_2)) V_R_2))) (c_FunDef_Oreduction__pair T_b (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) V_R_2) V_S_2))))) ) 6.35/6.61 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.61 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.61 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (hAPP c_Code__Numeral_Oof__nat (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP c_Code__Numeral_Onat__of V_n)) (hAPP c_Code__Numeral_Onat__of V_m))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) V_n) V_m)) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a)))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_m $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (= (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) V_m) (c_Divides_Odivmod__nat V_m _let_0))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_b_2)) (c_Groups_Ozero__class_Ozero T_b)))))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_n $$unsorted)) (= V_n (hAPP (c_Nat_Osize__class_Osize tc_Nat_Onat) V_n)) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (= (and (= _let_0 V_n_2) (= _let_0 V_m_2)) (= (hAPP _let_1 V_m_2) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP _let_1 V_n_2)))))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_n_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Osemiring__1 T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_b) V_n_2)) (c_Nat_Osemiring__1__class_ONats T_b)))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Enum_Oenum T_1)) (not (class_Enum_Oenum T_2)) (class_Enum_Oenum (tc_fun T_2 T_1))) ) 6.35/6.61 ( tc_HOL_Obool, tc_HOL_Obool ) 6.35/6.61 ( tc_HOL_Obool, tc_Nat_Onat ) 6.35/6.61 ( tc_HOL_Obool, tc_Int_Oint ) 6.35/6.61 ( tc_HOL_Obool, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.61 ( tc_HOL_Obool, tc_Product__Type_Ounit ) 6.35/6.61 ( tc_HOL_Obool, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.61 ( tc_Int_Oint, tc_Int_Oint ) 6.35/6.61 ( (tc_fun tc_Int_Oint tc_HOL_Obool), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Osemilattice__inf (tc_fun T_2 T_1))) ) 6.35/6.61 ( tc_HOL_Obool, tc_HOL_Obool ) 6.35/6.61 ( tc_Nat_Onat, tc_HOL_Obool ) 6.35/6.61 ( tc_Int_Oint, tc_HOL_Obool ) 6.35/6.61 ( tc_Int_Oint, tc_Int_Oint ) 6.35/6.61 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.35/6.61 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.35/6.61 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.35/6.61 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (let ((_let_1 (c_Set_Oimage tc_Nat_Onat tc_Int_Oint _let_0))) (= (= V_B_2 V_A_2) (= (hAPP _let_1 V_B_2) (hAPP _let_1 V_A_2))))) ) 6.35/6.61 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_w_2 $$unsorted) (V_v_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (let ((_let_1 (hAPP _let_0 V_v_2))) (let ((_let_2 (hAPP _let_0 V_w_2))) (or (not (class_Orderings_Olinorder T_b)) (not (class_Int_Onumber T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) _let_1) _let_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) _let_2) _let_1)))))))) ) 6.35/6.61 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 6.35/6.61 ( c_Int_OPls, (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) V_z) (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OMin)) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_z))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_z $$unsorted)) (or (hBOOL (hAPP c_Nat__Numeral_Oneg V_z)) (= V_z (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Int_Onat V_z)))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_m $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (or (not (class_Rings_Osemiring__1 T_a)) (= (hAPP _let_0 (hAPP c_Nat_OSuc V_m)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (c_Groups_Oone__class_Oone T_a)) (hAPP _let_0 V_m))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), tc_Int_Oint ) 6.35/6.61 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 _let_0)) (not (= (hAPP (c_Set_Oimage T_b T_c V_f_2) _let_0) _let_1)) (c_Fun_Obij__betw T_b T_c V_f_2 _let_0 _let_1)))) ) 6.35/6.61 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.35/6.61 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_v $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (hAPP _let_0 _let_1))) (let ((_let_3 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_4 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_5 (hAPP _let_3 V_v))) (let ((_let_6 (hBOOL (hAPP _let_2 _let_5)))) (let ((_let_7 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (let ((_let_8 (hAPP _let_4 V_v))) (let ((_let_9 (hAPP _let_7 _let_8))) (or (not (class_Int_Onumber__ring T_a)) (and (or _let_6 (= _let_9 (c_Groups_Ozero__class_Ozero T_a))) (or (not _let_6) (= _let_9 (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_v))))))))))))))) ) 6.35/6.61 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.61 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.61 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.61 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.61 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_P_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_c))) (= (c_Hilbert__Choice_OEps _let_0 (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c tc_HOL_Obool) V_P_2)) (c_Hilbert__Choice_OEps _let_0 (hAPP (hAPP (c_COMBS _let_0 T_c tc_HOL_Obool) (hAPP (hAPP (c_COMBB T_b (tc_fun T_c tc_HOL_Obool) _let_0) V_P_2) (c_Product__Type_Ofst T_b T_c))) (c_Product__Type_Osnd T_b T_c))))) ) 6.35/6.61 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), tc_Int_Oint, tc_Int_Oint ) 6.35/6.61 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)))) (= (hAPP (hAPP _let_0 V_B_2) V_A_2) (hAPP (hAPP _let_0 V_A_2) V_B_2))) ) 6.35/6.61 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( c_FunDef_Opair__less, (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.61 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.61 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_G_2 $$unsorted) (V_F_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (or (not (hBOOL (hAPP _let_0 V_F_2))) (not (hBOOL (hAPP _let_0 V_G_2))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_F_2) V_G_2))))) ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_k_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_k_2))) (= (c_SetInterval_Oord__class_OgreaterThanLessThan T_b V_k_2 V_l_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_M_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_M_2))) (not (forall ((B_h $$unsorted)) (not (c_Fun_Obij__betw T_b tc_Nat_Onat B_h V_M_2 (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Finite__Set_Ocard T_b) V_M_2)))) ))) ) 6.35/6.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (or (not (class_Rings_Osemiring__1 T_a)) (= _let_0 (hAPP (hAPP (c_Power_Opower__class_Opower T_a) _let_0) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))))))) ) 6.35/6.61 ( tc_Nat_Onat ) 6.35/6.61 ( tc_Int_Oint ) 6.35/6.61 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat))) (= (hAPP _let_0 (hAPP c_Nat_OSuc V_k_2)) (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) V_k_2) (hAPP _let_0 V_k_2)))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.61 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.61 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_y (hAPP (c_Product__Type_Osnd T_b T_a) (hAPP (hAPP (c_Product__Type_OPair T_b T_a) V_x) V_y))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.61 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.61 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_List_Oset T_b) (c_List_Olist_ONil T_b))) ) 6.35/6.61 ( tc_HOL_Obool ) 6.35/6.61 ( tc_Nat_Onat ) 6.35/6.61 ( tc_Int_Oint ) 6.35/6.61 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.61 ( tc_Product__Type_Ounit ) 6.35/6.61 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Complete__Lattice_OInf__class_OInf T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_a_2) (c_Complete__Lattice_OInf__class_OInf T_b V_A_2)))) ) 6.35/6.61 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_member T_b))) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2)) (not (= (hAPP V_f_2 V_x_2) (hAPP V_f_2 V_y_2))) (not (hBOOL (hAPP (hAPP _let_0 V_x_2) V_A_2))) (not (hBOOL (hAPP (hAPP _let_0 V_y_2) V_A_2))) (= V_y_2 V_x_2))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_SetInterval_Oord__class_OatMost T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP _let_0 V_u_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP _let_0 V_l_2)) (c_SetInterval_Oord__class_OgreaterThanAtMost T_b V_l_2 V_u_2))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Groups_Oab__semigroup__mult T_b)) (c_Finite__Set_Ofun__left__comm T_b T_b (c_Groups_Otimes__class_Otimes T_b))) ) 6.35/6.61 ( tc_Nat_Onat ) 6.35/6.61 ( tc_Int_Oint ) 6.35/6.61 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_v $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_2 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (let ((_let_3 (hAPP _let_1 V_v))) (let ((_let_4 (hAPP _let_2 _let_3))) (let ((_let_5 (hAPP _let_0 V_v))) (let ((_let_6 (hBOOL (hAPP c_Nat__Numeral_Oneg _let_5)))) (or (not (class_Int_Onumber__ring T_a)) (and (or _let_6 (= _let_4 (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_v))) (or (not _let_6) (= _let_4 (c_Groups_Ozero__class_Ozero T_a)))))))))))) ) 6.35/6.61 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.61 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.61 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.61 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.61 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_y_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Groups_Ozero__class_Ozero T_b)) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) V_y_2)))) ) 6.35/6.61 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.61 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.61 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.61 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.61 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Relation_ODomain T_b T_c))) (= (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert (tc_prod T_b T_c)) (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_a_2) V_b_2)) V_r_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (hAPP _let_0 V_r_2)))) ) 6.35/6.61 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_x_2) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (= V_A_2 _let_2) (not (hBOOL (hAPP _let_0 V_B_2))) (= V_B_2 _let_2) (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OInf__fin T_b V_B_2)) (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2))))))) ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (c_Groups_Oone__class_Oone T_a))) (hAPP _let_0 V_w)) (hAPP _let_0 (c_Int_Opred V_w))))) ) 6.35/6.61 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= V_A_2 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (c_Set_Oinsert T_b)) (c_Orderings_Obot__class_Obot _let_0))))) ) 6.35/6.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Int_Oring__1__class_OInts T_b))) (or (not (class_Rings_Oring__1 T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 V_b_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_b_2)) _let_1))))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2) (hAPP (c_Finite__Set_Ofold1 T_b (c_Lattices_Osemilattice__sup__class_Osup T_b)) V_A_2))) ) 6.35/6.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hAPP (c_Set_Oimage T_b T_b _let_0) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_x_2)) (hAPP (c_SetInterval_Oord__class_OatMost T_b) (hAPP _let_0 V_x_2))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP _let_2 V_a))) (not (hBOOL (hAPP _let_2 V_b))) (hBOOL (hAPP _let_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b))))))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_OwfP T_b V_r_2)) (c_Wellfounded_Oacyclic T_b (hAPP (c_Set_OCollect (tc_prod T_b T_b)) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_b tc_HOL_Obool) V_r_2)))) ) 6.35/6.61 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.61 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), tc_Int_Oint ) 6.35/6.61 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_a_2 V_a_2))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_w_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) V_w_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_w_2)) (c_Nat_Osemiring__1__class_ONats T_b)))) ) 6.35/6.61 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.61 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.61 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.61 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.61 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.61 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__sup__class_Osup T_a))) (or (not (class_Lattices_Osemilattice__sup T_a)) (= (hAPP (hAPP _let_0 V_b) V_a) (hAPP (hAPP _let_0 V_a) V_b)))) ) 6.35/6.61 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.61 ( c_FunDef_Opair__less, (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.35/6.61 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.35/6.61 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Wellfounded_Owf T_b V_r_2) (forall ((B_Q $$unsorted) (BOUND_VARIABLE_108681 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) BOUND_VARIABLE_108681) B_Q))) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) B_Q))) (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) B_y) B_x)) V_r_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) B_y) B_Q)))) ))) ))) )) ) 6.35/6.61 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.61 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.35/6.61 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Ogroup__add T_b)) (= (= V_b_2 V_a_2) (= (hAPP _let_0 V_a_2) (hAPP _let_0 V_b_2))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Groups_Ocomm__monoid__mult T_c)) (not (c_Fun_Oinj__on T_b T_c V_f_2 V_B_2)) (= (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__mult__class_Osetprod T_b T_c) V_f_2) V_B_2) (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__mult__class_Osetprod T_c T_c) (c_Fun_Oid T_c)) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_B_2)))) ) 6.35/6.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 6.35/6.61 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 6.35/6.61 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Osym T_b V_r_2)) (c_Relation_Osym T_b (c_Transitive__Closure_Otrancl T_b V_r_2))) ) 6.35/6.61 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (let ((_let_1 (c_Finite__Set_Ofold1 T_b _let_0))) (or (not (class_Lattices_Oab__semigroup__idem__mult T_b)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP _let_0 V_x_2) (hAPP _let_1 V_A_2)) (hAPP _let_1 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.61 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_2 (c_Big__Operators_Olattice_OInf__fin T_b _let_1 V_A_2))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_B_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= _let_2 (hAPP (hAPP _let_1 (c_Big__Operators_Olattice_OInf__fin T_b _let_1 V_B_2)) _let_2)))))) ) 6.35/6.61 ( v_G, v_Ga, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (= (c_SetInterval_Oord__class_OatLeastAtMost T_b V_a_2 V_b_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_a_2) V_b_2))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_C_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0))) (let ((_let_2 (hAPP _let_1 V_C_2))) (let ((_let_3 (c_Set_Oinsert T_b))) (let ((_let_4 (hAPP _let_3 V_a_2))) (= (hAPP _let_4 (hAPP _let_2 V_B_2)) (hAPP _let_2 (hAPP (hAPP (c_COMBB _let_0 _let_0 T_c) _let_4) V_B_2)))))))) ) 6.35/6.61 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oab__group__add T_a)) (= (c_Groups_Ozero__class_Ozero T_a) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) V_a))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_z_2 $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Nat_Onat _let_1))) (let ((_let_3 (tc_fun _let_1 _let_1))) (let ((_let_4 (tc_fun tc_Nat_Onat _let_3))) (= (hAPP c_Int_OAbs__Integ (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR _let_0 _let_1) (hAPP c_Int_ORep__Integ V_z_2)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat _let_1) (hAPP (hAPP (c_COMBB _let_2 _let_2 tc_Nat_Onat) (hAPP (c_COMBB _let_1 _let_1 tc_Nat_Onat) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel))) (hAPP (hAPP (c_COMBC tc_Nat_Onat _let_1 _let_2) (hAPP (hAPP (c_COMBB _let_4 (tc_fun _let_1 _let_2) tc_Nat_Onat) (c_COMBC tc_Nat_Onat _let_1 _let_1)) (hAPP (hAPP (c_COMBB (tc_fun tc_Nat_Onat _let_0) _let_4 tc_Nat_Onat) (hAPP (c_COMBB _let_0 _let_3 tc_Nat_Onat) (c_Set_Oinsert _let_0))) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat _let_0) (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat))))) (c_Orderings_Obot__class_Obot _let_1)))))) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_z_2))))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.61 ( c_Int_OMin ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (let ((_let_1 (hAPP _let_0 V_k_2))) (= (= V_n_2 V_m_2) (= (hAPP _let_1 V_m_2) (hAPP _let_1 V_n_2))))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((BOUND_VARIABLE_109331 $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_109331) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (= BOUND_VARIABLE_109331 (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) BOUND_VARIABLE_109331))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( c_Int_OMin ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((BOUND_VARIABLE_109340 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_109340) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (= (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) BOUND_VARIABLE_109340) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) BOUND_VARIABLE_109340))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.61 ( c_Int_OMin ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hAPP (c_Set_Oimage T_b T_b _let_0) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_x_2)) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) (hAPP _let_0 V_x_2))))) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.61 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_n_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_n_2) (hAPP (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) (c_SetInterval_Oord__class_OatLeastAtMost tc_Int_Oint (c_Groups_Ozero__class_Ozero tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n_2)))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop T_a))) (or (not (class_Lattices_Obounded__lattice__top T_a)) (= _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) _let_0)))) ) 6.35/6.61 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.61 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.35/6.61 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_n_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Osemiring__1 T_b)) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_b) V_n_2) (c_Nat_Osemiring__1__class_Oof__nat__aux T_b (hAPP (hAPP (c_COMBC T_b T_b T_b) (c_Groups_Oplus__class_Oplus T_b)) (c_Groups_Oone__class_Oone T_b)) V_n_2 (c_Groups_Ozero__class_Ozero T_b)))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (let ((_let_1 (hAPP _let_0 V_n))) (or (not (class_Rings_Olinordered__idom T_a)) (= _let_1 (hAPP (c_Groups_Oabs__class_Oabs T_a) _let_1))))) ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.35/6.61 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.61 ) 6.35/6.61 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (or (not (class_Groups_Osgn__if T_a)) (= _let_0 (c_Groups_Osgn__class_Osgn T_a _let_0)))) ) 6.35/6.61 ( tc_Nat_Onat ) 6.35/6.61 ( tc_Int_Oint ) 6.35/6.61 ( tc_Code__Numeral_Ocode__numeral ) 6.35/6.61 ) 6.35/6.62 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_y_2) V_x_2)))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_x) V_x)))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Oabs__class_Oabs T_a))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of T_a))) (let ((_let_2 (hAPP _let_1 V_x))) (let ((_let_3 (hAPP _let_0 _let_2))) (let ((_let_4 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_5 (hAPP _let_4 _let_2))) (let ((_let_6 (c_Groups_Ozero__class_Ozero T_a))) (let ((_let_7 (hBOOL (hAPP _let_5 _let_6)))) (or (not (class_Int_Onumber__ring T_a)) (not (class_Rings_Olinordered__idom T_a)) (and (or _let_7 (= _let_2 _let_3)) (or (not _let_7) (= _let_3 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) _let_2))))))))))))) ) 6.35/6.62 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.62 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.62 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.62 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.62 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.62 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.35/6.62 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.62 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.62 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.62 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_y_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_OBit1 c_Int_OPls)) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (c_Groups_Oone__class_Oone T_b)) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_y_2))))) ) 6.35/6.62 ( c_Int_OPls, tc_Nat_Onat ) 6.35/6.62 ( c_Int_OPls, tc_Int_Oint ) 6.35/6.62 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.35/6.62 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.35/6.62 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.35/6.62 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.35/6.62 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.62 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.62 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.35/6.62 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_b)))) ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_r_2)) (c_Wellfounded_Owf (tc_fun T_b tc_HOL_Obool) (c_Wellfounded_Omax__ext T_b V_r_2))) ) 6.35/6.62 ( c_FunDef_Opair__leq, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (c_Orderings_Obot__class_Obot T_a)) (c_Orderings_Otop__class_Otop T_a))) ) 6.35/6.62 ( tc_HOL_Obool ) 6.35/6.62 ( tc_Nat_Onat ) 6.35/6.62 ( tc_Int_Oint ) 6.35/6.62 ( (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 6.35/6.62 ( (tc_fun tc_HOL_Obool tc_HOL_Obool) ) 6.35/6.62 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.62 ( (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.62 ( (tc_fun tc_Product__Type_Ounit tc_HOL_Obool) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_a))) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) (hAPP _let_0 V_x)) (hAPP _let_0 V_y)) (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y))))) ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.62 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP _let_0 V_A_2))) (not (hBOOL (hAPP _let_0 V_B_2))) (not (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_2) V_A_2) V_B_2) (c_Orderings_Obot__class_Obot _let_2))) (= (hAPP _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_2) V_A_2) V_B_2)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP _let_1 V_A_2)) (hAPP _let_1 V_B_2))))))) ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.62 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_prod T_c T_b))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (= (hAPP (c_Relation_OImage T_c T_b V_r_2) (hAPP (hAPP (c_Set_Oinsert T_c) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool)))) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBC T_b _let_1 tc_HOL_Obool) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_1 tc_HOL_Obool) T_b) (c_member _let_0)) (hAPP (c_Product__Type_OPair T_c T_b) V_a_2))) V_r_2))))) ) 6.35/6.62 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (not (class_Divides_Osemiring__div T_a)) (= (c_Divides_Odiv__class_Omod T_a V_a V_b) (c_Divides_Odiv__class_Omod T_a (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_b) V_a) V_b))) ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (c_Lattices_Osemilattice__inf__class_Oinf _let_2))) (let ((_let_4 (hAPP _let_3 V_A_2))) (let ((_let_5 (hAPP _let_4 V_B_2))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (not (hBOOL (hAPP _let_0 V_B_2))) (= _let_5 (c_Orderings_Obot__class_Obot _let_2)) (= (hAPP (hAPP _let_1 (c_Big__Operators_Olattice_OInf__fin T_b _let_1 V_A_2)) (c_Big__Operators_Olattice_OInf__fin T_b _let_1 V_B_2)) (hAPP (hAPP _let_1 (c_Big__Operators_Olattice_OInf__fin T_b _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_2) V_A_2) V_B_2))) (c_Big__Operators_Olattice_OInf__fin T_b _let_1 _let_5)))))))))) ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.62 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2))) (not (hBOOL (hAPP (hAPP _let_0 V_c_2) V_d_2))) (= (and (= V_d_2 V_b_2) (= V_c_2 V_a_2)) (= (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_c_2) V_d_2) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_a_2) V_b_2))))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, c_Int_OMin, c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_rb_2 $$unsorted) (T_c $$unsorted) (V_ra_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_ra_2)) (not (c_Wellfounded_Owf T_c V_rb_2)) (c_Wellfounded_Owf (tc_prod T_b T_c) (c_Wellfounded_Olex__prod T_b T_c V_ra_2 V_rb_2))) ) 6.35/6.62 ( c_Wellfounded_Oless__than, tc_Nat_Onat, c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (hBOOL (hAPP (hAPP (c_member T_b) V_i_2) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_k_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_k_2) V_i_2)))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_k_2) V_i_2)) (hBOOL (hAPP (hAPP (c_member T_b) V_i_2) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_k_2))))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( v_G, v_Ga, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (= (hAPP c_Nat_OSuc V_x) (hAPP c_Nat_OSuc V_y))) (= V_y V_x)) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.62 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.62 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBS T_b tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_b) c_fdisj) (hAPP (hAPP (c_COMBC T_b T_b tc_HOL_Obool) c_fequal) V_a_2))) (hAPP (hAPP (c_COMBC T_b (tc_fun T_b tc_HOL_Obool) tc_HOL_Obool) (c_member T_b)) V_B_2))) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_B_2)) ) 6.35/6.62 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_n_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (class_Orderings_Oorder T_b)) (= (hAPP (hAPP (c_Set_Oinsert T_b) V_n_2) (c_Orderings_Obot__class_Obot _let_0)) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_n_2)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_n_2))))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.62 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_i_2 $$unsorted) (V_P_2 $$unsorted)) (= (hBOOL (hAPP V_P_2 (hAPP c_Int_Onat V_i_2))) (and (forall ((B_n $$unsorted)) (or (not (= V_i_2 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n))) (hBOOL (hAPP V_P_2 B_n))) ) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_i_2) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (hBOOL (hAPP V_P_2 (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Nat_OSuc ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Code__Numeral_Oof__nat ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Set_Oinsert tc_Nat_Onat) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat_OSuc ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Code__Numeral_Oof__nat ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) ) 6.35/6.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Nat_OSuc ) 6.35/6.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_k_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) V_k_2) (hAPP (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) (hAPP c_Nat_OSuc V_k_2))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.35/6.62 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.35/6.62 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (hAPP _let_0 V_x))) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP _let_1 V_y))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_z))) (hBOOL (hAPP _let_1 V_z))))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( c_Int_OPls, c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Oord T_1)) (class_Orderings_Oord (tc_fun T_2 T_1))) ) 6.35/6.62 ( tc_HOL_Obool, tc_HOL_Obool ) 6.35/6.62 ( tc_Nat_Onat, tc_HOL_Obool ) 6.35/6.62 ( tc_Int_Oint, tc_HOL_Obool ) 6.35/6.62 ( tc_Int_Oint, tc_Int_Oint ) 6.35/6.62 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.35/6.62 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.35/6.62 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.35/6.62 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (= (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_x_2) V_y_2) (c_Hilbert__Choice_OEps (tc_prod T_b T_c) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c tc_HOL_Obool) (hAPP (hAPP (c_COMBC T_b _let_1 _let_1) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_1 _let_1) T_b) (c_COMBB tc_HOL_Obool tc_HOL_Obool T_c)) (hAPP (hAPP (c_COMBB tc_HOL_Obool _let_0 T_b) c_fconj) (hAPP c_fequal V_x_2)))) (hAPP c_fequal V_y_2))))))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.62 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.35/6.62 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.62 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (let ((_let_1 (hAPP _let_0 V_x_2))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (c_Orderings_Obot__class_Obot _let_2))) (let ((_let_4 (hAPP _let_1 _let_3))) (= (hAPP (hAPP (c_Set_Oinsert _let_2) (hAPP (c_Relation_OImage T_b T_b V_r_2) _let_4)) (c_Orderings_Obot__class_Obot (tc_fun _let_2 tc_HOL_Obool))) (hAPP (hAPP (c_Equiv__Relations_Oquotient T_b) _let_4) V_r_2))))))) ) 6.35/6.62 ( c_Int_Ointrel, (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ( c_Int_Ointrel, (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_A_2) V_B_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2)))) ) 6.35/6.62 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hAPP (c_Set_Oimage T_b T_b _let_0) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_x_2)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) (hAPP _let_0 V_x_2))))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (c_Int_OBit1 V_l_2) (c_Int_OBit1 V_k_2)) (= V_l_2 V_k_2)) ) 6.35/6.62 ( c_Int_OPls, c_Int_OPls ) 6.35/6.62 ( c_Int_OPls, (c_Int_OBit1 c_Int_OPls) ) 6.35/6.62 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls ) 6.35/6.62 ( (c_Int_OBit1 c_Int_OPls), c_Int_OMin ) 6.35/6.62 ( c_Int_OMin, c_Int_OPls ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (let ((_let_2 (tc_fun T_c _let_0))) (= (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBB _let_1 tc_HOL_Obool T_b) (c_HOL_OAll T_c)) (hAPP (hAPP (c_COMBB _let_1 _let_1 T_b) (hAPP (c_COMBS T_c tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_c) c_fimplies) (hAPP (hAPP (c_COMBC T_c _let_1 tc_HOL_Obool) (c_member T_c)) V_A_2)))) (hAPP (hAPP (c_COMBC T_b _let_2 _let_1) (hAPP (hAPP (c_COMBB (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_2 _let_1) T_b) (c_COMBB _let_0 tc_HOL_Obool T_c)) (c_member T_b))) V_B_2)))) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) V_B_2))))) ) 6.35/6.62 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (hAPP (hAPP (c_Product__Type_OSigma T_b T_b) V_A_2) (hAPP (c_COMBK (tc_fun T_b tc_HOL_Obool) T_b) V_A_2))))) ) 6.35/6.62 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_k_2 $$unsorted) (V_f_2 $$unsorted) (V_n_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (or (not (forall ((B_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_i) V_n_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) (hAPP V_f_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) B_i) (c_Groups_Oone__class_Oone tc_Nat_Onat)))) (hAPP V_f_2 B_i)))) (c_Groups_Oone__class_Oone tc_Int_Oint)))) )) (not (hBOOL (hAPP (hAPP _let_0 (hAPP V_f_2 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) V_k_2))) (not (hBOOL (hAPP (hAPP _let_0 V_k_2) (hAPP V_f_2 V_n_2)))) (not (forall ((B_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) B_i) V_n_2))) (not (= V_k_2 (hAPP V_f_2 B_i)))) )))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OAbs__Integ, (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OAbs__Integ, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))) ) 6.35/6.62 ( c_Int_OMin, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.35/6.62 ( c_Int_OMin, c_Int_OAbs__Integ, (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_Osucc (c_Int_OBit1 V_k)) (c_Int_OBit0 (c_Int_Osucc V_k))) ) 6.35/6.62 ( c_Int_OPls ) 6.35/6.62 ( (c_Int_OBit1 c_Int_OPls) ) 6.35/6.62 ( c_Int_OMin ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A_2) (hAPP (hAPP (c_COMBC T_b _let_1 _let_1) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_1 _let_1) T_b) (c_Set_Oinsert _let_0)) (hAPP (hAPP (c_COMBB _let_0 _let_0 T_b) (c_Relation_OImage T_b T_b V_r_2)) (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (c_Set_Oinsert T_b)) (c_Orderings_Obot__class_Obot _let_0))))) (c_Orderings_Obot__class_Obot _let_1))) (hAPP (hAPP (c_Equiv__Relations_Oquotient T_b) V_A_2) V_r_2)))) ) 6.35/6.62 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero T_b)) V_a_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) V_a_2))))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2) (hAPP (hAPP (c_Finite__Set_Ofold T_b _let_0 (c_Set_Oinsert T_b)) V_B_2) V_A_2)))) ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.62 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (c_Orderings_Otop__class_Otop T_a) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x)))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.35/6.62 ( c_Int_OMin, tc_Int_Oint ) 6.35/6.62 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.62 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.35/6.62 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (c_Groups_Otimes__class_Otimes T_b))) (let ((_let_3 (c_Finite__Set_Ofold1 T_b _let_2))) (let ((_let_4 (c_Finite__Set_Ofinite T_b))) (or (not (class_Lattices_Oab__semigroup__idem__mult T_b)) (not (hBOOL (hAPP _let_4 V_A_2))) (= V_A_2 _let_1) (not (hBOOL (hAPP _let_4 V_B_2))) (= V_B_2 _let_1) (= (hAPP (hAPP _let_2 (hAPP _let_3 V_A_2)) (hAPP _let_3 V_B_2)) (hAPP _let_3 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2))))))))) ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.62 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.35/6.62 ) 6.35/6.62 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b)) V_a_2) V_A_2) (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)))) ) 6.35/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.35/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.35/6.62 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.35/6.62 ) 6.44/6.62 (instantiation (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_d $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0))) (let ((_let_2 (tc_fun T_c tc_HOL_Obool))) (let ((_let_3 (tc_fun T_c _let_0))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_d _let_3 _let_0) (hAPP (hAPP (c_COMBB _let_2 (tc_fun _let_3 _let_0) T_d) _let_1) V_B_2)) V_C_2)) (hAPP (hAPP _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d _let_2) V_A_2) V_B_2)) V_C_2)))))) ) 6.44/6.62 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.62 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.62 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (c_Complete__Lattice_OSup__class_OSup _let_0 (hAPP (c_Set_Oimage T_c _let_0 V_B_2) V_A_2)) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) V_B_2))) ) 6.44/6.62 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.62 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.62 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus T_b))) (or (not (class_Groups_Ocancel__semigroup__add T_b)) (= (= (hAPP (hAPP _let_0 V_c_2) V_a_2) (hAPP (hAPP _let_0 V_b_2) V_a_2)) (= V_c_2 V_b_2)))) ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_b))) (or (not (class_Rings_Olinordered__semidom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (hAPP _let_0 V_m_2)) (hAPP _let_0 V_n_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) V_n_2))))) ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= V_a (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_l_2) V_u_2))) (= (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_u_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_l_2)) (c_SetInterval_Oord__class_OgreaterThanLessThan T_b V_l_2 V_u_2)))) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) B_x) B_y)) (hAPP (hAPP _let_0 B_x) (hAPP (hAPP _let_0 B_y) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))))) )) (hBOOL (hAPP (hAPP (c_member T_b) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) V_A_2))) ) 6.44/6.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (c_Orderings_Oord__class_Omax T_b) (c_Orderings_Oord_Omin T_b (hAPP (c_COMBC T_b T_b tc_HOL_Obool) (c_Orderings_Oord__class_Oless__eq T_b))))) ) 6.44/6.62 ( tc_Nat_Onat ) 6.44/6.62 ( tc_Int_Oint ) 6.44/6.62 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.62 ( (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_b_2) (hAPP _let_1 V_a_2))) (hBOOL (hAPP (hAPP _let_0 V_a_2) (hAPP _let_1 V_b_2))))))) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_nat_H_2 $$unsorted) (V_nat_2 $$unsorted)) (= (= V_nat_H_2 V_nat_2) (= (hAPP c_Nat_OSuc V_nat_H_2) (hAPP c_Nat_OSuc V_nat_2))) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.62 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.62 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.62 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w) V_z))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_w) (c_Groups_Oone__class_Oone tc_Int_Oint))) V_z))) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.62 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.62 ( c_Int_OMin, c_Int_OMin ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_y_2) V_x_2)))) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 6.44/6.62 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.62 ( v_G, v_Ga, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ominus__class_Ominus T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (not (= (hAPP (hAPP _let_1 V_c_2) V_d_2) (hAPP (hAPP _let_1 V_a_2) V_b_2))) (= (hBOOL (hAPP (hAPP _let_0 V_c_2) V_d_2)) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2)))))) ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_c)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_c (hAPP (hAPP (c_COMBB T_c (tc_fun T_c T_c) T_b) (c_Lattices_Osemilattice__inf__class_Oinf T_c)) V_f_2)) (c_Orderings_Otop__class_Otop T_c)) V_A_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b T_c) V_A_2) V_f_2))) ) 6.44/6.62 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) (hAPP (c_Set_Oimage T_c T_b V_f_2) V_A_2))) (hAPP (c_Finite__Set_Ocard T_c) V_A_2)))) (not (c_Fun_Oinj__on T_c T_b V_f_2 V_A_2))) ) 6.44/6.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 6.44/6.62 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 6.44/6.62 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_Osucc (c_Int_OBit0 V_k)) (c_Int_OBit1 V_k)) ) 6.44/6.62 ( c_Int_OPls ) 6.44/6.62 ( (c_Int_OBit1 c_Int_OPls) ) 6.44/6.62 ( c_Int_OMin ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus T_b))) (or (not (class_Int_Oring__char__0 T_b)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) (c_Int_Oring__1__class_OInts T_b)))) (not (= (c_Groups_Ozero__class_Ozero T_b) (hAPP (hAPP _let_0 (hAPP (hAPP _let_0 (c_Groups_Oone__class_Oone T_b)) V_a_2)) V_a_2))))) ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (= V_a_2 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) (= V_a_2 (c_Groups_Ozero__class_Ozero T_b)))) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (hAPP c_Nat_OSuc _let_0))) (= (= _let_1 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m_2) V_n_2)) (or (and (= _let_1 V_m_2) (= _let_0 V_n_2)) (and (= _let_0 V_m_2) (= _let_1 V_n_2)))))) ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (or (not (class_Rings_Olinordered__semidom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m) V_n))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (hAPP _let_0 V_m)) (hAPP _let_0 V_n))))) ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_n_2 $$unsorted)) (= (= (c_Groups_Ozero__class_Ozero tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n_2)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_n_2)) ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (c_Fun_Oid (tc_prod T_b T_c)) (c_Product__Type_Oapfst T_b T_b T_c (c_Fun_Oid T_b))) ) 6.44/6.62 ( tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.62 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.62 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_a_2) V_b_2) (c_Complete__Lattice_OSup__class_OSup T_b (hAPP (hAPP _let_0 V_a_2) (hAPP (hAPP _let_0 V_b_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))))) ) 6.44/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.62 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (or (not (hBOOL (hAPP _let_0 V_A_2))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2))))) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.62 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.62 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OMin) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (c_Groups_Oone__class_Oone T_a)))) ) 6.44/6.62 ( tc_Nat_Onat ) 6.44/6.62 ( tc_Int_Oint ) 6.44/6.62 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_2 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_3 (hAPP _let_1 V_v_2))) (let ((_let_4 (hBOOL (hAPP c_Nat__Numeral_Oneg _let_3)))) (let ((_let_5 (hAPP _let_1 V_v_H_2))) (let ((_let_6 (hBOOL (hAPP c_Nat__Numeral_Oneg _let_5)))) (= (and (or _let_4 (and (or _let_6 (= V_v_H_2 V_v_2)) (or (not _let_6) (= _let_0 _let_3)))) (or (not _let_4) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_5) _let_0)))) (= (hAPP _let_2 V_v_2) (hAPP _let_2 V_v_H_2)))))))))) ) 6.44/6.62 ( c_Int_OPls, c_Int_OPls ) 6.44/6.62 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls) ) 6.44/6.62 ( c_Int_OMin, c_Int_OMin ) 6.44/6.62 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.62 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_a $$unsorted) (V_b $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_2 (c_Divides_OposDivAlg V_a V_b))) (let ((_let_3 (hAPP _let_1 V_a))) (let ((_let_4 (hBOOL (hAPP _let_3 V_b)))) (or (not (hBOOL (hAPP (hAPP _let_1 _let_0) V_b))) (and (or _let_4 (= _let_2 (hAPP (c_Divides_Oadjust V_b) (c_Divides_OposDivAlg V_a (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) V_b))))) (or (not _let_4) (= _let_2 (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) _let_0) V_a)))))))))) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.62 ( c_Int_OMin, c_Int_OMin ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (hAPP _let_1 V_x_2))) (or (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) (hAPP _let_2 V_A_2)) (hAPP _let_2 (c_Orderings_Obot__class_Obot _let_0)))))))) ) 6.44/6.62 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.62 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.62 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_y_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (not (class_Int_Onumber__ring T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (c_Groups_Ozero__class_Ozero T_b)) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_y_2))))) ) 6.44/6.62 ( c_Int_OPls, tc_Nat_Onat ) 6.44/6.62 ( c_Int_OPls, tc_Int_Oint ) 6.44/6.62 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.44/6.62 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.44/6.62 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.44/6.62 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.44/6.62 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.62 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.44/6.62 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.44/6.62 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.44/6.62 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (c_Orderings_Oord_Omax T_b (c_Orderings_Oord__class_Oless__eq T_b)) (c_Orderings_Oord__class_Omax T_b))) ) 6.44/6.62 ( tc_HOL_Obool ) 6.44/6.62 ( tc_Nat_Onat ) 6.44/6.62 ( tc_Int_Oint ) 6.44/6.62 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.62 ( (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_a_2) V_A_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2))))) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.62 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.62 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Relation_ODomain T_b T_c))) (= (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_c) tc_HOL_Obool)) V_A_2) V_B_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP _let_0 V_A_2)) (hAPP _let_0 V_B_2)))) ) 6.44/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.62 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (not (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) (c_Orderings_Obot__class_Obot T_a))) (not (= (c_Orderings_Otop__class_Otop T_a) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y))) (= V_y (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x))) ) 6.44/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.62 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_a_2) V_b_2))) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_a_2) V_b_2)))) ) 6.44/6.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.62 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((BOUND_VARIABLE_111500 $$unsorted) (BOUND_VARIABLE_111501 $$unsorted) (BOUND_VARIABLE_111502 $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun BOUND_VARIABLE_111501 tc_HOL_Obool)) (hAPP (c_Set_Oimage BOUND_VARIABLE_111502 BOUND_VARIABLE_111501 (hAPP (c_COMBK BOUND_VARIABLE_111501 BOUND_VARIABLE_111502) BOUND_VARIABLE_111500)) (c_Orderings_Obot__class_Obot (tc_fun BOUND_VARIABLE_111502 tc_HOL_Obool)))) ) 6.44/6.62 ( c_fTrue, tc_HOL_Obool, tc_Nat_Onat ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Olattice T_a)) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)))) ) 6.44/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.62 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.62 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP _let_2 V_a))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) _let_1) V_b))) (hBOOL (hAPP _let_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b))))))) ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.62 ) 6.44/6.62 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (not (= (hAPP V_f_2 V_x_2) (hAPP V_f_2 V_y_2))) (= V_y_2 V_x_2)) ) 6.44/6.62 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.62 ) 6.44/6.63 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (= (c_Groups_Oone__class_Oone T_a) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (c_Groups_Oone__class_Oone tc_Nat_Onat)))) ) 6.44/6.63 ( tc_Nat_Onat ) 6.44/6.63 ( tc_Int_Oint ) 6.44/6.63 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) _let_1))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_b) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_1))))) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_z_2 $$unsorted)) (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (let ((_let_1 (tc_fun _let_0 _let_0))) (let ((_let_2 (tc_fun tc_Nat_Onat _let_0))) (let ((_let_3 (tc_fun tc_Nat_Onat _let_1))) (= (c_Set_Othe__elem tc_Nat_Onat (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tc_prod tc_Nat_Onat tc_Nat_Onat) _let_0) (hAPP c_Int_ORep__Integ V_z_2)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat _let_0) (hAPP (hAPP (c_COMBC tc_Nat_Onat _let_0 _let_2) (hAPP (hAPP (c_COMBB _let_3 (tc_fun _let_0 _let_2) tc_Nat_Onat) (c_COMBC tc_Nat_Onat _let_0 _let_0)) (hAPP (hAPP (c_COMBB (tc_fun tc_Nat_Onat tc_Nat_Onat) _let_3 tc_Nat_Onat) (hAPP (c_COMBB tc_Nat_Onat _let_1 tc_Nat_Onat) (c_Set_Oinsert tc_Nat_Onat))) (c_Groups_Ominus__class_Ominus tc_Nat_Onat)))) (c_Orderings_Obot__class_Obot _let_0))))) (hAPP c_Int_Onat V_z_2)))))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_z $$unsorted) (V_z_H $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (or (not (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_H))) (not (hBOOL (hAPP (hAPP _let_0 V_z_H) V_z))) (= (hAPP c_Int_Onat (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_z) V_z_H)) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP c_Int_Onat V_z)) (hAPP c_Int_Onat V_z_H))))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( c_Int_OPls, c_Int_OMin ) 6.44/6.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( c_Int_OMin, c_Int_OMin ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Omonoid__add T_a)) (= V_a (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_r_2)) (c_Wellfounded_Oacyclic T_b V_r_2)) ) 6.44/6.63 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.44/6.63 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.44/6.63 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_k $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_2 (hAPP _let_1 V_k))) (let ((_let_3 (hBOOL (hAPP _let_2 _let_0)))) (let ((_let_4 (c_Int_Oring__1__class_Oof__int T_a))) (let ((_let_5 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (let ((_let_6 (hAPP _let_4 V_k))) (or (not (class_Rings_Oring__1 T_a)) (and (or (not _let_3) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (hAPP _let_5 (hAPP c_Int_Onat (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_k)))) _let_6)) (or _let_3 (= _let_6 (hAPP _let_5 (hAPP c_Int_Onat V_k))))))))))))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (and (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)) (not (= V_y_2 V_x_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2)))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) V_n) (hAPP c_Nat_OSuc V_n)) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.63 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.63 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (= V_A_2 (c_Complete__Lattice_OSup__class_OSup (tc_fun T_b tc_HOL_Obool) (hAPP (hAPP (c_Equiv__Relations_Oquotient T_b) V_A_2) V_r_2)))) ) 6.44/6.63 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (not (c_Int_Oiszero T_a (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OMin)))) ) 6.44/6.63 ( tc_Nat_Onat ) 6.44/6.63 ( tc_Int_Oint ) 6.44/6.63 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((BOUND_VARIABLE_111929 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_0) BOUND_VARIABLE_111929)) (= _let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Int_Onat BOUND_VARIABLE_111929))))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.63 ( c_Int_OMin ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) (c_Relation_OId__on T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 6.44/6.63 ( tc_Nat_Onat ) 6.44/6.63 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_u_2 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_0) V_u_2))) (= (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Int_Oint _let_0) V_u_2) (hAPP (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) (hAPP c_Int_Onat V_u_2)))))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.63 ( c_Int_OMin ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_d tc_HOL_Obool)))) (or (not (c_Fun_Obij__betw T_b T_c V_f_2 _let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (not (c_Fun_Obij__betw T_d T_b V_g_2 _let_1 _let_0)) (= (c_Hilbert__Choice_Oinv__into T_d T_c _let_1 (hAPP (c_Fun_Ocomp T_b T_c T_d V_f_2) V_g_2)) (hAPP (c_Fun_Ocomp T_b T_d T_c (c_Hilbert__Choice_Oinv__into T_d T_b _let_1 V_g_2)) (c_Hilbert__Choice_Oinv__into T_b T_c _let_0 V_f_2)))))) ) 6.44/6.63 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), tc_Int_Oint, c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.44/6.63 ( c_Int_Onat, tc_Int_Oint, c_Code__Numeral_Oof__nat, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 6.44/6.63 ( c_Code__Numeral_Onat__of, tc_Code__Numeral_Ocode__numeral, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Osemilattice__sup T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)) (= V_y_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) V_y_2)))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.63 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (hAPP _let_0 V_a))) (let ((_let_2 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_3 (c_Groups_Oone__class_Oone T_a))) (or (not (class_Fields_Olinordered__field T_a)) (not (hBOOL (hAPP _let_1 V_b))) (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Rings_Oinverse__class_Odivide T_a) (hAPP (hAPP _let_2 V_a) V_b)) (hAPP (hAPP _let_2 _let_3) _let_3))))))))) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_P_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (hAPP (c_Relation_ODomain T_b T_c) (hAPP (c_Set_OCollect (tc_prod T_b T_c)) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c tc_HOL_Obool) V_P_2))) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBB (tc_fun T_c tc_HOL_Obool) tc_HOL_Obool T_b) (c_HOL_OEx T_c)) V_P_2))) ) 6.44/6.63 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.63 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), tc_Int_Oint, tc_Int_Oint ) 6.44/6.63 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__sup T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Otrans T_b V_r_2)) (= V_r_2 (c_Transitive__Closure_Otrancl T_b V_r_2))) ) 6.44/6.63 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.44/6.63 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Equiv__Relations_Oquotient T_b))) (let ((_let_2 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_3 (tc_prod T_b T_b))) (let ((_let_4 (tc_fun _let_3 tc_HOL_Obool))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (c_Fun_Oinj__on T_b _let_2 (hAPP (hAPP (c_COMBC T_b _let_4 _let_2) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_4 _let_2) T_b) _let_1) (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (c_Set_Oinsert T_b)) (c_Orderings_Obot__class_Obot _let_0)))) V_r_2) V_A_2)) (= (hAPP (c_Finite__Set_Ocard T_b) V_A_2) (hAPP (c_Finite__Set_Ocard _let_0) (hAPP (hAPP _let_1 V_A_2) V_r_2))))))))) ) 6.44/6.63 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_m_2 $$unsorted) (V_w_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_w_2))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w_2) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP c_Int_Onat V_w_2)) V_m_2)))) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Int_OMin ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (c_List_Olinorder__class_Osorted T_a (c_List_Olist_ONil T_a))) ) 6.44/6.63 ( tc_Nat_Onat ) 6.44/6.63 ( tc_Int_Oint ) 6.44/6.63 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2)) _let_1)))))) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_b_H $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Product__Type_OPair T_a T_b))) (or (not (= (hAPP (hAPP _let_0 V_a) V_b) (hAPP (hAPP _let_0 V_a_H) V_b_H))) (and (= V_a_H V_a) (= V_b_H V_b)))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.63 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.63 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (c_Orderings_Oord__class_Omin T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (= V_A_2 _let_2) (not (hBOOL (hAPP _let_0 V_B_2))) (= V_B_2 _let_2) (= (hAPP (hAPP _let_3 (c_Big__Operators_Olattice_OInf__fin T_b _let_3 V_A_2)) (c_Big__Operators_Olattice_OInf__fin T_b _let_3 V_B_2)) (c_Big__Operators_Olattice_OInf__fin T_b _let_3 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2)))))))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.63 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_N_2 $$unsorted)) (= (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) V_N_2)) (not (forall ((B_m $$unsorted)) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_x) V_N_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) B_x) B_m))) )) ))) ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_n $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Nat_Onat))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (hBOOL (hAPP _let_2 V_n))) (hBOOL (hAPP _let_2 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) (c_Groups_Oone__class_Oone tc_Nat_Onat))) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))))))))) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.63 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (hAPP _let_0 V_z))) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_x))) (not (hBOOL (hAPP _let_1 V_y))) (hBOOL (hAPP _let_1 V_x))))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( v_G, v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_n $$unsorted)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP c_Int_Onat (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n)))) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (= V_A_2 (c_Orderings_Obot__class_Obot _let_0)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) (hAPP (c_Groups_Ouminus__class_Ouminus _let_0) V_A_2))))) ) 6.44/6.63 ( v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (c_Finite__Set_Ofinite T_b))) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP _let_2 V_A_2))) (= V_A_2 _let_1) (not (hBOOL (hAPP _let_2 V_B_2))) (= V_B_2 _let_1) (not (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OInf__fin T_b V_B_2)) (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2))))))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.63 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) V_n) V_m) (hAPP (hAPP c_Code__Numeral_Osubtract__code__numeral V_n) V_m)) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_k_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_k_2) (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) (hAPP c_Nat_OSuc V_k_2))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.63 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.63 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_F_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Finite__Set_Ofolding T_b T_c V_f_2 V_F_2)) (= (c_Fun_Oid T_c) (hAPP V_F_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 6.44/6.63 ( skv_1, skv_2, skv_3, skv_4 ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_S_2 $$unsorted)) (= (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Int_Oint) B_x) V_S_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) B_x))) ) (c_Nat__Transfer_Onat__set V_S_2)) ) 6.44/6.63 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_n_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) V_n_2) (hAPP (c_List_Oset tc_Nat_Onat) (c_List_Oupt (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_n_2))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_b $$unsorted)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 6.44/6.63 ( tc_HOL_Obool ) 6.44/6.63 ( tc_Nat_Onat ) 6.44/6.63 ( tc_Int_Oint ) 6.44/6.63 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.63 ( tc_Product__Type_Ounit ) 6.44/6.63 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (let ((_let_3 (hAPP _let_2 V_A_2))) (let ((_let_4 (hAPP _let_3 V_B_2))) (let ((_let_5 (c_Orderings_Oord__class_Omax T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (not (hBOOL (hAPP _let_0 V_B_2))) (= (c_Orderings_Obot__class_Obot _let_1) _let_4) (= (hAPP (hAPP _let_5 (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2))) (c_Big__Operators_Olinorder__class_OMax T_b _let_4)) (hAPP (hAPP _let_5 (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMax T_b V_B_2)))))))))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.63 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_S_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_S_2))) (= V_S_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP _let_0 (c_Big__Operators_Olinorder__class_OMin T_b V_S_2)) (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (c_Set_Oimage T_b T_b _let_0) V_S_2))))) ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_N_2 $$unsorted) (V_h_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__inf__class_Oinf T_b))) (= (hAPP V_h_2 (hAPP (hAPP _let_0 B_x) B_y)) (hAPP (hAPP _let_0 (hAPP V_h_2 B_x)) (hAPP V_h_2 B_y)))) )) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (= V_N_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP V_h_2 (c_Big__Operators_Olattice__class_OInf__fin T_b V_N_2)) (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (c_Set_Oimage T_b T_b V_h_2) V_N_2)))) ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Transitive__Closure_Otrancl T_b V_r_2) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) (c_Transitive__Closure_Ortrancl T_b V_r_2)) V_r_2)) ) 6.44/6.63 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_n $$unsorted)) (= (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_n)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))))) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.63 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_w_2 $$unsorted) (V_z_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (or (not (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_2))) (= (hBOOL (hAPP (hAPP _let_0 V_w_2) V_z_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP c_Int_Onat V_w_2)) (hAPP c_Int_Onat V_z_2)))))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( c_Int_OMin, c_Int_OMin ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) V_A_2))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (hAPP V_B_2 B_x)))) ) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tc_fun T_c tc_HOL_Obool)) V_A_2) V_B_2))))) ) 6.44/6.63 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (= (hAPP (c_Finite__Set_Ocard T_c) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)) (hAPP (c_Finite__Set_Ocard T_b) V_A_2))) (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2)) ) 6.44/6.63 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) B_x) B_y)) (hAPP (hAPP _let_0 B_x) (hAPP (hAPP _let_0 B_y) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))))) )) (hBOOL (hAPP (hAPP (c_member T_b) (c_Big__Operators_Olattice_OSup__fin T_b (c_Orderings_Oord__class_Omax T_b) V_A_2)) V_A_2))) ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_a))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_a) V_b))) (= V_a (c_Divides_Odiv__class_Omod tc_Int_Oint V_a V_b))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( c_Int_OMin, c_Int_OMin ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2) (c_Complete__Lattice_OSup__class_OSup T_b V_A_2))) ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Obounded__lattice T_1)) (class_Lattices_Obounded__lattice__top (tc_fun T_2 T_1))) ) 6.44/6.63 ( tc_HOL_Obool, tc_HOL_Obool ) 6.44/6.63 ( tc_Nat_Onat, tc_HOL_Obool ) 6.44/6.63 ( tc_Int_Oint, tc_HOL_Obool ) 6.44/6.63 ( tc_Int_Oint, tc_Int_Oint ) 6.44/6.63 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.44/6.63 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.44/6.63 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.44/6.63 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (or (not (class_Orderings_Oorder T_b)) (= (and (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2)) (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2))) (= V_y_2 V_x_2)))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.63 ( v_G, v_Ga, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_b $$unsorted) (T_c $$unsorted)) (= (c_Fun_Oid (tc_prod T_b T_c)) (c_Product__Type_Oapsnd T_c T_c T_b (c_Fun_Oid T_c))) ) 6.44/6.63 ( tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.63 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_k) c_Int_OMin) (c_Int_Osucc V_k)) ) 6.44/6.63 ( c_Int_OPls ) 6.44/6.63 ( c_Int_OMin ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_k) (c_Groups_Oone__class_Oone tc_Int_Oint)) (c_Int_Osucc V_k)) ) 6.44/6.63 ( c_Int_OPls ) 6.44/6.63 ( c_Int_OMin ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2))) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_B_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) (c_Big__Operators_Olattice__class_OSup__fin T_b V_B_2)) _let_1))))) ) 6.44/6.63 ( v_G, v_Ga, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Relation_OField T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Set_Oinsert T_b))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (hAPP (hAPP _let_2 V_a_2) (hAPP (hAPP _let_2 V_b_2) (c_Orderings_Obot__class_Obot _let_1)))) (hAPP _let_0 V_r_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_b_2)) V_r_2)))))) ) 6.44/6.63 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.63 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 _let_1) V_a_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) _let_1)))))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (or (not (c_Fun_Obij__betw T_b T_c V_f_2 _let_0 _let_1)) (= _let_1 (hAPP (c_Set_Oimage T_b T_c V_f_2) _let_0))))) ) 6.44/6.63 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.63 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.63 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_c))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool))))) (hBOOL (hAPP (c_Finite__Set_Ofinite _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool)))))) ) 6.44/6.63 ( tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.63 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (not (class_Int_Onumber__ring T_a)) (= (c_Groups_Oone__class_Oone T_a) (hAPP (c_Groups_Oabs__class_Oabs T_a) (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OMin)))) ) 6.44/6.63 ( tc_Nat_Onat ) 6.44/6.63 ( tc_Int_Oint ) 6.44/6.63 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_X_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Relation_OImage T_b T_b V_r_2) V_X_2)) V_X_2))) (= V_X_2 (hAPP (c_Relation_OImage T_b T_b (c_Transitive__Closure_Ortrancl T_b V_r_2)) V_X_2))) ) 6.44/6.63 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus _let_0))) (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) (hAPP _let_1 V_A_2)) (hAPP _let_1 V_B_2)) (hAPP _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2))))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.63 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_k $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Int_Oring__1__class_Oof__int T_a) V_k) (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_k))) ) 6.44/6.63 ( c_Int_OPls, tc_Nat_Onat ) 6.44/6.63 ( c_Int_OPls, tc_Int_Oint ) 6.44/6.63 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.44/6.63 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.44/6.63 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.44/6.63 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.44/6.63 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.44/6.63 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_v $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_v) (c_Int_OBit1 c_Int_OPls))) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP _let_0 V_v)) (c_Groups_Oone__class_Oone T_a))))) ) 6.44/6.63 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (or (not (class_Int_Onumber__ring T_b)) (not (class_Int_Oring__char__0 T_b)) (= (= (hAPP _let_0 V_y_2) (hAPP _let_0 V_x_2)) (= V_y_2 V_x_2)))) ) 6.44/6.63 ( c_Int_OPls, (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( c_Int_OPls, (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.44/6.63 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.44/6.63 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.44/6.63 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.44/6.63 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.44/6.63 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.44/6.63 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Nat_Onat ) 6.44/6.63 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.44/6.63 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.44/6.63 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) (not (forall ((B_x $$unsorted)) (let ((_let_0 (c_member T_b))) (or (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBS T_b tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_b) c_fconj) (hAPP (hAPP (c_COMBC T_b (tc_fun T_b tc_HOL_Obool) tc_HOL_Obool) _let_0) V_A_2))) (hAPP (hAPP (c_COMBC T_b T_c tc_HOL_Obool) (hAPP (hAPP (c_COMBB T_c (tc_fun T_c tc_HOL_Obool) T_b) c_fequal) V_f_2)) (hAPP V_f_2 B_x)))))) (not (hBOOL (hAPP (hAPP _let_0 B_x) V_A_2))))) ))) ) 6.44/6.63 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)))) ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_X_2 $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite _let_0) V_X_2))) (hBOOL (hAPP (hAPP (c_member (tc_prod _let_1 _let_1)) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) (c_Orderings_Obot__class_Obot _let_1)) V_X_2)) c_FunDef_Omax__weak))))) ) 6.44/6.63 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (hAPP _let_0 V_z))) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_x))) (not (hBOOL (hAPP _let_1 V_y))) (hBOOL (hAPP _let_1 V_x))))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__sup T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)))) ) 6.44/6.63 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ( c_FunDef_Opair__less, (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.44/6.63 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_i_2 $$unsorted) (V_d_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 V_d_2))) (let ((_let_2 (hBOOL (hAPP _let_1 V_i_2)))) (let ((_let_3 (c_Lazy__Sequence_Osmall__lazy_H V_d_2 V_i_2))) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Lazy__Sequence_Osmall__lazy_H__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) V_d_2) V_i_2)))) (and (or _let_2 (= (c_Lazy__Sequence_Oappend tc_Int_Oint (hAPP (c_Lazy__Sequence_Osingle tc_Int_Oint) V_i_2) (c_Lazy__Sequence_Osmall__lazy_H V_d_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_i_2) (c_Groups_Oone__class_Oone tc_Int_Oint)))) _let_3)) (or (not _let_2) (= (c_Lazy__Sequence_Oempty tc_Int_Oint) _let_3)))))))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.63 ( c_Int_OMin, c_Int_OMin ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_R_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_R_2)) (c_Wellfounded_OwfP T_b (c_FunDef_Oin__rel T_b T_b V_R_2))) ) 6.44/6.63 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.44/6.63 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.44/6.63 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (c_Groups_Oone__class_Oone T_a))) (or (not (class_Rings_Olinordered__idom T_a)) (= _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) _let_0)))) ) 6.44/6.63 ( tc_Nat_Onat ) 6.44/6.63 ( tc_Int_Oint ) 6.44/6.63 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (= V_A_2 _let_2) (not (hBOOL (hAPP _let_0 V_B_2))) (= V_B_2 _let_2) (not (= _let_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2))) (= (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMin T_b V_B_2)) (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2))))))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.63 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (not (= (c_Groups_Ozero__class_Ozero T_a) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b))) (= V_b (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a))) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Inductive_Ocomplete__lattice__class_Ogfp T_b V_f_2))) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (c_Orderings_Oorder__class_Omono T_b T_b V_f_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP V_f_2 _let_0)) _let_0)))) ) 6.44/6.63 ( c_Nat_OSuc, tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (c_SetInterval_Oord__class_OatLeastAtMost T_b V_l_2 V_u_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP (hAPP (c_Set_Oinsert T_b) V_l_2) (c_Orderings_Obot__class_Obot _let_0))) (c_SetInterval_Oord__class_OgreaterThanAtMost T_b V_l_2 V_u_2))))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.63 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (= (and (= _let_0 V_m_2) (= _let_0 V_n_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP _let_1 V_n_2)) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP _let_1 V_m_2))))))) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Olattice T_a)) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_x))) ) 6.44/6.63 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.44/6.63 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Product__Type_OPair T_b T_c))) (= (and (= V_b_H_2 V_b_2) (= V_a_H_2 V_a_2)) (= (hAPP (hAPP _let_0 V_a_2) V_b_2) (hAPP (hAPP _let_0 V_a_H_2) V_b_H_2)))) ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.63 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.63 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (let ((_let_2 (c_Groups_Oplus__class_Oplus T_b))) (or (not (class_Rings_Olinordered__idom T_b)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) (c_Int_Oring__1__class_OInts T_b)))) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_2 (hAPP (hAPP _let_2 (c_Groups_Oone__class_Oone T_b)) V_a_2)) V_a_2)) _let_1))))))) ) 6.44/6.63 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (forall ((B_x $$unsorted)) (or (not (= V_A_2 (hAPP (c_List_Oset T_b) B_x))) (not (forall ((B_y $$unsorted)) (or (not (c_List_Olinorder__class_Osorted T_b B_y)) (not (hBOOL (hAPP (c_List_Odistinct T_b) B_y))) (not (= V_A_2 (hAPP (c_List_Oset T_b) B_y))) (= B_x B_y)) )) (not (hBOOL (hAPP (c_List_Odistinct T_b) B_x))) (not (c_List_Olinorder__class_Osorted T_b B_x))) ))) ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (tc_fun T_b _let_0))) (= (hAPP (c_Set_OCollect _let_0) (hAPP (hAPP (c_COMBB _let_1 tc_HOL_Obool _let_0) (c_HOL_OEx T_b)) (hAPP (hAPP (c_COMBC _let_0 _let_2 _let_1) (hAPP (hAPP (c_COMBB (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_2 _let_1) _let_0) (c_COMBB _let_0 tc_HOL_Obool T_b)) c_fequal)) (hAPP (hAPP (c_COMBS T_b T_b _let_0) (c_Product__Type_OPair T_b T_b)) (c_COMBI T_b))))) (c_Relation_OId T_b))))) ) 6.44/6.63 ( tc_Nat_Onat ) 6.44/6.63 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.63 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((V_N_2 $$unsorted) (V_h_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (let ((_let_1 (c_Finite__Set_Ofold1 T_b _let_0))) (or (not (class_Lattices_Oab__semigroup__idem__mult T_b)) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (= (hAPP (hAPP _let_0 (hAPP V_h_2 B_x)) (hAPP V_h_2 B_y)) (hAPP V_h_2 (hAPP (hAPP _let_0 B_x) B_y))) )) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (= V_N_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP V_h_2 (hAPP _let_1 V_N_2)) (hAPP _let_1 (hAPP (c_Set_Oimage T_b T_b V_h_2) V_N_2)))))) ) 6.44/6.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_b)) (c_Finite__Set_Ofun__left__comm__idem T_b T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b))) ) 6.44/6.63 ( tc_HOL_Obool ) 6.44/6.63 ( tc_Nat_Onat ) 6.44/6.63 ( tc_Int_Oint ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (not (c_Int_Oiszero T_a (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit1 c_Int_OPls))))) ) 6.44/6.63 ( tc_Nat_Onat ) 6.44/6.63 ( tc_Int_Oint ) 6.44/6.63 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ) 6.44/6.63 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (c_Finite__Set_Ofun__left__comm__idem T_b T_b (c_Orderings_Oord__class_Omin T_b))) ) 6.44/6.63 ( tc_Nat_Onat ) 6.44/6.63 ( tc_Int_Oint ) 6.44/6.63 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.63 ) 6.44/6.64 (instantiation (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (= (or (and (= V_d_2 V_b_2) (= V_c_2 V_a_2)) (and (= V_c_2 V_b_2) (= V_d_2 V_a_2))) (= (hAPP (hAPP _let_0 V_c_2) (hAPP (hAPP _let_0 V_d_2) _let_1)) (hAPP (hAPP _let_0 V_a_2) (hAPP (hAPP _let_0 V_b_2) _let_1)))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_y)) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_x) V_y))) ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (c_Orderings_Oord__class_Omax T_b))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (c_Lattices_Osemilattice__inf__class_Oinf _let_2))) (let ((_let_4 (hAPP _let_3 V_A_2))) (let ((_let_5 (hAPP _let_4 V_B_2))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (not (hBOOL (hAPP _let_0 V_B_2))) (= _let_5 (c_Orderings_Obot__class_Obot _let_2)) (= (hAPP (hAPP _let_1 (c_Big__Operators_Olattice_OSup__fin T_b _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_2) V_A_2) V_B_2))) (c_Big__Operators_Olattice_OSup__fin T_b _let_1 _let_5)) (hAPP (hAPP _let_1 (c_Big__Operators_Olattice_OSup__fin T_b _let_1 V_A_2)) (c_Big__Operators_Olattice_OSup__fin T_b _let_1 V_B_2)))))))))) ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (= (= (hAPP (c_Set_Oimage T_c T_b V_f_2) _let_0) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))) (= (c_Fun_Oid T_b) (hAPP (c_Fun_Ocomp T_c T_b T_b V_f_2) (c_Hilbert__Choice_Oinv__into T_c T_b _let_0 V_f_2))))) ) 6.44/6.64 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.64 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.64 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Rings_Oring__1 T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (c_Groups_Oone__class_Oone T_b)) (c_Int_Oring__1__class_OInts T_b)))) ) 6.44/6.64 ( tc_Nat_Onat ) 6.44/6.64 ( tc_Int_Oint ) 6.44/6.64 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (or (not (= _let_1 (hAPP (c_Set_Oimage T_c T_b V_f_2) _let_0))) (c_Fun_Oinj__on T_b T_c (c_Hilbert__Choice_Oinv__into T_c T_b _let_0 V_f_2) _let_1)))) ) 6.44/6.64 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.64 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.64 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint))) (let ((_let_3 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_4 (hAPP _let_0 V_b_2))) (let ((_let_5 (hBOOL (hAPP _let_4 _let_1)))) (let ((_let_6 (hAPP _let_3 V_a_2))) (let ((_let_7 (hBOOL (hAPP _let_6 V_b_2)))) (let ((_let_8 (c_Divides_OposDivAlg V_a_2 V_b_2))) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Divides_OposDivAlg__rel) (hAPP (hAPP _let_2 V_a_2) V_b_2)))) (and (or (and (not _let_5) (not _let_7)) (= _let_8 (hAPP (hAPP _let_2 _let_1) V_a_2))) (or _let_7 _let_5 (= _let_8 (hAPP (c_Divides_Oadjust V_b_2) (c_Divides_OposDivAlg V_a_2 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) V_b_2)))))))))))))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_x) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (not (forall ((B_n $$unsorted)) (not (= V_x (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Nat_OSuc B_n))))) ))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OMin ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Orderings_Oord__class_Omin T_b)) V_a_2) V_A_2))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_x) V_y))) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_x))) (= V_y V_x))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.64 ( v_G, v_Ga, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_z $$unsorted)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Nat_Onat) V_z) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_z) V_z)) ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (c_Finite__Set_Ofun__left__comm__idem T_b T_b (c_Orderings_Oord__class_Omax T_b))) ) 6.44/6.64 ( tc_Nat_Onat ) 6.44/6.64 ( tc_Int_Oint ) 6.44/6.64 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (c_Finite__Set_Ofun__left__comm T_b (tc_List_Olist T_b) (c_List_Olinorder__class_Oinsort__key T_b T_b (c_COMBI T_b)))) ) 6.44/6.64 ( tc_Nat_Onat ) 6.44/6.64 ( tc_Int_Oint ) 6.44/6.64 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Inductive_Ocomplete__lattice__class_Olfp T_b V_f_2))) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (c_Orderings_Oorder__class_Omono T_b T_b V_f_2)) (= _let_0 (hAPP V_f_2 _let_0)))) ) 6.44/6.64 ( c_Nat_OSuc, tc_Nat_Onat ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Set_Oimage T_b T_c V_f_2))) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (= (= (hAPP _let_0 V_B_2) (hAPP _let_0 V_A_2)) (= V_B_2 V_A_2)))) ) 6.44/6.64 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.64 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.44/6.64 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Nat_Osize T_b)) (c_FunDef_Ois__measure T_b (c_Nat_Osize__class_Osize T_b))) ) 6.44/6.64 ( tc_HOL_Obool ) 6.44/6.64 ( tc_Nat_Onat ) 6.44/6.64 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ( tc_Product__Type_Ounit ) 6.44/6.64 ( tc_Code__Evaluation_Oterm ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_SetInterval_Oord__class_OatLeast T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_l_2) V_u_2)) (hAPP _let_0 V_u_2)) (hAPP _let_0 V_l_2)))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_2 (hAPP _let_0 V_v_2))) (let ((_let_3 (hBOOL (hAPP _let_2 V_v_H_2)))) (= (and _let_3 (or (not _let_3) (hBOOL (hAPP (hAPP _let_0 c_Int_OPls) V_v_H_2)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP _let_1 V_v_2)) (hAPP _let_1 V_v_H_2)))))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP _let_1 V_A_2)) (hAPP _let_1 V_B_2)) (hAPP _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) V_B_2)))))) ) 6.44/6.64 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (or (not (class_Orderings_Oorder T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2))) (= (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2)) (= V_x_2 V_y_2)))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.64 ( v_G, v_Ga, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_b $$unsorted)) (= (hAPP (c_Relation_ORange T_b T_b) (c_Relation_OId T_b)) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))) ) 6.44/6.64 ( tc_HOL_Obool ) 6.44/6.64 ( tc_Nat_Onat ) 6.44/6.64 ( tc_Int_Oint ) 6.44/6.64 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.64 ( tc_Product__Type_Ounit ) 6.44/6.64 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (hBOOL (hAPP _let_2 V_x_2))) (not (hBOOL (hAPP _let_2 V_y_2))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP c_Int_Onat V_x_2)) (hAPP c_Int_Onat V_y_2)))))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (= V_x_2 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_u_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_u_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_u_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_u_2) (c_Orderings_Obot__class_Obot _let_0)))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (= (hAPP (hAPP _let_0 V_m) V_n) (hAPP (hAPP _let_0 V_n) V_m))) ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (= V_x_2 (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_z $$unsorted)) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg V_z))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP c_Int_Onat V_z))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero T_b))) (or (not (class_Rings_Olinordered__idom T_b)) (= (= V_a_2 _let_0) (= _let_0 (c_Groups_Osgn__class_Osgn T_b V_a_2))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= V_x_2 (c_Big__Operators_Olattice_OSup__fin T_b (c_Orderings_Oord__class_Omax T_b) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (let ((_let_1 (hAPP _let_0 V_x_2))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_List_Olinorder__class_Oinsort__key T_b T_b (c_COMBI T_b)) V_x_2) (c_List_Olinorder__class_Osorted__list__of__set T_b (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) V_A_2) (hAPP _let_1 (c_Orderings_Obot__class_Obot _let_2))))) (c_List_Olinorder__class_Osorted__list__of__set T_b (hAPP _let_1 V_A_2))))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((B_G $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) v_G_H) B_G))) (c_Hoare__Mirabelle_Ohoare__derivs t_a B_G v_ts)) ) 6.44/6.64 ( v_Ga ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_2 (hAPP _let_0 V_v_2))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP _let_1 V_v_2)) (hAPP _let_1 V_v_H_2))) (or (hBOOL (hAPP _let_2 V_v_H_2)) (hBOOL (hAPP _let_2 c_Int_OPls))))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OPls, c_Int_OMin ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_v) V_w)) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (hAPP _let_0 V_v)) (hAPP _let_0 V_w))))) ) 6.44/6.64 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Oabs__class_Oabs T_a))) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (= (hAPP _let_0 V_a) (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_w_2 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (= (hAPP _let_0 (c_Int_OBit0 V_w_2)) (hAPP (hAPP (c_HOL_OLet tc_Nat_Onat tc_Nat_Onat) (hAPP _let_0 V_w_2)) (hAPP (hAPP (c_COMBS tc_Nat_Onat tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oplus__class_Oplus tc_Nat_Onat)) (c_COMBI tc_Nat_Onat))))) ) 6.44/6.64 ( c_Int_OPls ) 6.44/6.64 ( (c_Int_OBit1 c_Int_OPls) ) 6.44/6.64 ( c_Int_OMin ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (not (forall ((B_n $$unsorted)) (not (= V_z_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_w_2) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) )) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_w_2) V_z_2))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OPls, c_Int_OMin ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_b)) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) V_b))) ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) (= V_x (hAPP (hAPP (c_Orderings_Oord__class_Omin T_a) V_x) V_y))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 _let_0)) (= _let_0 (hAPP (c_Set_Oimage T_c T_b (c_Hilbert__Choice_Oinv__into T_b T_c _let_0 V_f_2)) (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))))) ) 6.44/6.64 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OMin) (hAPP (c_Int_Oring__1__class_Oof__int T_a) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin)))) ) 6.44/6.64 ( tc_Nat_Onat ) 6.44/6.64 ( tc_Int_Oint ) 6.44/6.64 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Relation_OField T_b) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)))) ) 6.44/6.64 ( tc_Nat_Onat ) 6.44/6.64 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_d $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (= (hAPP (c_Set_Oimage T_c T_b (hAPP (hAPP (c_COMBB T_d T_b T_c) V_f_2) V_g_2)) _let_0) (hAPP (c_Set_Oimage T_d T_b V_f_2) (hAPP (c_Set_Oimage T_c T_d V_g_2) _let_0)))) ) 6.44/6.64 ( c_Nat_OSuc, (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal), tc_Nat_Onat, (tc_fun tc_Nat_Onat tc_HOL_Obool), tc_Nat_Onat ) 6.44/6.64 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_fconj, tc_HOL_Obool, (tc_fun tc_HOL_Obool tc_HOL_Obool), tc_Int_Oint ) 6.44/6.64 ( c_Nitpick_Oint__gcd, (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal), (tc_fun tc_Int_Oint tc_Int_Oint), (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.64 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool), (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.64 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (tc_fun tc_Int_Oint tc_HOL_Obool), (tc_fun tc_Int_Oint tc_HOL_Obool), tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (c_Finite__Set_Ofinite T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_2 V_A_2))) (= V_A_2 _let_1) (not (hBOOL (hAPP _let_2 V_B_2))) (= V_B_2 _let_1) (= (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMax T_b V_B_2)) (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2))))))) ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP _let_2 V_a_2)) (hBOOL (hAPP _let_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2)))))))) ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b)) V_x_2) V_A_2))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_b) V_a))) (not (hBOOL (hAPP (hAPP _let_0 V_a) V_b))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (or (not (class_Orderings_Olinorder T_a)) (= V_y V_x) (hBOOL (hAPP (hAPP _let_0 V_x) V_y)) (hBOOL (hAPP (hAPP _let_0 V_y) V_x)))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Power_Opower T_b)) (= (c_Power_Opower__class_Opower T_b) (c_Power_Opower_Opower T_b (c_Groups_Oone__class_Oone T_b) (c_Groups_Otimes__class_Otimes T_b)))) ) 6.44/6.64 ( tc_Nat_Onat ) 6.44/6.64 ( tc_Int_Oint ) 6.44/6.64 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus T_a))) (or (not (class_Groups_Ocancel__semigroup__add T_a)) (not (= (hAPP (hAPP _let_0 V_b) V_a) (hAPP (hAPP _let_0 V_c) V_a))) (= V_c V_b))) ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 _let_1) V_a_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) _let_1)))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OPls, tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_w $$unsorted)) (let ((_let_0 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (let ((_let_2 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_3 (hAPP _let_2 V_w))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_3) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (= (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) _let_0) _let_3) (hAPP (c_Product__Type_Ofst tc_Int_Oint tc_Int_Oint) (hAPP c_Divides_OnegateSnd (c_Divides_OnegDivAlg (hAPP _let_1 _let_0) (hAPP _let_1 _let_3)))))))))) ) 6.44/6.64 ( c_Int_OPls ) 6.44/6.64 ( (c_Int_OBit1 c_Int_OPls) ) 6.44/6.64 ( c_Int_OMin ) 6.44/6.64 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.64 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_x) V_x)))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_A_2 $$unsorted)) (or (not (c_Nat__Transfer_Onat__set V_A_2)) (= (hAPP (c_Finite__Set_Ocard tc_Nat_Onat) (hAPP (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) V_A_2)) (hAPP (c_Finite__Set_Ocard tc_Int_Oint) V_A_2))) ) 6.44/6.64 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_l $$unsorted)) (or (not (c_List_Onat__list V_l)) (= V_l (c_List_Oembed__list (c_List_Oreturn__list V_l)))) ) 6.44/6.64 ( (c_List_Olist_ONil tc_Int_Oint) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (c_Groups_Ozero__class_Ozero T_a)) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_k_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_k_2))) (= (c_SetInterval_Oord__class_OgreaterThanAtMost T_b V_k_2 V_l_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 V_A_2)) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (= V_A_2 (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2))) ) 6.44/6.64 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_z))) (hBOOL (hAPP (hAPP _let_0 V_x) V_z)))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OPls, c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2)) (c_Fun_Obij__betw T_b T_c V_f_2 V_A_2 (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2))) ) 6.44/6.64 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.64 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.64 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.44/6.64 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hAPP (c_Set_Oimage T_b T_b _let_0) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_x_2)) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) (hAPP _let_0 V_x_2))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Owellorder T_b)) (c_Wellfounded_Owf T_b (hAPP (c_Set_OCollect (tc_prod T_b T_b)) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_b tc_HOL_Obool) (c_Orderings_Oord__class_Oless T_b))))) ) 6.44/6.64 ( tc_Nat_Onat ) 6.44/6.64 ( tc_Int_Oint ) 6.44/6.64 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP _let_2 V_a_2)) (hBOOL (hAPP _let_2 (c_Groups_Osgn__class_Osgn T_b V_a_2)))))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_w $$unsorted) (V_z $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (or (not (hBOOL (hAPP (hAPP _let_0 V_z) V_w))) (not (hBOOL (hAPP (hAPP _let_0 V_w) V_z))) (= V_w V_z))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OPls, c_Int_OMin ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( c_Int_OMin, c_Int_OPls ) 6.44/6.64 ( c_Int_OMin, c_Int_OMin ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (c_Groups_Oone__class_Oone T_a))) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) _let_0) _let_0))))) ) 6.44/6.64 ( tc_Nat_Onat ) 6.44/6.64 ( tc_Int_Oint ) 6.44/6.64 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_a_2 $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool))) (c_SetInterval_Oord_OatLeastAtMost tc_Nat_Onat (c_Rings_Odvd__class_Odvd tc_Nat_Onat) V_a_2 V_a_2)) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 _let_1) (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2))) (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_b $$unsorted)) (= (hAPP (c_Set_OCollect T_b) (hAPP (c_COMBK tc_HOL_Obool T_b) c_fTrue)) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))) ) 6.44/6.64 ( tc_HOL_Obool ) 6.44/6.64 ( tc_Nat_Onat ) 6.44/6.64 ( tc_Int_Oint ) 6.44/6.64 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.64 ( tc_Product__Type_Ounit ) 6.44/6.64 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ocard T_b))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (hAPP _let_1 V_x_2))) (let ((_let_3 (hAPP _let_2 V_A_2))) (let ((_let_4 (hAPP _let_0 V_A_2))) (let ((_let_5 (hAPP _let_0 _let_3))) (let ((_let_6 (c_member T_b))) (let ((_let_7 (hAPP _let_6 V_x_2))) (let ((_let_8 (hBOOL (hAPP _let_7 V_A_2)))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or (not _let_8) (= _let_4 _let_5)) (or _let_8 (= _let_5 (hAPP c_Nat_OSuc _let_4)))))))))))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (or (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2)))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) V_A_2))) ) 6.44/6.64 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.64 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.64 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 6.44/6.64 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (c_Product__Type_Omap__pair T_b T_b T_c T_c (c_COMBI T_b) (c_COMBI T_c)) (c_Fun_Oid (tc_prod T_b T_c))) ) 6.44/6.64 ( tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.64 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z))) (= (hAPP (c_Int_Oring__1__class_Oof__int T_a) V_z) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (hAPP c_Int_Onat V_z)))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (hAPP c_Code__Numeral_Oof__nat (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_n) V_m)) (hAPP (hAPP c_Code__Numeral_Osubtract__code__numeral (hAPP c_Code__Numeral_Oof__nat V_n)) (hAPP c_Code__Numeral_Oof__nat V_m))) ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_R_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Relation_OImage T_c T_b V_R_2) (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool)))) ) 6.44/6.64 ( c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Olattice (tc_fun T_2 T_1))) ) 6.44/6.64 ( tc_HOL_Obool, tc_HOL_Obool ) 6.44/6.64 ( tc_Nat_Onat, tc_HOL_Obool ) 6.44/6.64 ( tc_Int_Oint, tc_HOL_Obool ) 6.44/6.64 ( tc_Int_Oint, tc_Int_Oint ) 6.44/6.64 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.44/6.64 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.44/6.64 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.44/6.64 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (not (c_Int_Oiszero T_a (c_Groups_Oone__class_Oone T_a)))) ) 6.44/6.64 ( tc_Nat_Onat ) 6.44/6.64 ( tc_Int_Oint ) 6.44/6.64 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (= V_x (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (c_Groups_Osgn__class_Osgn T_a V_x)) (hAPP (c_Groups_Oabs__class_Oabs T_a) V_x)))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_z) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OMin)) V_z))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Olattice T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)))) ) 6.44/6.64 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.64 ( c_FunDef_Opair__less, (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.44/6.64 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) (c_Orderings_Obot__class_Obot _let_0)))) ) 6.44/6.64 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.64 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ocard T_b))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (hAPP _let_1 V_x_2))) (let ((_let_3 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_3) V_A_2) (hAPP _let_2 (c_Orderings_Obot__class_Obot _let_3))))) (hAPP _let_0 (hAPP _let_2 V_A_2)))))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (c_Orderings_Obot__class_Obot T_a) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x)))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_P_2 $$unsorted) (V_F_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_F_2))) (not (hBOOL (hAPP V_P_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) (not (forall ((B_x $$unsorted) (B_F $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) B_F))) (hBOOL (hAPP (hAPP (c_member T_b) B_x) B_F)) (not (hBOOL (hAPP V_P_2 B_F))) (hBOOL (hAPP V_P_2 (hAPP (hAPP (c_Set_Oinsert T_b) B_x) B_F)))) )) (hBOOL (hAPP V_P_2 V_F_2))) ) 6.44/6.64 ( (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.64 ( (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_prod T_b T_b))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (let ((_let_3 (tc_fun T_b tc_HOL_Obool))) (let ((_let_4 (c_COMBC T_b _let_2 tc_HOL_Obool))) (let ((_let_5 (tc_fun _let_2 tc_HOL_Obool))) (let ((_let_6 (c_COMBB _let_1 _let_5 T_b))) (let ((_let_7 (c_member _let_1))) (let ((_let_8 (hAPP _let_6 _let_7))) (let ((_let_9 (c_Product__Type_OPair T_b T_b))) (let ((_let_10 (c_Transitive__Closure_Ortrancl T_b V_r_2))) (= (c_Transitive__Closure_Otrancl T_b (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP _let_9 V_y_2) V_x_2)) V_r_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_2) (c_Transitive__Closure_Otrancl T_b V_r_2)) (hAPP (c_Set_OCollect _let_1) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_b tc_HOL_Obool) (hAPP (hAPP (c_COMBC T_b _let_3 _let_3) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_3 _let_3) T_b) (c_COMBB tc_HOL_Obool tc_HOL_Obool T_b)) (hAPP (hAPP (c_COMBB tc_HOL_Obool _let_0 T_b) c_fconj) (hAPP (hAPP _let_4 (hAPP _let_8 (hAPP (hAPP (c_COMBC T_b T_b _let_1) _let_9) V_y_2))) _let_10)))) (hAPP (hAPP _let_4 (hAPP _let_8 (hAPP _let_9 V_x_2))) _let_10))))))))))))))))) ) 6.44/6.64 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.64 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (or (not (class_Rings_Olinordered__semidom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (hAPP _let_0 V_m)) (hAPP _let_0 V_n)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m) V_n)))) ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Orderings_Oord__class_Omax T_b)) V_x_2) V_A_2))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.64 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_a_2)) V_b_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_b_2)) V_a_2)))))) ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.64 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.64 ) 6.44/6.64 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__sup__class_Osup T_a))) (or (not (class_Lattices_Olattice T_a)) (= (hAPP (hAPP _let_0 V_y) V_x) (hAPP (hAPP _let_0 V_x) V_y)))) ) 6.44/6.64 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.65 ( c_FunDef_Opair__less, (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.44/6.65 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.44/6.65 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_0) V_a))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_a) V_b))) (= _let_0 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_a) V_b)))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( c_Int_OMin, c_Int_OMin ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 V_i))) (or (not (hBOOL (hAPP _let_1 V_j))) (not (hBOOL (hAPP (hAPP _let_0 V_j) V_k))) (hBOOL (hAPP _let_1 V_k))))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( c_Int_OPls, c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( c_Int_OMin, c_Int_OMin, c_Int_OMin ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, c_Int_OMin ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (hAPP (c_Set_Oimage T_c T_b V_f_2) V_A_2)))) (not (c_Fun_Oinj__on T_c T_b V_f_2 V_A_2)) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) V_A_2))) ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 6.44/6.65 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 6.44/6.65 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (or (not (class_Orderings_Olinorder T_a)) (hBOOL (hAPP (hAPP _let_0 V_x) V_y)) (hBOOL (hAPP (hAPP _let_0 V_y) V_x)))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.65 ( v_G, v_Ga, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Groups_Ominus__class_Ominus _let_0))) (let ((_let_2 (hAPP _let_1 V_A_2))) (let ((_let_3 (c_Set_Oinsert T_b))) (let ((_let_4 (hAPP _let_3 V_x_2))) (let ((_let_5 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_6 (hAPP _let_4 _let_5))) (let ((_let_7 (hAPP _let_2 _let_6))) (let ((_let_8 (hAPP _let_4 V_A_2))) (let ((_let_9 (c_Big__Operators_Olattice__class_OSup__fin T_b _let_8))) (let ((_let_10 (= _let_5 _let_7))) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or _let_10 (= _let_9 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) (c_Big__Operators_Olattice__class_OSup__fin T_b _let_7)))) (or (not _let_10) (= V_x_2 _let_9))))))))))))))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.65 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Inductive_Ocomplete__lattice__class_Olfp T_b V_f_2))) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (c_Orderings_Oorder__class_Omono T_b T_b V_f_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP V_f_2 _let_0)) _let_0)))) ) 6.44/6.65 ( c_Nat_OSuc, tc_Nat_Onat ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_v_2 $$unsorted) (V_d_2 $$unsorted) (V_c_2 $$unsorted) (T_e $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_d $$unsorted)) (or (not (= (hAPP (c_Fun_Ocomp T_d T_c T_b V_a_2) V_b_2) (hAPP (c_Fun_Ocomp T_e T_c T_b V_c_2) V_d_2))) (= (hAPP V_a_2 (hAPP V_b_2 V_v_2)) (hAPP V_c_2 (hAPP V_d_2 V_v_2)))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Nat_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Nat_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Nat_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Nat_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((BOUND_VARIABLE_117939 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_117939) c_Int_OPls)) (= (hAPP _let_0 (c_Int_Osucc BOUND_VARIABLE_117939)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP _let_0 BOUND_VARIABLE_117939)) (c_Groups_Oone__class_Oone tc_Nat_Onat))))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( c_Int_OPls ) 6.44/6.65 ( (c_Int_OBit1 c_Int_OPls) ) 6.44/6.65 ( c_Int_OMin ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((BOUND_VARIABLE_117952 $$unsorted)) (let ((_let_0 (c_Groups_Oone__class_Oone tc_Nat_Onat))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_117952) c_Int_OPls))) (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) BOUND_VARIABLE_117952)) _let_0)))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( c_Int_OPls ) 6.44/6.65 ( (c_Int_OBit1 c_Int_OPls) ) 6.44/6.65 ( c_Int_OMin ) 6.44/6.65 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.65 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_a))) (or (not (class_Lattices_Oboolean__algebra T_a)) (= V_x (hAPP _let_0 (hAPP _let_0 V_x))))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_P_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Nat_Onat tc_Nat_Onat) c_Nitpick_Onat__gcd__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_a0_2) V_a1_2)))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Nat_Onat tc_Nat_Onat) c_Nitpick_Onat__gcd__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) B_x) B_y)))) (and (not (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) B_y)) (not (hBOOL (hAPP (hAPP V_P_2 B_y) (c_Divides_Odiv__class_Omod tc_Nat_Onat B_x B_y))))) (hBOOL (hAPP (hAPP V_P_2 B_x) B_y))) )) (hBOOL (hAPP (hAPP V_P_2 V_a0_2) V_a1_2))) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OPls, c_Int_OMin ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.44/6.65 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.65 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) ) 6.44/6.65 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.65 ( (c_Set_Oinsert tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Product__Type_OPair _let_1 _let_1))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.65 ( (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 6.44/6.65 ( (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.65 ( (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_fconj ) 6.44/6.65 ( (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Onat__of ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less ) 6.44/6.65 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 6.44/6.65 ( (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Groups_Oone__class_Oone tc_Int_Oint), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))) ) 6.44/6.65 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool) ) 6.44/6.65 ( (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) tc_Int_Oint), c_Nitpick_Oint__gcd, (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal) ) 6.44/6.65 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.65 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.65 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.65 ( (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat), c_Nat_OSuc, (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)), v_Ga, v_G ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omax__weak, c_FunDef_Omax__strict ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omin__weak, c_FunDef_Omin__strict ) 6.44/6.65 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), c_Int_OPls, c_Int_Onat ) 6.44/6.65 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), (c_Int_OBit1 c_Int_OPls), c_Int_Onat ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_R_2 $$unsorted) (T_b $$unsorted)) (= (c_Transitive__Closure_Ortrancl T_b V_R_2) (c_Transitive__Closure_Ortrancl T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_R_2) (c_Relation_OId T_b)))) ) 6.44/6.65 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.65 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_r_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_d $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (c_Set_Oimage T_c T_b (hAPP (c_Fun_Ocomp T_d T_b T_c V_f_2) V_g_2)) V_r_2) (hAPP (c_Set_Oimage T_d T_b V_f_2) (hAPP (c_Set_Oimage T_c T_d V_g_2) V_r_2))) ) 6.44/6.65 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint, tc_Int_Oint ) 6.44/6.65 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_a))) (or (not (class_Lattices_Oboolean__algebra T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_x) V_y))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_y)) (hAPP _let_1 V_x)))))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oab__semigroup__mult T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_b) B_x) B_y)) (hAPP (hAPP _let_0 B_x) (hAPP (hAPP _let_0 B_y) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))))) )) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (c_Finite__Set_Ofold1 T_b (c_Groups_Otimes__class_Otimes T_b)) V_A_2)) V_A_2))) ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_P_2 $$unsorted) (V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Nat_Onat))) (let ((_let_1 (hAPP V_P_2 V_n_2))) (let ((_let_2 (hBOOL (hAPP _let_1 V_m_2)))) (let ((_let_3 (not _let_2))) (or (and (hBOOL (hAPP (hAPP _let_0 V_m_2) V_n_2)) _let_3) (and (= V_n_2 V_m_2) _let_3) (and (hBOOL (hAPP (hAPP _let_0 V_n_2) V_m_2)) _let_3) _let_2))))) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OPls ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.44/6.65 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.44/6.65 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.65 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.65 ( (c_Set_Oinsert tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.65 ( (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Product__Type_OPair _let_1 _let_1))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.65 ( (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral) ) 6.44/6.65 ( (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), c_Int_Ointrel ) 6.44/6.65 ( (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint), c_fconj, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.44/6.65 ( (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)), c_Code__Numeral_Onat__of, (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), c_FunDef_Opair__less, (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.44/6.65 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)), (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))) ) 6.44/6.65 ( (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.65 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))), (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)) ) 6.44/6.65 ( (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) tc_Int_Oint), (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal), c_Nitpick_Oint__gcd ) 6.44/6.65 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 6.44/6.65 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 6.44/6.65 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 6.44/6.65 ( (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat), (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal), c_Nat_OSuc ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)), v_G, v_Ga ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omin__strict, c_FunDef_Omin__weak ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omax__strict, c_FunDef_Omax__weak ) 6.44/6.65 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), c_Int_Onat, c_Int_OPls ) 6.44/6.65 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), c_Int_Onat, (c_Int_OBit1 c_Int_OPls) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ocard T_b))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP _let_0 V_A_2)) (hAPP _let_0 V_B_2))))) ) 6.44/6.65 ( v_G, v_Ga, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)) V_a))) (= V_a (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a))) ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OPls, tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_m $$unsorted)) (let ((_let_0 (c_Divides_Odiv__class_Odiv tc_Nat_Onat))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_2 (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) (let ((_let_3 (hAPP _let_1 _let_2))) (= (hAPP c_Nat_OSuc (hAPP (hAPP _let_0 V_m) _let_3)) (hAPP (hAPP _let_0 (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_m))) _let_3)))))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP _let_2 V_a_2)) (hBOOL (hAPP _let_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2)))))))) ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) _let_0))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Finite__Set_Ocard T_b) _let_0))))) ) 6.44/6.65 ( tc_HOL_Obool ) 6.44/6.65 ( tc_Nat_Onat ) 6.44/6.65 ( tc_Int_Oint ) 6.44/6.65 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.65 ( tc_Product__Type_Ounit ) 6.44/6.65 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)) (= V_y_2 V_x_2))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_G_2 $$unsorted) (V_tsa_2 $$unsorted) (V_G_Ha_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Hoare__Mirabelle_Ohoare__derivs T_b V_G_Ha_2 V_tsa_2)) (not (c_Hoare__Mirabelle_Ohoare__derivs T_b V_G_2 V_G_Ha_2)) (c_Hoare__Mirabelle_Ohoare__derivs T_b V_G_2 V_tsa_2)) ) 6.44/6.65 ( v_Ga, v_ts, v_G_H, t_a ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_w $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (let ((_let_1 (hAPP _let_0 V_w))) (or (not (class_Groups_Omonoid__mult T_b)) (not (class_Int_Onumber T_b)) (= (hAPP (hAPP (c_Power_Opower__class_Opower T_b) _let_1) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_b) _let_1) _let_1))))) ) 6.44/6.65 ( c_Int_OPls, tc_Nat_Onat ) 6.44/6.65 ( c_Int_OPls, tc_Int_Oint ) 6.44/6.65 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.44/6.65 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.44/6.65 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.44/6.65 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.44/6.65 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.44/6.65 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.44/6.65 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.44/6.65 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) (hAPP (c_Set_Oimage T_b T_b V_f_2) V_A_2)))) (c_Fun_Oinj__on T_b T_b V_f_2 V_A_2)) ) 6.44/6.65 ( c_Nat_OSuc, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Obot T_1)) (class_Orderings_Obot (tc_fun T_2 T_1))) ) 6.44/6.65 ( tc_HOL_Obool, tc_HOL_Obool ) 6.44/6.65 ( tc_Nat_Onat, tc_HOL_Obool ) 6.44/6.65 ( tc_Int_Oint, tc_HOL_Obool ) 6.44/6.65 ( tc_Int_Oint, tc_Int_Oint ) 6.44/6.65 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.44/6.65 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.44/6.65 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.44/6.65 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (c_List_Olinorder__class_Osorted__list__of__set T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (c_List_Olist_ONil T_b))) ) 6.44/6.65 ( tc_HOL_Obool ) 6.44/6.65 ( tc_Nat_Onat ) 6.44/6.65 ( tc_Int_Oint ) 6.44/6.65 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.65 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.65 ( tc_Product__Type_Ounit ) 6.44/6.65 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_List_Olinorder__class_Osorted__list__of__set T_b V_A_2))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (= V_A_2 (hAPP (c_List_Oset T_b) _let_0)) (hBOOL (hAPP (c_List_Odistinct T_b) _let_0)) (c_List_Olinorder__class_Osorted T_b _let_0)))) ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Product__Type_Ocurry T_b T_c tc_HOL_Obool V_f_2) V_a_2) V_b_2))) (hBOOL (hAPP V_f_2 (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_a_2) V_b_2)))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.65 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_0 (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_2 (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel))) (let ((_let_3 (c_Set_Oinsert _let_1))) (let ((_let_4 (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))) (= (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP c_Int_OAbs__Integ (hAPP _let_2 (hAPP (hAPP _let_3 (hAPP (hAPP _let_0 V_x_2) V_y_2)) _let_4)))) (hAPP c_Int_OAbs__Integ (hAPP _let_2 (hAPP (hAPP _let_3 (hAPP (hAPP _let_0 V_y_2) V_x_2)) _let_4))))))))) ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) V_A_2))) ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= V_a (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) V_b))) ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ominus__class_Ominus T_b))) (or (not (class_Groups_Oab__group__add T_b)) (not (= (hAPP (hAPP _let_0 V_a_2) V_b_2) (hAPP (hAPP _let_0 V_c_2) V_d_2))) (= (= V_d_2 V_c_2) (= V_b_2 V_a_2)))) ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_b_2)) (hAPP _let_1 V_a_2))))))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_z $$unsorted)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) V_z) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_z) V_z)) ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (c_Complete__Lattice_OInf__class_OInf _let_0 (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot _let_0))) ) 6.44/6.65 ( tc_Nat_Onat ) 6.44/6.65 ( tc_Int_Oint ) 6.44/6.65 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_b)) (= (= V_x_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((BOUND_VARIABLE_118715 $$unsorted) (BOUND_VARIABLE_118716 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_1 (hAPP _let_0 BOUND_VARIABLE_118715))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) BOUND_VARIABLE_118716) c_Int_OPls))) (= _let_1 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP _let_0 BOUND_VARIABLE_118716)) _let_1))))) ) 6.44/6.65 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((BOUND_VARIABLE_118729 $$unsorted) (BOUND_VARIABLE_118730 $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_2 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_3 (hAPP _let_1 BOUND_VARIABLE_118729))) (let ((_let_4 (hBOOL (hAPP _let_3 c_Int_OPls)))) (let ((_let_5 (hAPP _let_2 BOUND_VARIABLE_118730))) (let ((_let_6 (hAPP _let_0 _let_5))) (let ((_let_7 (hAPP _let_2 BOUND_VARIABLE_118729))) (let ((_let_8 (hAPP _let_6 _let_7))) (or (hBOOL (hAPP (hAPP _let_1 BOUND_VARIABLE_118730) c_Int_OPls)) (and (or _let_4 (= _let_8 (hAPP _let_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) BOUND_VARIABLE_118730) BOUND_VARIABLE_118729)))) (or (not _let_4) (= _let_5 _let_8))))))))))))) ) 6.44/6.65 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ogroup__add T_b)) (= (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_b_2) (c_Groups_Ozero__class_Ozero T_b)) (= V_b_2 V_a_2))) ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_n_2 $$unsorted)) (= (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Nat_OSuc V_n_2)) (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_n_2)) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.65 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Complete__Lattice_OInf__class_OInf T_b V_A_2) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b)) (c_Orderings_Otop__class_Otop T_b)) V_A_2))) ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (let ((_let_1 (hAPP _let_0 V_x_2))) (let ((_let_2 (hAPP _let_1 V_A_2))) (let ((_let_3 (c_Big__Operators_Olattice__class_OInf__fin T_b _let_2))) (let ((_let_4 (tc_fun T_b tc_HOL_Obool))) (let ((_let_5 (c_Groups_Ominus__class_Ominus _let_4))) (let ((_let_6 (hAPP _let_5 V_A_2))) (let ((_let_7 (c_Orderings_Obot__class_Obot _let_4))) (let ((_let_8 (hAPP _let_1 _let_7))) (let ((_let_9 (hAPP _let_6 _let_8))) (let ((_let_10 (= _let_7 _let_9))) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or (not _let_10) (= V_x_2 _let_3)) (or _let_10 (= _let_3 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_x_2) (c_Big__Operators_Olattice__class_OInf__fin T_b _let_9))))))))))))))))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.65 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Finite__Set_Ofun__left__comm__idem T_b T_c V_f_2)) (c_Finite__Set_Ofun__left__comm__idem T_d T_c (hAPP (hAPP (c_COMBB T_b (tc_fun T_c T_c) T_d) V_f_2) V_g_2))) ) 6.44/6.65 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint, c_fconj, tc_HOL_Obool, tc_HOL_Obool ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (hBOOL (hAPP (hAPP (c_member T_b) V_i_2) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_k_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_i_2) V_k_2)))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Finite__Set_Ofinite T_b)) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBC T_b T_b tc_HOL_Obool) c_fequal) V_a_2))) V_B_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_B_2)) ) 6.44/6.65 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Ogroup__add T_b)) (= (= V_a_2 (hAPP _let_0 V_b_2)) (= V_b_2 (hAPP _let_0 V_a_2))))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_d_2 $$unsorted)) (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint tc_HOL_Obool))) (= (c_Int_Oint__ge__less__than V_d_2) (hAPP (c_Set_OCollect (tc_prod tc_Int_Oint tc_Int_Oint)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Int_Oint tc_Int_Oint tc_HOL_Obool) (hAPP (hAPP (c_COMBS tc_Int_Oint _let_1 _let_1) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_1 _let_1) tc_Int_Oint) (c_COMBB tc_HOL_Obool tc_HOL_Obool tc_Int_Oint)) (hAPP (hAPP (c_COMBB tc_HOL_Obool _let_0 tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_d_2)))) (c_Orderings_Oord__class_Oless tc_Int_Oint))))))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( c_Int_OMin ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 _let_0)) (= (hAPP (c_Fun_Ocomp T_c T_b T_b (c_Hilbert__Choice_Oinv__into T_b T_c _let_0 V_f_2)) V_f_2) (c_Fun_Oid T_b)))) ) 6.44/6.65 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_P_2 $$unsorted) (V_y_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) V_y_2) c_Int_OInteg))) (not (forall ((B_x $$unsorted)) (hBOOL (hAPP V_P_2 (hAPP c_Int_ORep__Integ B_x))) )) (hBOOL (hAPP V_P_2 V_y_2))) ) 6.44/6.65 ( c_Nat_OSuc, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( c_Nat_OSuc, (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.65 ( c_Nat_OSuc, (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin ) 6.44/6.65 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.65 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.65 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.65 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.65 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls), c_Int_OMin ) 6.44/6.65 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.65 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), c_Int_OMin ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin ) 6.44/6.65 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.65 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.65 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool), c_fequal ) 6.44/6.65 ( c_Code__Numeral_Oof__nat, (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.65 ( c_Code__Numeral_Oof__nat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.65 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.65 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.65 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_OPls ) 6.44/6.65 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 c_Int_OPls) ) 6.44/6.65 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_OMin ) 6.44/6.65 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.65 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.65 ( (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.65 ( c_Nat__Numeral_Oneg, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( c_Nat__Numeral_Oneg, (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.65 ( c_Nat__Numeral_Oneg, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin) ) 6.44/6.65 ( (c_Finite__Set_Ofinite tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.65 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( c_Int_OAbs__Integ, (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))) ) 6.44/6.65 ( c_Int_OAbs__Integ, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) ) 6.44/6.65 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) ) 6.44/6.65 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.65 ( (c_Finite__Set_Ofinite tc_Int_Oint), (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.44/6.65 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), c_Int_OPls ) 6.44/6.65 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit1 c_Int_OPls) ) 6.44/6.65 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.65 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.65 ( (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( c_Int_Onat, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.65 ( c_Int_Onat, (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.65 ( c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.65 ( c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.65 ( (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.65 ( (c_Set_Oinsert tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.65 ( (c_Nat_Osize__class_Osize tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.65 ( (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 6.44/6.65 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls), c_Int_OPls ) 6.44/6.65 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls), c_Int_OMin ) 6.44/6.65 ( (c_Set_Oimage tc_Nat_Onat tc_Nat_Onat c_Nat_OSuc), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 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(hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 c_FunDef_Opair__leq)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))) ) 6.44/6.65 ( (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat), (c_Groups_Oabs__class_Oabs tc_Int_Oint) ) 6.44/6.65 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.65 ( (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))), 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c_fequal) ) 6.44/6.65 ( (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)), c_Nat_OSuc ) 6.44/6.65 ( (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)), v_G ) 6.44/6.65 ( (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) v_G), v_Ga ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omin__strict ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omax__strict ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omax__strict))))), c_FunDef_Omax__weak ) 6.44/6.65 ( (c_Finite__Set_Ocard tc_HOL_Obool), (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)) ) 6.44/6.65 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.65 ( (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.65 ( (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.65 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), c_Int_Onat ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omin__strict))))), c_FunDef_Omin__weak ) 6.44/6.65 ( (c_COMBK tc_HOL_Obool tc_Nat_Onat), c_fTrue ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (or (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2)) _let_1)))))) ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (hAPP _let_1 V_a_2))) (= (hAPP _let_2 V_A_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP _let_2 (c_Orderings_Obot__class_Obot _let_0))) V_A_2))))) ) 6.44/6.65 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= V_f_2 (hAPP (c_Fun_Ocomp T_b T_c T_b V_f_2) (c_Fun_Oid T_b))) ) 6.44/6.65 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (c_Relation_Oconverse T_c T_b))) (= (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_c T_b) tc_HOL_Obool)) V_r_2) V_s_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_c) tc_HOL_Obool)) (hAPP _let_0 V_r_2)) (hAPP _let_0 V_s_2)))) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.65 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.65 ) 6.44/6.65 (instantiation (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_b_2) V_a_2))) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_a_2) V_b_2))) ) 6.44/6.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.65 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.65 ) 6.44/6.66 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Fields_Olinordered__field T_a)) (not (forall ((B_e $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)) B_e))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_y) B_e)))) )) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) ) 6.44/6.66 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.66 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Groups_Ocomm__monoid__add T_c)) (not (c_Fun_Oinj__on T_b T_c V_f_2 V_B_2)) (= (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__add__class_Osetsum T_b T_c) V_f_2) V_B_2) (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__add__class_Osetsum T_c T_c) (c_Fun_Oid T_c)) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_B_2)))) ) 6.44/6.66 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.66 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 6.44/6.66 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 6.44/6.66 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_SetInterval_Oord__class_OgreaterThan T_b))) (or (not (class_Orderings_Olinorder T_b)) (= (= V_y_2 V_x_2) (= (hAPP _let_0 V_x_2) (hAPP _let_0 V_y_2))))) ) 6.44/6.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_A_2 $$unsorted)) (or (not (c_Nat__Transfer_Onat__set V_A_2)) (= V_A_2 (hAPP (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) (hAPP (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) V_A_2)))) ) 6.44/6.66 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__sup T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) (= V_y (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y))) ) 6.44/6.66 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.66 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.66 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.66 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.66 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (forall ((B_x $$unsorted)) (= B_x (hAPP V_f_2 (hAPP (c_Hilbert__Choice_Oinv__into T_c T_b (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)) V_f_2) B_x))) ) (= (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_Oimage T_c T_b V_f_2) (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool))))) ) 6.44/6.66 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.66 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.66 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (or (not (class_Lattices_Oab__semigroup__idem__mult T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (c_Finite__Set_Ofold1 T_b _let_0) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_a_2) V_A_2)))) ) 6.44/6.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.66 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.66 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.66 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (c_Groups_Ozero__class_Ozero T_a) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)))) ) 6.44/6.66 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.66 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Finite__Set_Ofinite T_b)) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))))) ) 6.44/6.66 ( tc_HOL_Obool ) 6.44/6.66 ( tc_Nat_Onat ) 6.44/6.66 ( tc_Int_Oint ) 6.44/6.66 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.66 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.66 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.66 ( tc_Product__Type_Ounit ) 6.44/6.66 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Groups_Omonoid__add T_a)) (= (c_Groups_Ozero__class_Ozero T_a) (hAPP (c_List_Omonoid__add__class_Olistsum T_a) (c_List_Olist_ONil T_a)))) ) 6.44/6.66 ( tc_Nat_Onat ) 6.44/6.66 ( tc_Int_Oint ) 6.44/6.66 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (= V_A_2 _let_2) (not (hBOOL (hAPP _let_0 V_B_2))) (= V_B_2 _let_2) (= (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMin T_b V_B_2)) (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2))))))) ) 6.44/6.66 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.66 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.66 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Lattices_Osemilattice__inf__class_Oinf _let_0))) (let ((_let_2 (hAPP _let_1 V_A_2))) (let ((_let_3 (hAPP _let_2 V_B_2))) (let ((_let_4 (c_Lattices_Osemilattice__sup__class_Osup T_b))) (let ((_let_5 (c_Finite__Set_Ofinite T_b))) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP _let_5 V_A_2))) (not (hBOOL (hAPP _let_5 V_B_2))) (= (c_Orderings_Obot__class_Obot _let_0) _let_3) (= (hAPP (hAPP _let_4 (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OSup__fin T_b V_B_2)) (hAPP (hAPP _let_4 (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2))) (c_Big__Operators_Olattice__class_OSup__fin T_b _let_3)))))))))) ) 6.44/6.66 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.66 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.66 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_v $$unsorted) (V_u $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (let ((_let_1 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_2 (hAPP _let_0 V_u))) (let ((_let_3 (hAPP _let_1 _let_2))) (let ((_let_4 (hAPP _let_0 V_v))) (let ((_let_5 (hAPP _let_3 _let_4))) (let ((_let_6 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_7 (hAPP _let_6 _let_2))) (let ((_let_8 (hBOOL (hAPP _let_7 _let_4)))) (or (not (class_Orderings_Oord T_b)) (not (class_Int_Onumber T_b)) (and (or (not _let_8) (= _let_2 _let_5)) (or _let_8 (= _let_4 _let_5))))))))))))) ) 6.44/6.66 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 6.44/6.66 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Int_Oint ) 6.44/6.66 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 6.44/6.66 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP _let_2 V_a))) (not (hBOOL (hAPP _let_2 V_b))) (hBOOL (hAPP _let_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b))))))) ) 6.44/6.66 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_n_2 $$unsorted)) (= (hAPP (c_List_Oset tc_Nat_Onat) (c_List_Oupt (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP c_Nat_OSuc V_n_2))) (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_n_2)) ) 6.44/6.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.66 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.66 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (c_Groups_Oone__class_Oone T_a))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) _let_0) _let_0) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))))) ) 6.44/6.66 ( tc_Nat_Onat ) 6.44/6.66 ( tc_Int_Oint ) 6.44/6.66 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_2 (hAPP _let_1 _let_0))) (or (not (hBOOL (hAPP _let_2 V_k_2))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_k_2) V_i_2)) (hBOOL (hAPP _let_2 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_i_2) V_k_2)))))))) ) 6.44/6.66 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.66 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.66 ( c_Int_OPls, c_Int_OMin ) 6.44/6.66 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.66 ( c_Int_OMin, c_Int_OMin ) 6.44/6.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_k_2 $$unsorted)) (let ((_let_0 (c_SetInterval_Oord__class_OatMost tc_Nat_Onat))) (let ((_let_1 (hAPP c_Nat_OSuc V_k_2))) (= (hAPP _let_0 _let_1) (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) _let_1) (hAPP _let_0 V_k_2))))) ) 6.44/6.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.66 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.66 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (c_Nitpick_Onat__gcd V_x_2 V_y_2))) (let ((_let_2 (= _let_0 V_y_2))) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Nat_Onat tc_Nat_Onat) c_Nitpick_Onat__gcd__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_x_2) V_y_2)))) (and (or (not _let_2) (= V_x_2 _let_1)) (or _let_2 (= _let_1 (c_Nitpick_Onat__gcd V_y_2 (c_Divides_Odiv__class_Omod tc_Nat_Onat V_x_2 V_y_2))))))))) ) 6.44/6.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2)) _let_1)) (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)))))) ) 6.44/6.66 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (c_Finite__Set_Ocard T_b) V_A_2) (hAPP (hAPP (hAPP (c_Finite__Set_Ofold__image tc_Nat_Onat T_b (c_Groups_Oplus__class_Oplus tc_Nat_Onat)) (hAPP (c_COMBK tc_Nat_Onat T_b) (c_Groups_Oone__class_Oone tc_Nat_Onat))) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_A_2))) ) 6.44/6.66 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.66 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.66 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 6.44/6.66 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_d tc_HOL_Obool)))) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (not (c_Fun_Oinj__on T_d T_b V_g_2 _let_0)) (c_Fun_Oinj__on T_d T_c (hAPP (c_Fun_Ocomp T_b T_c T_d V_f_2) V_g_2) _let_0))) ) 6.44/6.66 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), tc_Int_Oint, c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.44/6.66 ( c_Int_Onat, tc_Int_Oint, c_Code__Numeral_Oof__nat, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 6.44/6.66 ( c_Code__Numeral_Onat__of, tc_Code__Numeral_Ocode__numeral, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (= _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) _let_0)))) ) 6.44/6.66 ( tc_Nat_Onat ) 6.44/6.66 ( tc_Int_Oint ) 6.44/6.66 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Fields_Olinordered__field__inverse__zero T_a)) (not (forall ((B_z $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (or (not (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero T_a)) B_z))) (not (hBOOL (hAPP (hAPP _let_0 B_z) (c_Groups_Oone__class_Oone T_a)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) B_z) V_x)) V_y)))) )) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) ) 6.44/6.66 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.66 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.66 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_k_2 $$unsorted)) (= (= c_Int_OMin (c_Int_OBit1 V_k_2)) (= c_Int_OMin V_k_2)) ) 6.44/6.66 ( c_Int_OPls ) 6.44/6.66 ( (c_Int_OBit1 c_Int_OPls) ) 6.44/6.66 ( c_Int_OMin ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (c_Orderings_Oord__class_Omax T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (= V_A_2 _let_2) (not (hBOOL (hAPP _let_0 V_B_2))) (= V_B_2 _let_2) (= (hAPP (hAPP _let_3 (c_Big__Operators_Olattice_OSup__fin T_b _let_3 V_A_2)) (c_Big__Operators_Olattice_OSup__fin T_b _let_3 V_B_2)) (c_Big__Operators_Olattice_OSup__fin T_b _let_3 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2)))))))) ) 6.44/6.66 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.66 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.66 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) B_x) B_y)) (hAPP (hAPP _let_0 B_x) (hAPP (hAPP _let_0 B_y) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))))) )) (hBOOL (hAPP (hAPP (c_member T_b) (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) V_A_2))) ) 6.44/6.66 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.66 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus T_b))) (let ((_let_1 (hAPP _let_0 V_a_2))) (or (not (class_Groups_Ocancel__semigroup__add T_b)) (= (= V_c_2 V_b_2) (= (hAPP _let_1 V_b_2) (hAPP _let_1 V_c_2)))))) ) 6.44/6.66 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_v $$unsorted)) (= (hAPP c_Int_Onat (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v)) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v)) ) 6.44/6.66 ( c_Int_OPls ) 6.44/6.66 ( (c_Int_OBit1 c_Int_OPls) ) 6.44/6.66 ( c_Int_OMin ) 6.44/6.66 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.66 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.66 ) 6.44/6.66 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__sup__class_Osup T_b)) V_a_2) V_A_2))) ) 6.44/6.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.68 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.68 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_v $$unsorted)) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v)))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v))) ) 6.44/6.68 ( c_Int_OPls ) 6.44/6.68 ( (c_Int_OBit1 c_Int_OPls) ) 6.44/6.68 ( c_Int_OMin ) 6.44/6.68 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.68 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_P_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_List_Oupto__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) V_a0_2) V_a1_2)))) (not (forall ((B_i $$unsorted) (B_j $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_List_Oupto__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) B_i) B_j)))) (and (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) B_i) B_j)) (not (hBOOL (hAPP (hAPP V_P_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) B_i) (c_Groups_Oone__class_Oone tc_Int_Oint))) B_j)))) (hBOOL (hAPP (hAPP V_P_2 B_i) B_j))) )) (hBOOL (hAPP (hAPP V_P_2 V_a0_2) V_a1_2))) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OPls, c_Int_OMin ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.44/6.68 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.68 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.68 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) ) 6.44/6.68 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.68 ( (c_Set_Oinsert tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.68 ( (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))) ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Product__Type_OPair _let_1 _let_1))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.68 ( (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 6.44/6.68 ( (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.68 ( (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_fconj ) 6.44/6.68 ( (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Onat__of ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less ) 6.44/6.68 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 6.44/6.68 ( (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Groups_Oone__class_Oone tc_Int_Oint), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))) ) 6.44/6.68 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool) ) 6.44/6.68 ( (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) tc_Int_Oint), c_Nitpick_Oint__gcd, (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal) ) 6.44/6.68 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.68 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.68 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.68 ( (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat), c_Nat_OSuc, (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)), v_Ga, v_G ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omax__weak, c_FunDef_Omax__strict ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omin__weak, c_FunDef_Omin__strict ) 6.44/6.68 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), c_Int_OPls, c_Int_Onat ) 6.44/6.68 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), (c_Int_OBit1 c_Int_OPls), c_Int_Onat ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (let ((_let_1 (= V_x _let_0))) (let ((_let_2 (c_Groups_Osgn__class_Osgn T_a V_x))) (let ((_let_3 (c_Groups_Oone__class_Oone T_a))) (let ((_let_4 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_5 (hAPP _let_4 _let_0))) (let ((_let_6 (hBOOL (hAPP _let_5 V_x)))) (or (not (class_Groups_Osgn__if T_a)) (and (or (not _let_1) (= _let_0 _let_2)) (or _let_1 (and (or _let_6 (= _let_2 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) _let_3))) (or (not _let_6) (= _let_2 _let_3))))))))))))) ) 6.44/6.68 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ( c_Int_OPls, tc_Int_Oint ) 6.44/6.68 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_n $$unsorted)) (= V_n (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP c_Nat_OSuc V_n)) (c_Groups_Oone__class_Oone tc_Nat_Onat))) ) 6.44/6.68 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.68 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.68 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) ) 6.44/6.68 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.68 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.68 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_N_2 $$unsorted) (V_h_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__sup__class_Osup T_b))) (= (hAPP V_h_2 (hAPP (hAPP _let_0 B_x) B_y)) (hAPP (hAPP _let_0 (hAPP V_h_2 B_x)) (hAPP V_h_2 B_y)))) )) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (= V_N_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP V_h_2 (c_Big__Operators_Olattice__class_OSup__fin T_b V_N_2)) (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (c_Set_Oimage T_b T_b V_h_2) V_N_2)))) ) 6.44/6.68 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_b))) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_b) (c_Groups_Oone__class_Oone tc_Int_Oint)) (c_Divides_Odiv__class_Omod tc_Int_Oint (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin) V_b))) ) 6.44/6.68 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.68 ( c_Int_OPls ) 6.44/6.68 ( c_Int_OMin ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_l_2 V_u_2)) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_u_2)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_l_2))) ) 6.44/6.68 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.68 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.68 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_u_2 $$unsorted)) (= (hAPP (c_Finite__Set_Ocard tc_Nat_Onat) (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_u_2)) (hAPP c_Nat_OSuc V_u_2)) ) 6.44/6.68 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.68 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.68 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_k_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (c_Groups_Ouminus__class_Ouminus (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_k_2)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_k_2))) ) 6.44/6.68 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_m $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_1 (c_Groups_Oone__class_Oone T_a))) (or (not (class_Rings_Ocomm__semiring__1 T_a)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (hAPP (hAPP _let_0 _let_1) _let_1)) V_m) (hAPP (hAPP _let_0 V_m) V_m))))) ) 6.44/6.68 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (c_Groups_Ozero__class_Ozero T_a) (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OPls))) ) 6.44/6.68 ( tc_Nat_Onat ) 6.44/6.68 ( tc_Int_Oint ) 6.44/6.68 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Inductive_Ocomplete__lattice__class_Ogfp T_b V_f_2))) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (c_Orderings_Oorder__class_Omono T_b T_b V_f_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) _let_0) (hAPP V_f_2 _let_0))))) ) 6.44/6.68 ( c_Nat_OSuc, tc_Nat_Onat ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) (c_Transitive__Closure_Otrancl T_b V_r_2)) (c_Relation_OId T_b)) (c_Transitive__Closure_Ortrancl T_b V_r_2)) ) 6.44/6.68 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (= V_A_2 (hAPP (c_Set_Ovimage T_b T_c V_f_2) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) ) 6.44/6.68 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.68 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.44/6.68 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_c))) (= (c_Fun_Oid _let_0) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c _let_0) (c_Product__Type_OPair T_b T_c)))) ) 6.44/6.68 ( tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.68 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.68 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP _let_1 V_A_2)) (hAPP _let_1 V_B_2)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_A_2) V_B_2))))) ) 6.44/6.68 ( v_G, v_Ga, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (let ((_let_2 (c_Set_Oimage T_b T_c V_f_2))) (or (not (c_Fun_Obij__betw T_b T_c V_f_2 (c_Orderings_Otop__class_Otop _let_0) (c_Orderings_Otop__class_Otop _let_1))) (= (hAPP _let_2 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_d _let_0) V_A_2) V_B_2)) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_d _let_1) V_A_2) (hAPP (hAPP (c_COMBB _let_0 _let_1 T_d) _let_2) V_B_2))))))) ) 6.44/6.68 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (hAPP _let_1 V_x_2))) (let ((_let_3 (hAPP _let_2 V_A_2))) (let ((_let_4 (tc_fun T_b tc_HOL_Obool))) (let ((_let_5 (c_Groups_Ominus__class_Ominus _let_4))) (let ((_let_6 (hAPP _let_5 V_A_2))) (let ((_let_7 (c_Orderings_Obot__class_Obot _let_4))) (let ((_let_8 (hAPP _let_2 _let_7))) (let ((_let_9 (hAPP _let_6 _let_8))) (let ((_let_10 (c_Big__Operators_Olattice_OSup__fin T_b _let_0 _let_3))) (let ((_let_11 (= _let_7 _let_9))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or _let_11 (= (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 _let_9)) _let_10)) (or (not _let_11) (= V_x_2 _let_10)))))))))))))))) ) 6.44/6.68 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.68 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.68 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) c_Int_OMin) V_k) (c_Int_Opred V_k)) ) 6.44/6.68 ( c_Int_OPls ) 6.44/6.68 ( c_Int_OMin ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_k $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) V_k) (c_Groups_Osgn__class_Osgn T_a V_k)) (hAPP (c_Groups_Oabs__class_Oabs T_a) V_k))) ) 6.44/6.68 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_tsa_2 $$unsorted) (V_ts_H_2 $$unsorted) (V_G_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Hoare__Mirabelle_Ohoare__derivs T_b V_G_2 V_ts_H_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple T_b) tc_HOL_Obool)) V_tsa_2) V_ts_H_2))) (c_Hoare__Mirabelle_Ohoare__derivs T_b V_G_2 V_tsa_2)) ) 6.44/6.68 ( v_G, v_G_H, v_Ga, t_a ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) (= V_y (hAPP (hAPP (c_Orderings_Oord__class_Omax T_a) V_x) V_y))) ) 6.44/6.68 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.68 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.68 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.68 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) _let_0))) (not (c_Fun_Oinj__on T_b T_b V_f_2 _let_0)) (= _let_0 (hAPP (c_Set_Oimage T_b T_b V_f_2) _let_0)))) ) 6.44/6.68 ( c_Nat_OSuc, tc_Nat_Onat ) 6.44/6.68 ) 6.44/6.68 (instantiation (forall ((V_P_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Lazy__Sequence_Osmall__lazy_H__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) V_a0_2) V_a1_2)))) (not (forall ((B_d $$unsorted) (B_i $$unsorted)) (let ((_let_0 (hAPP V_P_2 B_d))) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Lazy__Sequence_Osmall__lazy_H__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) B_d) B_i)))) (and (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) B_d) B_i))) (not (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) B_i) (c_Groups_Oone__class_Oone tc_Int_Oint)))))) (hBOOL (hAPP _let_0 B_i)))) )) (hBOOL (hAPP (hAPP V_P_2 V_a0_2) V_a1_2))) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OPls, c_Int_OMin ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.68 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.44/6.68 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.68 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.68 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) ) 6.44/6.68 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.68 ( (c_Set_Oinsert tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.68 ( (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))) ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Product__Type_OPair _let_1 _let_1))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.68 ( (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 6.44/6.68 ( (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.68 ( (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_fconj ) 6.44/6.68 ( (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Onat__of ) 6.44/6.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less ) 6.44/6.68 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 6.44/6.68 ( (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Groups_Oone__class_Oone tc_Int_Oint), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))) ) 6.44/6.69 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool) ) 6.44/6.69 ( (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) tc_Int_Oint), c_Nitpick_Oint__gcd, (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal) ) 6.44/6.69 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.69 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.69 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.69 ( (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat), c_Nat_OSuc, (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal) ) 6.44/6.69 ( (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)), v_Ga, v_G ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omax__weak, c_FunDef_Omax__strict ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omin__weak, c_FunDef_Omin__strict ) 6.44/6.69 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), c_Int_OPls, c_Int_Onat ) 6.44/6.69 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), (c_Int_OBit1 c_Int_OPls), c_Int_Onat ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (or (not (class_Rings_Oring__1 T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) V_m))) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n)) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (hAPP _let_0 V_m)) (hAPP _let_0 V_n))))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((BOUND_VARIABLE_121939 $$unsorted) (BOUND_VARIABLE_121940 $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) BOUND_VARIABLE_121940) BOUND_VARIABLE_121939)) (= (c_Groups_Ozero__class_Ozero tc_Int_Oint) (c_Nat__Transfer_Otsub BOUND_VARIABLE_121939 BOUND_VARIABLE_121940))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( c_Int_OPls, c_Int_OMin ) 6.44/6.69 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( c_Int_OMin, c_Int_OMin ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_r_2)) (c_Wellfounded_Owf (tc_fun T_b tc_HOL_Obool) (c_Wellfounded_Omin__ext T_b V_r_2))) ) 6.44/6.69 ( c_FunDef_Opair__leq, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.69 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_P_2 $$unsorted) (V_y_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) V_y_2) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (not (forall ((B_x $$unsorted)) (hBOOL (hAPP V_P_2 (hAPP c_Code__Numeral_Onat__of B_x))) )) (hBOOL (hAPP V_P_2 V_y_2))) ) 6.44/6.69 ( c_Nat_OSuc, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( c_Nat_OSuc, (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.69 ( c_Nat_OSuc, (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.69 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin ) 6.44/6.69 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.69 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.69 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.69 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.69 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls), c_Int_OMin ) 6.44/6.69 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.69 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), c_Int_OMin ) 6.44/6.69 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin ) 6.44/6.69 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.69 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.69 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool), c_fequal ) 6.44/6.69 ( c_Code__Numeral_Oof__nat, (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.69 ( c_Code__Numeral_Oof__nat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.69 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.69 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.69 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_OPls ) 6.44/6.69 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 c_Int_OPls) ) 6.44/6.69 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_OMin ) 6.44/6.69 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.69 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.69 ( (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.69 ( c_Nat__Numeral_Oneg, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( c_Nat__Numeral_Oneg, (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.69 ( c_Nat__Numeral_Oneg, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin) ) 6.44/6.69 ( (c_Finite__Set_Ofinite tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.69 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( c_Int_OAbs__Integ, (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))) ) 6.44/6.69 ( c_Int_OAbs__Integ, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) ) 6.44/6.69 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) ) 6.44/6.69 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.69 ( (c_Finite__Set_Ofinite tc_Int_Oint), (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.44/6.69 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), c_Int_OPls ) 6.44/6.69 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit1 c_Int_OPls) ) 6.44/6.69 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.69 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.44/6.69 ( (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( c_Int_Onat, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( c_Int_Onat, (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.69 ( c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.69 ( c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.69 ( (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.69 ( (c_Set_Oinsert tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.69 ( (c_Nat_Osize__class_Osize tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.69 ( (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 6.44/6.69 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls), c_Int_OPls ) 6.44/6.69 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls), c_Int_OMin ) 6.44/6.69 ( (c_Set_Oimage tc_Nat_Onat tc_Nat_Onat c_Nat_OSuc), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 c_FunDef_Opair__leq)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 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(c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)), v_G ) 6.44/6.69 ( (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) v_G), v_Ga ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omin__strict ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omax__strict ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omax__strict))))), c_FunDef_Omax__weak ) 6.44/6.69 ( (c_Finite__Set_Ocard tc_HOL_Obool), (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)) ) 6.44/6.69 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.69 ( (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.44/6.69 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), c_Int_Onat ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omin__strict))))), c_FunDef_Omin__weak ) 6.44/6.69 ( (c_COMBK tc_HOL_Obool tc_Nat_Onat), c_fTrue ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (class_Groups_Oordered__comm__monoid__add T_b)) (not (hBOOL (hAPP _let_2 V_x_2))) (not (hBOOL (hAPP _let_2 V_y_2))) (= (and (= V_y_2 _let_1) (= V_x_2 _let_1)) (= _let_1 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_x_2) V_y_2))))))) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_c)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_c (hAPP (hAPP (c_COMBB T_c (tc_fun T_c T_c) T_b) (c_Lattices_Osemilattice__sup__class_Osup T_c)) V_f_2)) (c_Orderings_Obot__class_Obot T_c)) V_A_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b T_c) V_A_2) V_f_2))) ) 6.44/6.69 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 6.44/6.69 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 6.44/6.69 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (forall ((B_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP V_f_2 B_n)) (hAPP V_f_2 (hAPP c_Nat_OSuc B_n)))) ) (c_Orderings_Oorder__class_Omono tc_Nat_Onat T_b V_f_2))) ) 6.44/6.69 ( c_Nat_OSuc, tc_Nat_Onat ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((BOUND_VARIABLE_122166 $$unsorted) (BOUND_VARIABLE_122167 $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) BOUND_VARIABLE_122167)))) (= (hAPP (hAPP _let_0 (c_Groups_Oone__class_Oone tc_Nat_Onat)) BOUND_VARIABLE_122166) (hAPP c_Nat_OSuc (hAPP (hAPP _let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) BOUND_VARIABLE_122167)) BOUND_VARIABLE_122166))))) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Int_OBit1 c_Int_OPls) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((BOUND_VARIABLE_122181 $$unsorted) (BOUND_VARIABLE_122182 $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (or (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) BOUND_VARIABLE_122182))) (= (hAPP c_Nat_OSuc (hAPP (hAPP _let_0 (hAPP _let_1 BOUND_VARIABLE_122182)) BOUND_VARIABLE_122181)) (hAPP (hAPP _let_0 (hAPP _let_1 (c_Int_Osucc BOUND_VARIABLE_122182))) BOUND_VARIABLE_122181))))) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), c_Int_OPls ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Int_OBit1 c_Int_OPls) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Transitive__Closure_Otrancl T_b V_r_2) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) V_r_2) (c_Transitive__Closure_Ortrancl T_b V_r_2))) ) 6.44/6.69 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (= (= V_y_2 V_x_2) (= (hAPP V_f_2 V_y_2) (hAPP V_f_2 V_x_2)))) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) (= V_B_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_B_2) V_A_2))))) ) 6.44/6.69 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_i $$unsorted) (V_j $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_j) V_i))) (= (c_List_Olist_ONil tc_Int_Oint) (c_List_Oupto V_i V_j))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( c_Int_OMin, c_Int_OMin ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_n_2 $$unsorted)) (let ((_let_0 (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat))) (= (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Set_Oimage tc_Nat_Onat tc_Nat_Onat c_Nat_OSuc) (hAPP _let_0 V_n_2))) (hAPP _let_0 (hAPP c_Nat_OSuc V_n_2)))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.69 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (c_Big__Operators_Olattice_OInf__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_x_2) V_A_2)))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.69 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.69 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (c_Groups_Ozero__class_Ozero T_a) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) V_a))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2) (c_Complete__Lattice_OInf__class_OInf T_b V_A_2))) ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (c_Groups_Oone__class_Oone T_a)) (c_Groups_Osgn__class_Osgn T_a V_a))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Lazy__Sequence_Osmall__lazy T_1)) (not (class_Lazy__Sequence_Osmall__lazy T_2)) (class_Lazy__Sequence_Osmall__lazy (tc_prod T_2 T_1))) ) 6.44/6.69 ( tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.69 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.69 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_a) _let_0))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_b) V_a))) (= _let_0 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_a) V_b)))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.44/6.69 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.44/6.69 ( c_Int_OMin, c_Int_OMin ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_l_2) V_u_2))) (= (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_l_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (c_SetInterval_Oord__class_OgreaterThanLessThan T_b V_l_2 V_u_2)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_u_2)))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_N_2 $$unsorted) (V_M_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_M_2) V_N_2))) (= V_M_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Big__Operators_Olinorder__class_OMin T_b V_N_2)) (c_Big__Operators_Olinorder__class_OMin T_b V_M_2))))) ) 6.44/6.69 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_nat $$unsorted)) (= (c_Nat_Onat_Onat__size (hAPP c_Nat_OSuc V_nat)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Nat_Onat_Onat__size V_nat)) (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.69 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_b))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) B_x) B_y)) (hAPP (hAPP _let_0 B_x) (hAPP (hAPP _let_0 B_y) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))))) )) (hBOOL (hAPP (hAPP (c_member T_b) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)) V_A_2))) ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_OBit1 (c_Int_Opred V_k)) (c_Int_Opred (c_Int_OBit0 V_k))) ) 6.44/6.69 ( c_Int_OPls ) 6.44/6.69 ( (c_Int_OBit1 c_Int_OPls) ) 6.44/6.69 ( c_Int_OMin ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_l $$unsorted)) (let ((_let_0 (c_Groups_Ominus__class_Ominus tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 c_Int_OMin))) (= (c_Int_OBit0 (hAPP _let_1 V_l)) (hAPP _let_1 (c_Int_OBit1 V_l))))) ) 6.44/6.69 ( c_Int_OPls ) 6.44/6.69 ( (c_Int_OBit1 c_Int_OPls) ) 6.44/6.69 ( c_Int_OMin ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((T_c $$unsorted) (V_D_2 $$unsorted) (V_C_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted)) (let ((_let_0 (tc_fun T_c tc_HOL_Obool))) (let ((_let_1 (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_0))) (let ((_let_2 (hAPP _let_1 V_A_2))) (or (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) V_A_2))) (= (hAPP V_D_2 B_x) (hAPP V_C_2 B_x))) )) (= (hAPP _let_2 V_C_2) (hAPP _let_2 V_D_2)))))) ) 6.44/6.69 ( tc_Nat_Onat, (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2)) (= V_A_2 (hAPP (c_Set_Oimage T_c T_b (c_Fun_Othe__inv__into T_b T_c V_A_2 V_f_2)) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.69 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.44/6.69 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)))) ) 6.44/6.69 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.69 ( c_FunDef_Opair__less, (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.69 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.69 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (= _let_0 (hAPP (c_Set_Oimage T_b T_b (c_Fun_Oid T_b)) _let_0))) ) 6.44/6.69 ( tc_HOL_Obool ) 6.44/6.69 ( tc_Nat_Onat ) 6.44/6.69 ( tc_Int_Oint ) 6.44/6.69 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.69 ( tc_Product__Type_Ounit ) 6.44/6.69 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_b $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 c_Int_OMin))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_b))) (= _let_1 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) _let_1) V_b))))) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.44/6.69 ( c_Int_OPls ) 6.44/6.69 ( c_Int_OMin ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member _let_0) V_A_2) (hAPP (c_Set_OPow T_b) V_B_2)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2)))) ) 6.44/6.69 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_l_2) V_u_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP (hAPP (c_Set_Oinsert T_b) V_l_2) (c_Orderings_Obot__class_Obot _let_0))) (c_SetInterval_Oord__class_OgreaterThanLessThan T_b V_l_2 V_u_2)) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_l_2) V_u_2)))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (= V_A_2 _let_2) (not (hBOOL (hAPP _let_0 V_B_2))) (= V_B_2 _let_2) (not (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2) _let_2)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OSup__fin T_b V_B_2)) (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2))))))) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.69 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Nat_Osemiring__char__0 T_b)) (c_Fun_Oinj__on tc_Nat_Onat T_b (c_Nat_Osemiring__1__class_Oof__nat T_b) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)))) ) 6.44/6.69 ( tc_Nat_Onat ) 6.44/6.69 ( tc_Int_Oint ) 6.44/6.69 ( tc_Code__Numeral_Ocode__numeral ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero T_b))) (or (not (class_Int_Oring__char__0 T_b)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) (c_Int_Oring__1__class_OInts T_b)))) (= (= V_a_2 _let_0) (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2))))) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2)) (= V_y_2 V_x_2)))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.44/6.69 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) _let_0))) (not (= _let_0 (hAPP (c_Set_Oimage T_b T_b V_f_2) _let_0))) (c_Fun_Oinj__on T_b T_b V_f_2 _let_0))) ) 6.44/6.69 ( c_Nat_OSuc, tc_Nat_Onat ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_d $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c _let_0))) (let ((_let_2 (tc_fun T_c tc_HOL_Obool))) (let ((_let_3 (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0))) (= (hAPP (hAPP _let_3 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d _let_2) V_A_2) V_B_2)) V_C_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_d _let_1 _let_0) (hAPP (hAPP (c_COMBB _let_2 (tc_fun _let_1 _let_0) T_d) _let_3) V_B_2)) V_C_2))))))) ) 6.44/6.69 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.69 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.69 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_b_2)) (c_Groups_Ozero__class_Ozero T_b)))))) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2))) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_B_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) (c_Big__Operators_Olattice__class_OInf__fin T_b V_B_2)) _let_1))))) ) 6.44/6.69 ( v_G, v_Ga, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((BOUND_VARIABLE_123499 $$unsorted) (BOUND_VARIABLE_123500 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 BOUND_VARIABLE_123500))) (let ((_let_2 (hAPP _let_0 BOUND_VARIABLE_123499))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_1) _let_2))) (= (c_List_Oupto _let_1 _let_2) (hAPP (hAPP (c_List_Olist_OCons tc_Int_Oint) _let_1) (c_List_Oupto (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) _let_1) (c_Groups_Oone__class_Oone tc_Int_Oint)) _let_2))))))) ) 6.44/6.69 ( c_Int_OPls, c_Int_OPls ) 6.44/6.69 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls ) 6.44/6.69 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls ) 6.44/6.69 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((BOUND_VARIABLE_123517 $$unsorted) (BOUND_VARIABLE_123518 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 BOUND_VARIABLE_123518))) (let ((_let_2 (hAPP _let_0 BOUND_VARIABLE_123517))) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_1) _let_2)) (= (c_List_Olist_ONil tc_Int_Oint) (c_List_Oupto _let_1 _let_2)))))) ) 6.44/6.69 ( c_Int_OPls, c_Int_OPls ) 6.44/6.69 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls ) 6.44/6.69 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls ) 6.44/6.69 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (c_List_Olist_ONil T_a))) (= _let_0 (hAPP (c_List_Orev T_a) _let_0))) ) 6.44/6.69 ( tc_Nat_Onat ) 6.44/6.69 ( tc_Int_Oint ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (c_Orderings_Obot__class_Obot T_a) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x)) V_x))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.44/6.69 ( c_Int_OMin, tc_Int_Oint ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_2 (c_Finite__Set_Ofold1 T_b _let_1))) (or (not (class_Orderings_Olinorder T_b)) (= V_A_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP _let_2 V_B_2)) (hAPP _let_2 V_A_2))))))) ) 6.44/6.69 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_k_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_k_2) (hAPP (c_Groups_Ouminus__class_Ouminus (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_k_2)))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_n $$unsorted)) (= V_n (hAPP c_Int_Onat (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n))) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted)) (or (not (hBOOL (hAPP V_P_2 V_n_2))) (hBOOL (hAPP V_P_2 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (= (c_Orderings_Oord__class_OLeast tc_Nat_Onat V_P_2) (hAPP c_Nat_OSuc (c_Orderings_Oord__class_OLeast tc_Nat_Onat (hAPP (hAPP (c_COMBB tc_Nat_Onat tc_HOL_Obool tc_Nat_Onat) V_P_2) c_Nat_OSuc))))) ) 6.44/6.69 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.44/6.69 ( c_Nat_OSuc, (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Nat__Numeral_Oneg ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert tc_Nat_Onat) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat__Numeral_Oneg ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_Onat ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))))) ) 6.44/6.69 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.44/6.69 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.44/6.69 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 6.44/6.69 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 6.44/6.69 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 6.44/6.69 ( c_fequal, (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.44/6.69 ( c_fequal, (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) ) 6.44/6.69 ( (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))) ) 6.44/6.69 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat) ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Nat_Onat) ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Set_Oimage tc_Nat_Onat tc_Nat_Onat c_Nat_OSuc) ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.44/6.69 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) ) 6.44/6.69 ( c_fconj, (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Oint__of ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral) ) 6.44/6.69 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.44/6.69 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.44/6.69 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 6.44/6.69 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.44/6.69 ( c_Int_Ointrel, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool)))) ) 6.44/6.69 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Product__Type_OPair _let_1 _let_1))) ) 6.44/6.69 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_1 _let_1) (c_Orderings_Obot__class_Obot _let_1)))) ) 6.44/6.69 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0))) ) 6.44/6.69 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.44/6.69 ( c_Int_OMin, (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 6.44/6.69 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) ) 6.44/6.69 ( c_Int_OMin, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.44/6.69 ( c_Int_OMin, (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 6.44/6.69 ( c_Int_OMin, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.44/6.69 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 6.44/6.69 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 6.44/6.69 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 6.44/6.69 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.44/6.69 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) ) 6.44/6.69 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.44/6.69 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.44/6.69 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Nat_OSuc ) 6.44/6.69 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.44/6.69 ( c_Int_Onat, (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat) ) 6.44/6.69 ( c_Code__Numeral_Onat__of, (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 6.44/6.69 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) ) 6.44/6.69 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.44/6.69 ( c_Nitpick_Oint__gcd, (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal))) ) 6.44/6.69 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.44/6.69 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.44/6.69 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.44/6.69 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (c_Set_Oinsert (tc_prod (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1)))) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 c_FunDef_Opair__leq)))) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 c_FunDef_Opair__leq)))) ) 6.44/6.69 ( c_FunDef_Omax__weak, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omax__strict))))) ) 6.44/6.69 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral)) ) 6.44/6.69 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin), c_Nat__Numeral_Oneg ) 6.44/6.69 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))) ) 6.44/6.69 ( c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))) ) 6.44/6.69 ( c_fFalse, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.44/6.69 ( v_Ga, (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) v_G) ) 6.44/6.69 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.44/6.69 ( c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 6.44/6.69 ( c_fTrue, (c_COMBK tc_HOL_Obool tc_Nat_Onat) ) 6.44/6.69 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) c_FunDef_Opair__less)) ) 6.44/6.69 ( (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) ) 6.44/6.69 ( (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)) ) 6.44/6.69 ( (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal), (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) tc_Int_Oint) ) 6.44/6.69 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)))) ) 6.44/6.69 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))), (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.44/6.69 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 6.44/6.69 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), (c_Product__Type_Oprod_Oprod__case tc_Int_Oint tc_Int_Oint tc_HOL_Obool) ) 6.44/6.69 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))) ) 6.44/6.69 ( c_FunDef_Omin__weak, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omin__strict))))) ) 6.44/6.69 ( c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))) ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Int_Oint) ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Finite__Set_Ocard tc_Product__Type_Ounit) ) 6.44/6.69 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat)), (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.44/6.69 ( (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal), (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) ) 6.44/6.69 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.44/6.69 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)), (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.44/6.69 ( v_G, (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) ) 6.44/6.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), (c_Finite__Set_Ocard tc_HOL_Obool) ) 6.44/6.69 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.44/6.69 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)) ) 6.44/6.69 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))), c_Int_OAbs__Integ ) 6.44/6.69 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)) ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), c_Int_OAbs__Integ ) 6.44/6.69 ) 6.44/6.69 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__sup__class_Osup T_b)) V_x_2) V_A_2) (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) ) 6.44/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.44/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.44/6.69 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.69 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.44/6.69 ) 6.52/6.69 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (hAPP _let_1 V_x_2))) (let ((_let_3 (hAPP _let_2 V_A_2))) (let ((_let_4 (c_Big__Operators_Olattice_OInf__fin T_b _let_0 _let_3))) (let ((_let_5 (tc_fun T_b tc_HOL_Obool))) (let ((_let_6 (c_Groups_Ominus__class_Ominus _let_5))) (let ((_let_7 (hAPP _let_6 V_A_2))) (let ((_let_8 (c_Orderings_Obot__class_Obot _let_5))) (let ((_let_9 (hAPP _let_2 _let_8))) (let ((_let_10 (hAPP _let_7 _let_9))) (let ((_let_11 (= _let_8 _let_10))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or (not _let_11) (= V_x_2 _let_4)) (or _let_11 (= _let_4 (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 _let_10)))))))))))))))))) ) 6.52/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.69 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.69 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.69 ) 6.52/6.69 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Lattices_Oboolean__algebra T_b)) (= (= (hAPP _let_0 V_y_2) (hAPP _let_0 V_x_2)) (= V_y_2 V_x_2)))) ) 6.52/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.52/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.69 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.69 ) 6.52/6.69 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (c_Relation_ORange T_c T_b))) (= (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_c T_b) tc_HOL_Obool)) V_A_2) V_B_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP _let_0 V_A_2)) (hAPP _let_0 V_B_2)))) ) 6.52/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.69 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.69 ) 6.52/6.69 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBC T_b T_b tc_HOL_Obool) c_fequal) V_a_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 6.52/6.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.69 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.69 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.69 ) 6.52/6.69 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (hAPP _let_0 _let_1))) (or (not (hBOOL (hAPP _let_2 V_x))) (not (hBOOL (hAPP _let_2 V_y))) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP c_Int_Onat V_x)) (hAPP c_Int_Onat V_y)) (hAPP c_Int_Onat (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_x) V_y))))))) ) 6.52/6.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.52/6.69 ) 6.52/6.70 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_SetInterval_Oord__class_OgreaterThan T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (c_SetInterval_Oord__class_OgreaterThanAtMost T_b V_l_2 V_u_2)) (hAPP _let_0 V_u_2)) (hAPP _let_0 V_l_2)))) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.52/6.70 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (= (hAPP c_Code__Numeral_Oof__nat V_n_2) (hAPP c_Code__Numeral_Oof__nat V_m_2)) (= V_m_2 V_n_2)) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_n) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) V_m))) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Otop T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) (c_Orderings_Otop__class_Otop T_a)))) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.70 ( v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (hAPP (c_Groups_Ouminus__class_Ouminus _let_0) (c_Orderings_Otop__class_Otop _let_0)) (c_Orderings_Obot__class_Obot _let_0))) ) 6.52/6.70 ( tc_HOL_Obool ) 6.52/6.70 ( tc_Nat_Onat ) 6.52/6.70 ( tc_Int_Oint ) 6.52/6.70 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.70 ( tc_Product__Type_Ounit ) 6.52/6.70 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Relation_OImage T_b T_b V_r_2))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (or (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) (hAPP _let_0 (hAPP (hAPP _let_1 V_b_2) _let_2))) (hAPP _let_0 (hAPP (hAPP _let_1 V_a_2) _let_2))))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_b_2) V_A_2))) (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_b_2)) V_r_2)))))) ) 6.52/6.70 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_v_H $$unsorted)) (= (hAPP c_Int_Onat (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v_H))) (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Nat_Onat) (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v_H))) ) 6.52/6.70 ( c_Int_OPls ) 6.52/6.70 ( (c_Int_OBit1 c_Int_OPls) ) 6.52/6.70 ( c_Int_OMin ) 6.52/6.70 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.70 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((T_d $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_Product__Type_Ointernal__split T_b T_c T_d) (c_Product__Type_Oprod_Oprod__case T_b T_c T_d)) ) 6.52/6.70 ( tc_HOL_Obool, tc_Nat_Onat, tc_Nat_Onat ) 6.52/6.70 ( tc_HOL_Obool, tc_Int_Oint, tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_m $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_1 (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) (let ((_let_2 (hAPP _let_0 _let_1))) (= (c_Divides_Odiv__class_Omod tc_Nat_Onat (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_m)) _let_2) (c_Divides_Odiv__class_Omod tc_Nat_Onat V_m _let_2))))) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.52/6.70 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hBOOL (hAPP (hAPP (c_member T_b) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) V_A_2))) ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_1 (hAPP _let_0 V_a))) (or (not (class_Groups_Ocancel__semigroup__add T_a)) (not (= (hAPP _let_1 V_b) (hAPP _let_1 V_c))) (= V_c V_b)))) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq (tc_fun T_b T_c)))) (or (not (class_Orderings_Oord T_c)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless (tc_fun T_b T_c)) V_f_2) V_g_2)) (and (not (hBOOL (hAPP (hAPP _let_0 V_g_2) V_f_2))) (hBOOL (hAPP (hAPP _let_0 V_f_2) V_g_2)))))) ) 6.52/6.70 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.52/6.70 ( v_G, v_Ga, (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_w $$unsorted)) (let ((_let_0 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_2 (hAPP _let_1 V_w))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) _let_2))) (= (hAPP (c_Product__Type_Ofst tc_Int_Oint tc_Int_Oint) (c_Divides_OposDivAlg _let_0 _let_2)) (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) _let_0) _let_2)))))) ) 6.52/6.70 ( c_Int_OPls ) 6.52/6.70 ( (c_Int_OBit1 c_Int_OPls) ) 6.52/6.70 ( c_Int_OMin ) 6.52/6.70 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.70 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Ozero__class_Ozero T_a)) (c_Groups_Oone__class_Oone T_a)))) ) 6.52/6.70 ( tc_Nat_Onat ) 6.52/6.70 ( tc_Int_Oint ) 6.52/6.70 ( tc_Code__Numeral_Ocode__numeral ) 6.52/6.70 ( (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Nat_Osemiring__1__class_ONats T_b))) (or (not (class_Rings_Osemiring__1 T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 V_b_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_b_2)) _let_1))))) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (hAPP _let_0 V_a))) (let ((_let_2 (c_Groups_Ozero__class_Ozero T_a))) (let ((_let_3 (hBOOL (hAPP _let_1 _let_2)))) (let ((_let_4 (c_Groups_Oabs__class_Oabs T_a))) (let ((_let_5 (hAPP _let_4 V_a))) (or (not (class_Groups_Oabs__if T_a)) (and (or _let_3 (= V_a _let_5)) (or (not _let_3) (= _let_5 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a))))))))))) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (hAPP (c_Finite__Set_Ofold__image T_b T_c V_f_2) V_g_2) (c_Finite__Set_Ofold T_c T_b (hAPP (hAPP (c_COMBB T_b (tc_fun T_b T_b) T_c) V_f_2) V_g_2))) ) 6.52/6.70 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_fconj, tc_Int_Oint, tc_HOL_Obool ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (hAPP _let_0 V_A_2))) (let ((_let_2 (c_Set_Oinsert T_b))) (let ((_let_3 (hAPP _let_2 V_a_2))) (= (hAPP _let_3 (hAPP _let_1 V_B_2)) (hAPP _let_1 (hAPP _let_3 V_B_2))))))) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus T_a))) (or (not (class_Rings_Ocomm__semiring__1 T_a)) (= (hAPP (hAPP _let_0 V_c) V_a) (hAPP (hAPP _let_0 V_a) V_c)))) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_k) (hAPP c_Code__Numeral_Onat__of (hAPP (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) V_k))) ) 6.52/6.70 ( c_Int_OPls ) 6.52/6.70 ( (c_Int_OBit1 c_Int_OPls) ) 6.52/6.70 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.70 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_OBit0 V_k) (c_Int_Opred (c_Int_OBit1 V_k))) ) 6.52/6.70 ( c_Int_OPls ) 6.52/6.70 ( (c_Int_OBit1 c_Int_OPls) ) 6.52/6.70 ( c_Int_OMin ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_a) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_b) V_a))) (= V_a (c_Divides_Odiv__class_Omod tc_Int_Oint V_a V_b))) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.52/6.70 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.70 ( c_Int_OMin, c_Int_OMin ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool)))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (hAPP (c_Finite__Set_Ofold__image (tc_fun T_c tc_HOL_Obool) T_b (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_c tc_HOL_Obool))) (hAPP (hAPP (c_COMBC T_b (tc_fun T_c tc_HOL_Obool) (tc_fun T_c tc_HOL_Obool)) (hAPP (hAPP (c_COMBB T_c (tc_fun (tc_fun T_c tc_HOL_Obool) (tc_fun T_c tc_HOL_Obool)) T_b) (c_Set_Oinsert T_c)) V_f_2)) _let_0)) _let_0) V_A_2) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) ) 6.52/6.70 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.70 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.70 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Orderings_Oord__class_Omax T_b)) V_a_2) V_A_2))) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.70 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Int_Oring__1__class_Oof__int T_a) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v)) (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_v))) ) 6.52/6.70 ( c_Int_OPls, tc_Nat_Onat ) 6.52/6.70 ( c_Int_OPls, tc_Int_Oint ) 6.52/6.70 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.52/6.70 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.52/6.70 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.52/6.70 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.52/6.70 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.70 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.52/6.70 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.52/6.70 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.52/6.70 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_a $$unsorted)) (= (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_a) (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_a) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin))) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.52/6.70 ( c_Int_OMin ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 V_b) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_1))))) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (c_Orderings_Oord__class_Omax T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (= V_A_2 _let_2) (not (hBOOL (hAPP _let_0 V_B_2))) (= V_B_2 _let_2) (not (= _let_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2))) (= (hAPP (hAPP _let_3 (c_Big__Operators_Olattice_OSup__fin T_b _let_3 V_A_2)) (c_Big__Operators_Olattice_OSup__fin T_b _let_3 V_B_2)) (c_Big__Operators_Olattice_OSup__fin T_b _let_3 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2)))))))) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.70 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Relation_Oconverse T_b T_b))) (or (not (c_Wellfounded_Owf T_b (hAPP _let_0 V_r_2))) (c_Wellfounded_Owf T_b (hAPP _let_0 (c_Transitive__Closure_Otrancl T_b V_r_2))))) ) 6.52/6.70 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Obounded__lattice T_1)) (class_Lattices_Obounded__lattice (tc_fun T_2 T_1))) ) 6.52/6.70 ( tc_HOL_Obool, tc_HOL_Obool ) 6.52/6.70 ( tc_Nat_Onat, tc_HOL_Obool ) 6.52/6.70 ( tc_Int_Oint, tc_HOL_Obool ) 6.52/6.70 ( tc_Int_Oint, tc_Int_Oint ) 6.52/6.70 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.52/6.70 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.52/6.70 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.52/6.70 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_m_2 $$unsorted) (V_Q_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (or (not (hBOOL (hAPP V_P_2 V_n_2))) (not (hBOOL (hAPP V_Q_2 V_m_2))) (hBOOL (hAPP V_P_2 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (not (forall ((B_k $$unsorted)) (= (hBOOL (hAPP V_P_2 (hAPP c_Nat_OSuc B_k))) (hBOOL (hAPP V_Q_2 B_k))) )) (= (hAPP c_Nat_OSuc (c_Orderings_Oord__class_OLeast tc_Nat_Onat V_Q_2)) (c_Orderings_Oord__class_OLeast tc_Nat_Onat V_P_2))) ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool), (c_Orderings_Oord__class_Oless tc_Nat_Onat), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.52/6.70 ( c_Nat_OSuc, (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)), c_Nat_OSuc, (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Nat__Numeral_Oneg, (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Nat__Numeral_Oneg ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat, (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), c_Code__Numeral_Oof__nat, (c_Groups_Oone__class_Oone tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)), (c_Groups_Oone__class_Oone tc_Nat_Onat), (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc, (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Code__Numeral_Oof__nat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert tc_Nat_Onat) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osize__class_Osize tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat__Numeral_Oneg, (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat__Numeral_Oneg ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_Onat, (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_Onat ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))))), (c_Groups_Oone__class_Oone tc_Int_Oint), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))))) ) 6.52/6.70 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.52/6.70 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.52/6.70 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls), c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 6.52/6.70 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin), c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 6.52/6.70 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral), c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 6.52/6.70 ( c_fequal, (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool), c_fequal, (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.52/6.70 ( c_fequal, (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint), c_fequal, (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) ) 6.52/6.70 ( (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))), (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))) ) 6.52/6.70 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat), (c_Groups_Oabs__class_Oabs tc_Int_Oint), (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat) ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Nat_Onat) ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Set_Oimage tc_Nat_Onat tc_Nat_Onat c_Nat_OSuc), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Set_Oimage tc_Nat_Onat tc_Nat_Onat c_Nat_OSuc) ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.52/6.70 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) ) 6.52/6.70 ( c_fconj, (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint), c_fconj, (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Oint__of, (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Oint__of ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral) ) 6.52/6.70 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.52/6.70 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.52/6.70 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral), (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 6.52/6.70 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.52/6.70 ( c_Int_Ointrel, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool)))), c_Int_Ointrel, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool)))) ) 6.52/6.70 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Product__Type_OPair _let_1 _let_1))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod 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(c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 6.52/6.70 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls), c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) ) 6.52/6.70 ( c_Int_OMin, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), c_Int_OMin, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.52/6.70 ( c_Int_OMin, (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 6.52/6.70 ( c_Int_OMin, (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_OMin, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.52/6.70 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls), c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 6.52/6.70 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin), c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 6.52/6.70 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin), c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 6.52/6.70 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.52/6.70 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) ) 6.52/6.70 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.52/6.70 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.52/6.70 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Nat_OSuc, (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Nat_OSuc ) 6.52/6.70 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc, (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.52/6.70 ( c_Int_Onat, (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), c_Int_Onat, (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat) ) 6.52/6.70 ( c_Code__Numeral_Onat__of, (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)), c_Code__Numeral_Onat__of, (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 6.52/6.70 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) ) 6.52/6.70 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.52/6.70 ( c_Nitpick_Oint__gcd, (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal))), c_Nitpick_Oint__gcd, (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal))) ) 6.52/6.70 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.52/6.70 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.52/6.70 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.52/6.70 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (c_Set_Oinsert (tc_prod (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (c_Set_Oinsert (tc_prod (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1)))) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 c_FunDef_Opair__leq)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 c_FunDef_Opair__leq)))) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 c_FunDef_Opair__leq)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 c_FunDef_Opair__leq)))) ) 6.52/6.70 ( c_FunDef_Omax__weak, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 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(c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))) ) 6.52/6.70 ( c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))) ) 6.52/6.70 ( c_fFalse, (c_Nat_Osize__class_Osize tc_HOL_Obool), c_fFalse, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.52/6.70 ( v_Ga, (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) v_G), v_Ga, (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) v_G) ) 6.52/6.70 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.52/6.70 ( c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool), c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 6.52/6.70 ( c_fTrue, (c_COMBK tc_HOL_Obool tc_Nat_Onat), c_fTrue, (c_COMBK tc_HOL_Obool tc_Nat_Onat) ) 6.52/6.70 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) c_FunDef_Opair__less)), (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) c_FunDef_Opair__less)) ) 6.52/6.70 ( (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool), (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) ) 6.52/6.70 ( (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)), (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)) ) 6.52/6.70 ( (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal), (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) tc_Int_Oint), (hAPP (c_COMBB tc_Int_Oint 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tc_HOL_Obool)))) ) 6.52/6.70 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))), (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))), (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.52/6.70 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC 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(c_Product__Type_Oprod_Oprod__case tc_Int_Oint tc_Int_Oint tc_HOL_Obool) ) 6.52/6.70 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))) ) 6.52/6.70 ( c_FunDef_Omin__weak, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omin__strict))))), c_FunDef_Omin__weak, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omin__strict))))) ) 6.52/6.70 ( c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))) ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Int_Oint), (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Int_Oint) ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit 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(c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool), (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.52/6.70 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)), (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)), (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)), (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.52/6.70 ( v_G, (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)), v_G, (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), (c_Finite__Set_Ocard tc_HOL_Obool), (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), (c_Finite__Set_Ocard tc_HOL_Obool) ) 6.52/6.70 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.52/6.70 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)) ) 6.52/6.70 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))), c_Int_OAbs__Integ, (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))), c_Int_OAbs__Integ ) 6.52/6.70 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), c_Int_OAbs__Integ, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), c_Int_OAbs__Integ ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Relation_OField T_b))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP _let_0 V_r_2)) (hAPP _let_0 V_s_2)) (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) V_s_2)))) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.70 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Enum_Oenum T_1)) (not (class_Enum_Oenum T_2)) (class_Enum_Oenum (tc_prod T_2 T_1))) ) 6.52/6.70 ( tc_Nat_Onat, tc_Nat_Onat ) 6.52/6.70 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (= V_b V_a) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_b) V_a))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_b) V_a))) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.52/6.70 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 6.52/6.70 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.52/6.70 ( v_G, v_Ga, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b T_c))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))))) ) 6.52/6.70 ( tc_HOL_Obool, tc_HOL_Obool ) 6.52/6.70 ( tc_HOL_Obool, tc_Nat_Onat ) 6.52/6.70 ( tc_HOL_Obool, tc_Int_Oint ) 6.52/6.70 ( tc_HOL_Obool, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.70 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.70 ( tc_HOL_Obool, tc_Product__Type_Ounit ) 6.52/6.70 ( tc_HOL_Obool, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.52/6.70 ( tc_Int_Oint, tc_Int_Oint ) 6.52/6.70 ( (tc_fun tc_Int_Oint tc_HOL_Obool), tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Otrans T_b V_r_2)) (c_Relation_Otrans T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (c_Relation_OId T_b)))) ) 6.52/6.70 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.70 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_n_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Oring__1 T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_b) V_n_2)) (c_Int_Oring__1__class_OInts T_b)))) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_P_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP V_P_2 V_A_2))) (not (forall ((B_a $$unsorted) (B_A $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) B_A))) (not (hBOOL (hAPP (hAPP (c_member T_b) B_a) B_A))) (not (hBOOL (hAPP V_P_2 B_A))) (hBOOL (hAPP V_P_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) B_A) (hAPP (hAPP (c_Set_Oinsert T_b) B_a) (c_Orderings_Obot__class_Obot _let_0))))))) )) (hBOOL (hAPP V_P_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 6.52/6.70 ( (c_Finite__Set_Ofinite tc_Int_Oint), (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.52/6.70 ( (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Osgn__class_Osgn T_a V_a))) (or (not (class_Rings_Olinordered__idom T_a)) (= _let_0 (c_Groups_Osgn__class_Osgn T_a _let_0)))) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= V_x_2 (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.70 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_M_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_M_2))) (not (forall ((B_h $$unsorted)) (not (c_Fun_Obij__betw tc_Nat_Onat T_b B_h (c_SetInterval_Oord__class_OatLeastAtMost tc_Nat_Onat (c_Groups_Oone__class_Oone tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) V_M_2)) V_M_2)) ))) ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oab__group__add T_a)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) V_b) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_b)))) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_l_2)) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_l_2 V_u_2)) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_u_2))) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.52/6.70 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.70 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b T_c))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))))) (= (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Finite__Set_Ocard T_c) (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))))) ) 6.52/6.70 ( tc_HOL_Obool, tc_HOL_Obool ) 6.52/6.70 ( tc_HOL_Obool, tc_Nat_Onat ) 6.52/6.70 ( tc_HOL_Obool, tc_Int_Oint ) 6.52/6.70 ( tc_HOL_Obool, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.70 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.70 ( tc_HOL_Obool, tc_Product__Type_Ounit ) 6.52/6.70 ( tc_HOL_Obool, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.52/6.70 ( tc_Int_Oint, tc_Int_Oint ) 6.52/6.70 ( (tc_fun tc_Int_Oint tc_HOL_Obool), tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Big__Operators_Olattice_OInf__fin T_b (c_Orderings_Oord__class_Omin T_b) V_A_2)) (c_Big__Operators_Olattice_OSup__fin T_b (c_Orderings_Oord__class_Omax T_b) V_A_2)))) ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Osemilattice__sup (tc_fun T_2 T_1))) ) 6.52/6.70 ( tc_HOL_Obool, tc_HOL_Obool ) 6.52/6.70 ( tc_Nat_Onat, tc_HOL_Obool ) 6.52/6.70 ( tc_Int_Oint, tc_HOL_Obool ) 6.52/6.70 ( tc_Int_Oint, tc_Int_Oint ) 6.52/6.70 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.52/6.70 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.52/6.70 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.52/6.70 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_x_2) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.70 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_n_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (c_Groups_Ozero__class_Ozero T_b)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_b) V_n_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_n_2)))) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_m $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Ozero__class_Ozero T_a)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) V_m)))) ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.52/6.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.52/6.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.52/6.70 ) 6.52/6.70 (instantiation (forall ((V_P_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Nitpick_Onorm__frac__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) V_a0_2) V_a1_2)))) (not (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Nitpick_Onorm__frac__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) B_a) B_b)))) (and (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) B_b) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (not (hBOOL (hAPP (hAPP V_P_2 (hAPP _let_0 B_a)) (hAPP _let_0 B_b))))) (hBOOL (hAPP (hAPP V_P_2 B_a) B_b)))) )) (hBOOL (hAPP (hAPP V_P_2 V_a0_2) V_a1_2))) ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OPls, c_Int_OMin ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.70 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.70 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.52/6.70 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.52/6.70 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.52/6.70 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) ) 6.52/6.70 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.52/6.70 ( (c_Set_Oinsert tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.52/6.70 ( (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))) ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Product__Type_OPair _let_1 _let_1))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.52/6.70 ( (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 6.52/6.70 ( (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.52/6.70 ( (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_fconj ) 6.52/6.70 ( (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Onat__of ) 6.52/6.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less ) 6.52/6.71 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 6.52/6.71 ( (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Groups_Oone__class_Oone tc_Int_Oint), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))) ) 6.52/6.71 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool) ) 6.52/6.71 ( (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) tc_Int_Oint), c_Nitpick_Oint__gcd, (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal) ) 6.52/6.71 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.52/6.71 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.52/6.71 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.52/6.71 ( (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat), c_Nat_OSuc, (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal) ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)), v_Ga, v_G ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omax__weak, c_FunDef_Omax__strict ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omin__weak, c_FunDef_Omin__strict ) 6.52/6.71 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), c_Int_OPls, c_Int_Onat ) 6.52/6.71 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), (c_Int_OBit1 c_Int_OPls), c_Int_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Groups_Ouminus T_1)) (class_Groups_Ouminus (tc_fun T_2 T_1))) ) 6.52/6.71 ( tc_HOL_Obool, tc_HOL_Obool ) 6.52/6.71 ( tc_Nat_Onat, tc_HOL_Obool ) 6.52/6.71 ( tc_Int_Oint, tc_HOL_Obool ) 6.52/6.71 ( tc_Int_Oint, tc_Int_Oint ) 6.52/6.71 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.52/6.71 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.52/6.71 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.52/6.71 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_2 (c_Orderings_Otop__class_Otop (tc_fun T_d tc_HOL_Obool)))) (or (not (= _let_1 (hAPP (c_Set_Oimage T_c T_b V_f_2) _let_0))) (not (= _let_2 (hAPP (c_Set_Oimage T_b T_d V_g_2) _let_1))) (= (hAPP (c_Set_Oimage T_c T_d (hAPP (c_Fun_Ocomp T_b T_d T_c V_g_2) V_f_2)) _let_0) _let_2))))) ) 6.52/6.71 ( c_Code__Numeral_Oof__nat, tc_Code__Numeral_Ocode__numeral, c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.52/6.71 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, c_Code__Numeral_Onat__of, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral ) 6.52/6.71 ( c_Int_Onat, tc_Nat_Onat, (c_Groups_Oabs__class_Oabs tc_Int_Oint), tc_Int_Oint, tc_Int_Oint ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_x_2 $$unsorted) (V_P_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (hBOOL (hAPP V_P_2 V_x_2))) (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP V_P_2 B_y))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) B_y))) )) (= V_x_2 (c_Orderings_Oord__class_OLeast T_b V_P_2))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Code__Numeral_Oof__nat, tc_HOL_Obool ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Otop T_1)) (class_Orderings_Otop (tc_fun T_2 T_1))) ) 6.52/6.71 ( tc_HOL_Obool, tc_HOL_Obool ) 6.52/6.71 ( tc_Nat_Onat, tc_HOL_Obool ) 6.52/6.71 ( tc_Int_Oint, tc_HOL_Obool ) 6.52/6.71 ( tc_Int_Oint, tc_Int_Oint ) 6.52/6.71 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.52/6.71 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.52/6.71 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.52/6.71 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (or (not (class_Groups_Oab__semigroup__mult T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2)) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_a_2) V_A_2) (hAPP (c_Finite__Set_Ofold1 T_b _let_0) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_SetInterval_Oord__class_OlessThan T_b))) (or (not (class_Orderings_Olinorder T_b)) (= (= (hAPP _let_0 V_y_2) (hAPP _let_0 V_x_2)) (= V_y_2 V_x_2)))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice_OSup__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 V_A_2))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_126398 $$unsorted)) (let ((_let_0 (c_member T_b))) (or (not (hBOOL (hAPP (hAPP _let_0 B_x) V_A_2))) (not (hBOOL (hAPP (hAPP _let_0 BOUND_VARIABLE_126398) V_A_2))) (not (= (hAPP V_f_2 B_x) (hAPP V_f_2 BOUND_VARIABLE_126398))) (= B_x BOUND_VARIABLE_126398))) )) ) 6.52/6.71 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_G_2 $$unsorted) (V_tsa_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple T_b) tc_HOL_Obool)) V_tsa_2) V_G_2))) (c_Hoare__Mirabelle_Ohoare__derivs T_b V_G_2 V_tsa_2)) ) 6.52/6.71 ( v_Ga, v_ts, t_a ) 6.52/6.71 ( v_Ga, v_G, t_a ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (= V_A_2 _let_2) (not (hBOOL (hAPP _let_0 V_B_2))) (= V_B_2 _let_2) (not (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2) _let_2)) (= (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMax T_b V_B_2)) (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2))))))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ocard T_b))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP c_Nat_OSuc (hAPP _let_0 V_A_2))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_a) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (c_Groups_Oone__class_Oone T_a))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.71 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (or (not (class_Groups_Ogroup__add T_a)) (= _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) _let_0)))) ) 6.52/6.71 ( tc_Nat_Onat ) 6.52/6.71 ( tc_Int_Oint ) 6.52/6.71 ( tc_Code__Numeral_Ocode__numeral ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (not (class_Int_Onumber__ring T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_x_2) c_Int_OPls)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_x_2)) (c_Groups_Ozero__class_Ozero T_b))))) ) 6.52/6.71 ( c_Int_OPls, tc_Nat_Onat ) 6.52/6.71 ( c_Int_OPls, tc_Int_Oint ) 6.52/6.71 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.52/6.71 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.52/6.71 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.52/6.71 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.52/6.71 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.52/6.71 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.52/6.71 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.52/6.71 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (= (hAPP (hAPP _let_0 (hAPP c_Nat_OSuc V_m)) V_n) (hAPP c_Nat_OSuc (hAPP (hAPP _let_0 V_m) V_n)))) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 V_b) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_1))))) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olattice_OSup__fin T_b _let_0 V_A_2) (hAPP (c_Finite__Set_Ofold1 T_b _let_0) V_A_2)))) ) 6.52/6.71 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.71 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (c_Big__Operators_Olattice_OSup__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_x_2) V_A_2)))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_b $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted)) (or (not (class_Orderings_Oord T_c)) (not (forall ((B_x $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_c) (hAPP V_f_2 B_x)) (hAPP V_g_2 B_x))) )) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b T_c)) V_f_2) V_g_2))) ) 6.52/6.71 ( (tc_Hoare__Mirabelle_Otriple t_a), v_Ga, v_G, tc_HOL_Obool ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (c_Orderings_Otop__class_Otop _let_0) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) (hAPP (c_Groups_Ouminus__class_Ouminus _let_0) V_A_2)))) ) 6.52/6.71 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.71 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice_OInf__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 V_A_2))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_d_2 $$unsorted)) (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (= (c_Int_Oint__ge__less__than2 V_d_2) (hAPP (c_Set_OCollect (tc_prod tc_Int_Oint tc_Int_Oint)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Int_Oint tc_Int_Oint tc_HOL_Obool) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_d_2)))) (c_Orderings_Oord__class_Oless tc_Int_Oint)))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( c_Int_OMin ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((BOUND_VARIABLE_126989 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (or (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) BOUND_VARIABLE_126989))) (= (hAPP c_Nat_OSuc (hAPP _let_0 BOUND_VARIABLE_126989)) (hAPP _let_0 (c_Int_Osucc BOUND_VARIABLE_126989))))) ) 6.52/6.71 ( c_Int_OPls ) 6.52/6.71 ( (c_Int_OBit1 c_Int_OPls) ) 6.52/6.71 ( c_Int_OMin ) 6.52/6.71 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.71 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((BOUND_VARIABLE_127001 $$unsorted)) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) BOUND_VARIABLE_127001)))) (= (c_Groups_Oone__class_Oone tc_Nat_Onat) (hAPP c_Nat_OSuc (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) BOUND_VARIABLE_127001)))) ) 6.52/6.71 ( c_Int_OPls ) 6.52/6.71 ( (c_Int_OBit1 c_Int_OPls) ) 6.52/6.71 ( c_Int_OMin ) 6.52/6.71 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.71 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_Y_2 $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite _let_0) V_Y_2))) (= _let_2 V_Y_2) (hBOOL (hAPP (hAPP (c_member (tc_prod _let_1 _let_1)) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) V_Y_2)) c_FunDef_Omax__strict)))))) ) 6.52/6.71 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((BOUND_VARIABLE_127086 $$unsorted)) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) BOUND_VARIABLE_127086)))) (= (c_Groups_Ozero__class_Ozero tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) BOUND_VARIABLE_127086)))) ) 6.52/6.71 ( c_Int_OPls ) 6.52/6.71 ( (c_Int_OBit1 c_Int_OPls) ) 6.52/6.71 ( c_Int_OMin ) 6.52/6.71 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.71 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((BOUND_VARIABLE_127076 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 BOUND_VARIABLE_127076))) (or (hBOOL (hAPP c_Nat__Numeral_Oneg _let_1)) (= _let_1 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) BOUND_VARIABLE_127076)))))) ) 6.52/6.71 ( c_Int_OPls ) 6.52/6.71 ( (c_Int_OBit1 c_Int_OPls) ) 6.52/6.71 ( c_Int_OMin ) 6.52/6.71 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.71 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_member (tc_prod T_b T_b)))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (let ((_let_2 (hAPP _let_1 V_a_2))) (let ((_let_3 (c_Transitive__Closure_Otrancl T_b V_r_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_b_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_b_2) V_c_2)) _let_3))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Wellfounded_Opred__nat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_z $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_z) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP c_Int_Onat V_z))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.52/6.71 ( c_Int_OMin ) 6.52/6.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.52/6.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) (hBOOL (hAPP (hAPP (c_member _let_0) V_A_2) (hAPP (c_Set_OPow T_b) V_B_2))))) ) 6.52/6.71 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (forall ((B_f $$unsorted)) (not (forall ((B_i $$unsorted)) (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) (hAPP B_f (hAPP c_Nat_OSuc B_i))) (hAPP B_f B_i))) V_r_2)) )) ) (c_Wellfounded_Owf T_b V_r_2)) ) 6.52/6.71 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 6.52/6.71 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 6.52/6.71 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_z) V_z) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) V_z))) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Finite__Set_Ofinite T_1)) (not (class_Finite__Set_Ofinite T_2)) (class_Finite__Set_Ofinite (tc_prod T_2 T_1))) ) 6.52/6.71 ( tc_Nat_Onat, tc_Nat_Onat ) 6.52/6.71 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_b $$unsorted) (T_c $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Relation_ORange T_c T_b) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_c T_b) tc_HOL_Obool)))) ) 6.52/6.71 ( tc_Nat_Onat, tc_Nat_Onat ) 6.52/6.71 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (= (c_Fun_Oinj__on T_b T_c V_f_2 _let_0) (= (c_Fun_Oid T_b) (hAPP (c_Fun_Ocomp T_c T_b T_b (c_Hilbert__Choice_Oinv__into T_b T_c _let_0 V_f_2)) V_f_2)))) ) 6.52/6.71 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_SetInterval_Oord__class_OlessThan T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP _let_0 V_u_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP _let_0 V_l_2)) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_l_2) V_u_2))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_z $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_0) V_z))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_z))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.52/6.71 ( c_Int_OMin ) 6.52/6.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.52/6.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_P_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Divides_OposDivAlg__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) V_a0_2) V_a1_2)))) (not (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_0 (hAPP V_P_2 B_a))) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Divides_OposDivAlg__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) B_a) B_b)))) (and (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) B_b) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) B_a) B_b))) (not (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) B_b))))) (hBOOL (hAPP _let_0 B_b)))) )) (hBOOL (hAPP (hAPP V_P_2 V_a0_2) V_a1_2))) ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OPls, c_Int_OMin ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 6.52/6.71 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.52/6.71 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.52/6.71 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) ) 6.52/6.71 ( (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.52/6.71 ( (c_Set_Oinsert tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.52/6.71 ( (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Product__Type_OPair _let_1 _let_1))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.52/6.71 ( (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 6.52/6.71 ( (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 6.52/6.71 ( (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_fconj ) 6.52/6.71 ( (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Onat__of ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less ) 6.52/6.71 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 6.52/6.71 ( (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Groups_Oone__class_Oone tc_Int_Oint), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))) ) 6.52/6.71 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool) ) 6.52/6.71 ( (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) tc_Int_Oint), c_Nitpick_Oint__gcd, (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal) ) 6.52/6.71 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.52/6.71 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.52/6.71 ( (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.52/6.71 ( (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat), c_Nat_OSuc, (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal) ) 6.52/6.71 ( (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)), v_Ga, v_G ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omax__weak, c_FunDef_Omax__strict ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))), c_FunDef_Omin__weak, c_FunDef_Omin__strict ) 6.52/6.71 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), c_Int_OPls, c_Int_Onat ) 6.52/6.71 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), (c_Int_OBit1 c_Int_OPls), c_Int_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ocard T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Set_Oinsert T_b))) (let ((_let_3 (hAPP _let_2 V_x_2))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP _let_0 (hAPP _let_3 V_A_2)) (hAPP c_Nat_OSuc (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP _let_3 (c_Orderings_Obot__class_Obot _let_1))))))))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_SetInterval_Oord__class_OatMost T_b))) (or (not (class_Orderings_Olinorder T_b)) (= (= V_y_2 V_x_2) (= (hAPP _let_0 V_y_2) (hAPP _let_0 V_x_2))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (or (not (c_Wellfounded_Owf T_b V_R_2)) (not (c_Wellfounded_Owf T_b V_S_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_1) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) V_R_2) V_S_2)) V_R_2))) (c_Wellfounded_Owf T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_R_2) V_S_2))))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.71 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= V_a (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OPls)))) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_k $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_k))) (not (forall ((B_n $$unsorted)) (or (not (= V_k (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) B_n)))) ))) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.52/6.71 ( c_Int_OPls ) 6.52/6.71 ( c_Int_OMin ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_m_2 $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2) (hAPP c_Int_OAbs__Integ (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_m_2) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))))) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.52/6.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.52/6.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Code__Numeral_Ocode__numeral) (hAPP c_Code__Numeral_Oof__nat V_n)) (hAPP c_Code__Numeral_Oof__nat V_m)) (hAPP c_Code__Numeral_Oof__nat (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) V_m))) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_Q_2 $$unsorted) (T_c $$unsorted) (V_P_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (hAPP (c_Set_OCollect T_b) V_P_2)))) (= (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP V_P_2 B_y))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (hAPP (c_Set_OCollect T_c) (hAPP (hAPP (c_COMBC T_c T_b tc_HOL_Obool) V_Q_2) B_y))))) ) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (hAPP (c_Set_OCollect T_c) (hAPP (hAPP (c_COMBB _let_0 tc_HOL_Obool T_c) (c_HOL_OEx T_b)) (hAPP (hAPP (c_COMBB _let_0 _let_0 T_c) (hAPP (c_COMBS T_b tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_b) c_fconj) V_P_2))) V_Q_2)))))))) ) 6.52/6.71 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), tc_Int_Oint, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Lattices_Osemilattice__sup T_b)) (c_Finite__Set_Ofun__left__comm__idem T_b T_b (c_Lattices_Osemilattice__sup__class_Osup T_b))) ) 6.52/6.71 ( tc_HOL_Obool ) 6.52/6.71 ( tc_Nat_Onat ) 6.52/6.71 ( tc_Int_Oint ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (c_Finite__Set_Ofinite T_b))) (let ((_let_3 (c_Orderings_Oord__class_Omin T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_2 V_A_2))) (= V_A_2 _let_1) (not (hBOOL (hAPP _let_2 V_B_2))) (= V_B_2 _let_1) (not (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2))) (= (hAPP (hAPP _let_3 (c_Big__Operators_Olattice_OInf__fin T_b _let_3 V_A_2)) (c_Big__Operators_Olattice_OInf__fin T_b _let_3 V_B_2)) (c_Big__Operators_Olattice_OInf__fin T_b _let_3 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)))))))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= V_B_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2)))) ) 6.52/6.71 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Orderings_Obot__class_Obot T_b) (c_Complete__Lattice_OInf__class_OInf T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))))) ) 6.52/6.71 ( tc_HOL_Obool ) 6.52/6.71 ( tc_Nat_Onat ) 6.52/6.71 ( tc_Int_Oint ) 6.52/6.71 ( (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 6.52/6.71 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.71 ( (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.71 ( tc_Product__Type_Ounit ) 6.52/6.71 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_v_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 V_v_2))) (= (and (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) _let_1)) (= V_m_2 (hAPP c_Int_Onat _let_1))) (= _let_1 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2))))) ) 6.52/6.71 ( (c_Int_OBit1 c_Int_OPls), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.52/6.71 ( c_Int_OMin, (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.52/6.71 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.52/6.71 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_N_2 $$unsorted) (V_h_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (= (hAPP (hAPP _let_0 (hAPP V_h_2 B_x)) (hAPP V_h_2 B_y)) (hAPP V_h_2 (hAPP (hAPP _let_0 B_x) B_y))) )) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (= V_N_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP V_h_2 (c_Big__Operators_Olattice_OSup__fin T_b _let_0 V_N_2)) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 (hAPP (c_Set_Oimage T_b T_b V_h_2) V_N_2))))) ) 6.52/6.71 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (or (not (class_Orderings_Olinorder T_b)) (= (or (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2)) (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2))) (not (= V_y_2 V_x_2))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (let ((_let_1 (c_Finite__Set_Ofold1 T_b _let_0))) (or (not (class_Groups_Oab__semigroup__mult T_b)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (hAPP (hAPP _let_0 V_x_2) (hAPP _let_1 V_A_2)) (hAPP _let_1 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Groups_Ominus__class_Ominus T_b))) (let ((_let_1 (c_Orderings_Oord__class_Oless T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (not (= (hAPP (hAPP _let_0 V_c_2) V_d_2) (hAPP (hAPP _let_0 V_a_2) V_b_2))) (= (hBOOL (hAPP (hAPP _let_1 V_c_2) V_d_2)) (hBOOL (hAPP (hAPP _let_1 V_a_2) V_b_2)))))) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_a) (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a)))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ( v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (c_Wellfounded_Owf T_b V_r_2)) (not (c_Wellfounded_Owf T_b V_s_2)) (not (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) (hAPP (c_Relation_ODomain T_b T_b) V_r_2)) (hAPP (c_Relation_ORange T_b T_b) V_s_2)))) (c_Wellfounded_Owf T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) V_s_2)))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.71 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2)))) ) 6.52/6.71 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (hAPP _let_0 V_a_2))) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP _let_1 (c_Groups_Ozero__class_Ozero T_b))) (hBOOL (hAPP _let_1 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2))))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ( v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olinorder__class_OMin T_b V_A_2) (hAPP (c_Finite__Set_Ofold1 T_b (c_Orderings_Oord__class_Omin T_b)) V_A_2))) ) 6.52/6.71 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.71 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (c_Groups_Oone__class_Oone T_a)) (hAPP _let_0 V_w)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Int_OBit1 c_Int_OPls)) V_w))))) ) 6.52/6.71 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Groups_Ominus T_1)) (class_Groups_Ominus (tc_fun T_2 T_1))) ) 6.52/6.71 ( tc_HOL_Obool, tc_HOL_Obool ) 6.52/6.71 ( tc_Nat_Onat, tc_HOL_Obool ) 6.52/6.71 ( tc_Int_Oint, tc_HOL_Obool ) 6.52/6.71 ( tc_Int_Oint, tc_Int_Oint ) 6.52/6.71 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.52/6.71 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.52/6.71 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.52/6.71 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (let ((_let_3 (hAPP _let_2 V_A_2))) (let ((_let_4 (hAPP _let_3 V_B_2))) (let ((_let_5 (c_Orderings_Oord__class_Omin T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (not (hBOOL (hAPP _let_0 V_B_2))) (= (c_Orderings_Obot__class_Obot _let_1) _let_4) (= (hAPP (hAPP _let_5 (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2))) (c_Big__Operators_Olinorder__class_OMin T_b _let_4)) (hAPP (hAPP _let_5 (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMin T_b V_B_2)))))))))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_A_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (c_Wellfounded_Owf T_b V_R_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) (hAPP (c_Relation_OImage T_b T_b V_R_2) V_A_2)))) (= V_A_2 (c_Orderings_Obot__class_Obot _let_0)))) ) 6.52/6.71 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) (hAPP _let_1 V_b_2))) (hBOOL (hAPP (hAPP _let_0 V_b_2) (hAPP _let_1 V_a_2))))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2)) (= V_B_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.52/6.71 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_A_2) V_A_2)) ) 6.52/6.71 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.71 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (hAPP (c_Set_Oimage T_c T_b V_f_2) V_A_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_c _let_0 _let_0) (hAPP (hAPP (c_COMBB T_b (tc_fun _let_0 _let_0) T_c) (c_Set_Oinsert T_b)) V_f_2)) (c_Orderings_Obot__class_Obot _let_0))))) ) 6.52/6.71 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.52/6.71 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.52/6.71 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Fields_Ofield__inverse__zero T_a)) (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Rings_Oinverse__class_Odivide T_a) V_x) (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OMin)) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_k $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (= (c_Int_OBit1 (c_Int_Opred (hAPP _let_0 V_k))) (hAPP _let_0 (c_Int_OBit1 V_k)))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.52/6.71 ( c_Int_OMin ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a) (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (hAPP (hAPP (c_Product__Type_OSigma T_b T_b) V_A_2) (hAPP (c_COMBK _let_0 T_b) V_A_2))))) (hBOOL (hAPP (c_Finite__Set_Ofinite _let_0) (hAPP (hAPP (c_Equiv__Relations_Oquotient T_b) V_A_2) V_r_2))))) ) 6.52/6.71 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Opreorder T_1)) (class_Orderings_Opreorder (tc_fun T_2 T_1))) ) 6.52/6.71 ( tc_HOL_Obool, tc_HOL_Obool ) 6.52/6.71 ( tc_Nat_Onat, tc_HOL_Obool ) 6.52/6.71 ( tc_Int_Oint, tc_HOL_Obool ) 6.52/6.71 ( tc_Int_Oint, tc_Int_Oint ) 6.52/6.71 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.52/6.71 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.52/6.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.52/6.71 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.52/6.71 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_k $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Int_Oint))) (= (c_Int_OBit1 V_k) (hAPP (hAPP _let_0 (hAPP (hAPP _let_0 (c_Groups_Oone__class_Oone tc_Int_Oint)) V_k)) V_k))) ) 6.52/6.71 ( c_Int_OPls ) 6.52/6.71 ( (c_Int_OBit1 c_Int_OPls) ) 6.52/6.71 ( c_Int_OMin ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_N_2 $$unsorted) (V_h_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (= (hAPP V_h_2 (hAPP (hAPP _let_0 B_x) B_y)) (hAPP (hAPP _let_0 (hAPP V_h_2 B_x)) (hAPP V_h_2 B_y)))) )) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (= V_N_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP V_h_2 (c_Big__Operators_Olinorder__class_OMin T_b V_N_2)) (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (c_Set_Oimage T_b T_b V_h_2) V_N_2)))) ) 6.52/6.71 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Finite__Set_Ofinite T_2)) (not (class_Finite__Set_Ofinite T_1)) (class_Finite__Set_Ofinite (tc_fun T_2 T_1))) ) 6.52/6.71 ( tc_HOL_Obool, tc_HOL_Obool ) 6.52/6.71 ( tc_HOL_Obool, tc_Nat_Onat ) 6.52/6.71 ( tc_HOL_Obool, tc_Int_Oint ) 6.52/6.71 ( tc_HOL_Obool, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.71 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.71 ( tc_HOL_Obool, tc_Product__Type_Ounit ) 6.52/6.71 ( tc_HOL_Obool, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.52/6.71 ( tc_Int_Oint, tc_Int_Oint ) 6.52/6.71 ( (tc_fun tc_Int_Oint tc_HOL_Obool), tc_Int_Oint ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_w $$unsorted)) (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (= (hAPP _let_1 (hAPP _let_0 V_w)) (hAPP _let_0 (hAPP _let_1 V_w))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.52/6.71 ( c_Int_OPls ) 6.52/6.71 ( (c_Int_OBit1 c_Int_OPls) ) 6.52/6.71 ( c_Int_OMin ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Ominus__class_Ominus T_a))) (or (not (class_Groups_Oab__group__add T_a)) (= (hAPP (hAPP _let_0 V_b) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (hAPP (hAPP _let_0 V_a) V_b))))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Ozero__class_Ozero T_a)) V_a))) (= V_a (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a))) ) 6.52/6.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.71 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.52/6.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_Opred V_k) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_k) (c_Groups_Oone__class_Oone tc_Int_Oint))) ) 6.52/6.71 ( c_Int_OPls ) 6.52/6.71 ( c_Int_OMin ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Rings_Osemiring__1 T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (c_Groups_Oone__class_Oone T_b)) (c_Nat_Osemiring__1__class_ONats T_b)))) ) 6.52/6.71 ( tc_Nat_Onat ) 6.52/6.71 ( tc_Int_Oint ) 6.52/6.71 ( tc_Code__Numeral_Ocode__numeral ) 6.52/6.71 ) 6.52/6.71 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (hAPP (c_Relation_ODomain T_b T_c) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_c) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) ) 6.52/6.71 ( tc_Nat_Onat, tc_Nat_Onat ) 6.52/6.71 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.71 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.71 ) 6.52/6.72 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (c_Groups_Otimes__class_Otimes T_b))) (let ((_let_3 (c_Finite__Set_Ofold1 T_b _let_2))) (let ((_let_4 (c_Finite__Set_Ofinite T_b))) (or (not (class_Groups_Oab__semigroup__mult T_b)) (not (hBOOL (hAPP _let_4 V_A_2))) (= V_A_2 _let_1) (not (hBOOL (hAPP _let_4 V_B_2))) (= V_B_2 _let_1) (not (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2))) (= (hAPP (hAPP _let_2 (hAPP _let_3 V_A_2)) (hAPP _let_3 V_B_2)) (hAPP _let_3 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2))))))))) ) 6.52/6.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.72 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_1 (hAPP _let_0 V_a))) (or (not (class_Groups_Ocancel__ab__semigroup__add T_a)) (not (= (hAPP _let_1 V_c) (hAPP _let_1 V_b))) (= V_c V_b)))) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (T_d $$unsorted) (T_c $$unsorted)) (= (c_Product__Type_Omap__pair T_b T_b T_c T_d (c_Fun_Oid T_b) V_f_2) (c_Product__Type_Oapsnd T_c T_d T_b V_f_2)) ) 6.52/6.72 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint, tc_Int_Oint, tc_Int_Oint ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b T_c))) (or (not (class_Enum_Oenum T_b)) (not (class_Orderings_Oorder T_c)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_f_2) V_g_2)) (and (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_f_2) V_g_2)) (hBOOL (hAPP (c_Enum_Oenum__class_Oenum__ex T_b) (hAPP (hAPP (c_COMBB tc_HOL_Obool tc_HOL_Obool T_b) c_fNot) (hAPP (hAPP (c_COMBS T_b T_c tc_HOL_Obool) (hAPP (hAPP (c_COMBB T_c (tc_fun T_c tc_HOL_Obool) T_b) c_fequal) V_f_2)) V_g_2)))))))) ) 6.52/6.72 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus _let_0))) (= (hAPP _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) V_B_2)) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) (hAPP (hAPP (c_COMBB _let_0 _let_0 T_c) _let_1) V_B_2))))) ) 6.52/6.72 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.52/6.72 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.52/6.72 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (T_e $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_d $$unsorted) (BOUND_VARIABLE_129234 $$unsorted)) (or (not (= (hAPP (c_Fun_Ocomp T_d T_c T_b V_a_2) V_b_2) (hAPP (c_Fun_Ocomp T_e T_c T_b V_c_2) V_d_2))) (= (hAPP V_c_2 (hAPP V_d_2 BOUND_VARIABLE_129234)) (hAPP V_a_2 (hAPP V_b_2 BOUND_VARIABLE_129234)))) ) 6.52/6.72 ( c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Nat_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.72 ( c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Nat_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.52/6.72 ( c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Nat_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 6.52/6.72 ( c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Nat_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_w_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (or (not (class_Int_Onumber__ring T_b)) (not (class_Int_Oring__char__0 T_b)) (= (c_Int_Oiszero T_b (hAPP _let_0 (c_Int_OBit0 V_w_2))) (c_Int_Oiszero T_b (hAPP _let_0 V_w_2))))) ) 6.52/6.72 ( c_Int_OPls, tc_Nat_Onat ) 6.52/6.72 ( c_Int_OPls, tc_Int_Oint ) 6.52/6.72 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.52/6.72 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.52/6.72 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Finite__Set_Ocard T_b))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP _let_0 V_A_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))))) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.72 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.72 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Odistrib__lattice T_1)) (class_Lattices_Odistrib__lattice (tc_fun T_2 T_1))) ) 6.52/6.72 ( tc_HOL_Obool, tc_HOL_Obool ) 6.52/6.72 ( tc_Nat_Onat, tc_HOL_Obool ) 6.52/6.72 ( tc_Int_Oint, tc_HOL_Obool ) 6.52/6.72 ( tc_Int_Oint, tc_Int_Oint ) 6.52/6.72 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 6.52/6.72 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 6.52/6.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))), tc_HOL_Obool ) 6.52/6.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 6.52/6.72 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 6.52/6.72 ( (tc_Hoare__Mirabelle_Otriple t_a), tc_HOL_Obool ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_y_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (not (class_Int_Onumber__ring T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Int_OBit1 c_Int_OPls)) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Groups_Oone__class_Oone T_b)) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_y_2))))) ) 6.52/6.72 ( c_Int_OPls, tc_Nat_Onat ) 6.52/6.72 ( c_Int_OPls, tc_Int_Oint ) 6.52/6.72 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.52/6.72 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.52/6.72 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.52/6.72 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.52/6.72 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.72 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.52/6.72 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.52/6.72 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.52/6.72 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Big__Operators_Olinorder__class_OMin T_b V_A_2))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_B_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= _let_1 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) (c_Big__Operators_Olinorder__class_OMin T_b V_B_2)) _let_1))))) ) 6.52/6.72 ( v_G, v_Ga, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((BOUND_VARIABLE_129519 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_2 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_3 (hAPP _let_2 _let_0))) (let ((_let_4 (hBOOL (hAPP _let_3 BOUND_VARIABLE_129519)))) (let ((_let_5 (c_Groups_Osgn__class_Osgn tc_Int_Oint BOUND_VARIABLE_129519))) (or (= _let_0 BOUND_VARIABLE_129519) (and (or (not _let_4) (= _let_1 _let_5)) (or _let_4 (= (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) _let_1) _let_5)))))))))) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 6.52/6.72 ( c_Int_OPls ) 6.52/6.72 ( c_Int_OMin ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_SetInterval_Oord__class_OatLeast T_b))) (or (not (class_Orderings_Olinorder T_b)) (= (= V_y_2 V_x_2) (= (hAPP _let_0 V_y_2) (hAPP _let_0 V_x_2))))) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oab__group__add T_b)) (= (= V_b_2 V_a_2) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_b_2) (c_Groups_Ozero__class_Ozero T_b)))) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_x))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_z) V_y))) (hBOOL (hAPP (hAPP _let_0 V_z) V_x)))) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.72 ( c_Int_OMin, c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) (= V_x (hAPP (hAPP (c_Orderings_Oord__class_Omax T_a) V_x) V_y))) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.72 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.52/6.72 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.72 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.52/6.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.72 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_w $$unsorted)) (= (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w) (hAPP (c_Int_Oring__1__class_Oof__int tc_Int_Oint) V_w)) ) 6.52/6.72 ( c_Int_OPls ) 6.52/6.72 ( (c_Int_OBit1 c_Int_OPls) ) 6.52/6.72 ( c_Int_OMin ) 6.52/6.72 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.72 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_m $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) V_m)) (c_Groups_Ozero__class_Ozero T_a))))) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 6.52/6.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.52/6.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) V_n) (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_n))) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 6.52/6.72 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_k_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_k_2) (hAPP (c_Groups_Ouminus__class_Ouminus (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_k_2)))) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Groups_Oabs__class_Oabs T_a))) (let ((_let_1 (c_Groups_Ominus__class_Ominus T_a))) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (= (hAPP _let_0 (hAPP (hAPP _let_1 V_a) V_b)) (hAPP _let_0 (hAPP (hAPP _let_1 V_b) V_a)))))) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (= (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_x_2) V_y_2) (c_HOL_OThe (tc_prod T_b T_c) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c tc_HOL_Obool) (hAPP (hAPP (c_COMBC T_b _let_1 _let_1) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_1 _let_1) T_b) (c_COMBB tc_HOL_Obool tc_HOL_Obool T_c)) (hAPP (hAPP (c_COMBB tc_HOL_Obool _let_0 T_b) c_fconj) (hAPP c_fequal V_x_2)))) (hAPP c_fequal V_y_2))))))) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 6.52/6.72 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 6.52/6.72 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.52/6.72 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool))) ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (not (class_Int_Onumber__ring T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_x_2)) (c_Groups_Ozero__class_Ozero T_b))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_x_2) c_Int_OPls)))) ) 6.52/6.72 ( c_Int_OPls, tc_Nat_Onat ) 6.52/6.72 ( c_Int_OPls, tc_Int_Oint ) 6.52/6.72 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 6.52/6.72 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 6.52/6.72 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 6.52/6.72 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 6.52/6.72 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.72 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.52/6.72 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.52/6.72 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 6.52/6.72 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Finite__Set_Ofun__left__comm T_b T_c V_f_2)) (c_Finite__Set_Ofun__left__comm T_d T_c (hAPP (hAPP (c_COMBB T_b (tc_fun T_c T_c) T_d) V_f_2) V_g_2))) ) 6.52/6.72 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint, c_fconj, tc_HOL_Obool, tc_HOL_Obool ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) ) 6.52/6.72 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 6.52/6.72 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 6.52/6.72 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 6.52/6.72 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 6.52/6.72 ) 6.52/6.72 (instantiation (forall ((V_x_2 $$unsorted) (V_P_2 $$unsorted)) (or (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) B_y) c_Int_OInteg))) (hBOOL (hAPP V_P_2 (hAPP c_Int_OAbs__Integ B_y)))) )) (hBOOL (hAPP V_P_2 V_x_2))) ) 6.52/6.72 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.52/6.72 ( c_Nat_OSuc, (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Nat__Numeral_Oneg ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert tc_Nat_Onat) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat__Numeral_Oneg ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_Onat ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))))) ) 6.52/6.72 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.52/6.72 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.52/6.72 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 6.52/6.72 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 6.52/6.72 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 6.52/6.72 ( c_fequal, (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.52/6.72 ( c_fequal, (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) ) 6.52/6.72 ( (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (c_COMBB _let_1 _let_1 tc_Int_Oint))) ) 6.52/6.72 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat) ) 6.52/6.72 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Nat_Onat) ) 6.52/6.72 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.52/6.72 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Set_Oimage tc_Nat_Onat tc_Nat_Onat c_Nat_OSuc) ) 6.52/6.72 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 6.52/6.72 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) ) 6.52/6.72 ( c_fconj, (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Oint__of ) 6.52/6.72 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral) ) 6.52/6.72 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.52/6.72 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.52/6.72 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 6.52/6.72 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.52/6.72 ( c_Int_Ointrel, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool)))) ) 6.52/6.72 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Product__Type_OPair _let_1 _let_1))) ) 6.52/6.72 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_1 _let_1) (c_Orderings_Obot__class_Obot _let_1)))) ) 6.52/6.72 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0))) ) 6.52/6.72 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 6.52/6.72 ( c_Int_OMin, (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 6.52/6.72 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) ) 6.52/6.72 ( c_Int_OMin, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 6.52/6.72 ( c_Int_OMin, (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 6.52/6.72 ( c_Int_OMin, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.52/6.72 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 6.52/6.72 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 6.52/6.72 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 6.52/6.72 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.52/6.72 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) ) 6.52/6.72 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.52/6.72 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.52/6.72 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Nat_OSuc ) 6.52/6.72 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc ) 6.52/6.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.52/6.72 ( c_Int_Onat, (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat) ) 6.52/6.72 ( c_Code__Numeral_Onat__of, (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) ) 6.52/6.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.52/6.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 6.52/6.72 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) ) 6.52/6.72 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 6.52/6.72 ( c_Nitpick_Oint__gcd, (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal))) ) 6.52/6.72 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.52/6.72 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 6.52/6.72 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 6.52/6.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 6.52/6.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 6.52/6.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 6.52/6.72 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))) ) 6.52/6.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_1 _let_1)))) ) 6.52/6.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (c_Set_Oinsert (tc_prod (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1)))) ) 6.52/6.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 c_FunDef_Opair__leq)))) ) 6.52/6.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 c_FunDef_Opair__leq)))) ) 6.52/6.72 ( c_FunDef_Omax__weak, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omax__strict))))) ) 6.52/6.72 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral)) ) 6.52/6.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin), c_Nat__Numeral_Oneg ) 6.52/6.72 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))) ) 6.52/6.72 ( c_FunDef_Omin__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))) ) 6.52/6.72 ( c_fFalse, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 6.52/6.72 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.52/6.72 ( v_Ga, (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) v_G) ) 6.52/6.72 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (c_Orderings_Otop__class_Otop _let_0))) ) 6.52/6.72 ( c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 6.52/6.72 ( c_fTrue, (c_COMBK tc_HOL_Obool tc_Nat_Onat) ) 6.52/6.72 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) c_FunDef_Opair__less)) ) 6.52/6.72 ( (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) ) 6.52/6.72 ( (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (c_COMBB _let_0 _let_0 tc_Int_Oint)) ) 6.52/6.72 ( (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal), (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) tc_Int_Oint) ) 6.52/6.72 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)))) ) 6.52/6.72 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)))), (c_COMBC tc_Int_Oint tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 6.52/6.72 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 6.52/6.72 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), (c_Product__Type_Oprod_Oprod__case tc_Int_Oint tc_Int_Oint tc_HOL_Obool) ) 6.52/6.72 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)))) ) 6.52/6.72 ( c_FunDef_Omin__weak, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_3 _let_3) c_FunDef_Omin__strict))))) ) 6.52/6.74 ( c_FunDef_Omax__strict, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_prod _let_1 _let_1))) (let ((_let_3 (tc_fun _let_2 tc_HOL_Obool))) (c_Product__Type_OPair _let_3 _let_3))))) ) 6.52/6.74 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Int_Oint) ) 6.52/6.74 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Finite__Set_Ocard tc_Product__Type_Ounit) ) 6.52/6.74 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat)), (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.52/6.74 ( (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal), (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) ) 6.52/6.74 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 6.52/6.74 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)), (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.52/6.74 ( v_G, (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool)) ) 6.52/6.74 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), (c_Finite__Set_Ocard tc_HOL_Obool) ) 6.52/6.74 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.52/6.74 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)) ) 6.52/6.74 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))), c_Int_OAbs__Integ ) 6.52/6.74 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 6.52/6.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel)) ) 6.52/6.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), c_Int_OAbs__Integ ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (hAPP c_Nat_OSuc _let_0))) (= (or (and (= _let_1 V_n_2) (= _let_0 V_m_2)) (and (= _let_1 V_m_2) (= _let_0 V_n_2))) (= _let_1 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m_2) V_n_2))))) ) 6.52/6.74 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (c_Groups_Ozero__class_Ozero T_a) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) V_a))) ) 6.52/6.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Int_Oring__1__class_OInts T_b))) (or (not (class_Rings_Oring__1 T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) _let_1))))) ) 6.52/6.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( c_Int_OMin, tc_Int_Oint ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Int_Oring__1__class_OInts T_b))) (or (not (class_Rings_Oring__1 T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 V_b_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_b_2)) _let_1))))) ) 6.52/6.74 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_w $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (hAPP _let_0 _let_1))) (let ((_let_3 (c_Groups_Oplus__class_Oplus tc_Int_Oint))) (let ((_let_4 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_5 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_6 (hAPP _let_3 _let_4))) (let ((_let_7 (hAPP _let_5 V_w))) (let ((_let_8 (hAPP _let_6 _let_7))) (let ((_let_9 (c_Divides_OnegDivAlg _let_4 _let_7))) (let ((_let_10 (hBOOL (hAPP _let_2 _let_8)))) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_1) _let_7))) (and (or (not _let_10) (= (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) (hAPP _let_5 c_Int_OMin)) _let_8) _let_9)) (or _let_10 (= _let_9 (hAPP (c_Divides_Oadjust _let_7) (c_Divides_OnegDivAlg _let_4 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP _let_5 (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) _let_7)))))))))))))))))) ) 6.52/6.74 ( c_Int_OPls ) 6.52/6.74 ( (c_Int_OBit1 c_Int_OPls) ) 6.52/6.74 ( c_Int_OMin ) 6.52/6.74 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.74 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (or (not (class_Orderings_Olinorder T_b)) (= (not (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2))) (or (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2)) (= V_y_2 V_x_2))))) ) 6.52/6.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 6.52/6.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.52/6.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_A_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Relation_OImage T_b T_b V_r_2))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (or (not (= (hAPP _let_0 (hAPP (hAPP _let_1 V_a_2) _let_2)) (hAPP _let_0 (hAPP (hAPP _let_1 V_b_2) _let_2)))) (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_b_2) V_A_2))) (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_b_2)) V_r_2)))))) ) 6.52/6.74 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (or (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP _let_0 (c_Groups_Osgn__class_Osgn T_b V_a_2)) _let_1)) (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)))))) ) 6.52/6.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_N_2 $$unsorted) (V_h_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (= (hAPP V_h_2 (hAPP (hAPP _let_0 B_x) B_y)) (hAPP (hAPP _let_0 (hAPP V_h_2 B_x)) (hAPP V_h_2 B_y)))) )) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (= V_N_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP V_h_2 (c_Big__Operators_Olinorder__class_OMax T_b V_N_2)) (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (c_Set_Oimage T_b T_b V_h_2) V_N_2)))) ) 6.52/6.74 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_b))) (or (not (class_Rings_Olinordered__semidom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP _let_0 V_m_2)) (hAPP _let_0 V_n_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_n_2))))) ) 6.52/6.74 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.52/6.74 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.52/6.74 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.52/6.74 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2)) (= (hAPP (c_Finite__Set_Ocard T_c) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)) (hAPP (c_Finite__Set_Ocard T_b) V_A_2))) ) 6.52/6.74 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 6.52/6.74 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.52/6.74 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.52/6.74 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (forall ((B_x $$unsorted)) (let ((_let_0 (c_member T_b))) (let ((_let_1 (hAPP _let_0 B_x))) (or (not (hBOOL (hAPP _let_1 V_A_2))) (hBOOL (hAPP _let_1 V_B_2))))) )) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2))) ) 6.52/6.74 ( v_Ga, v_G, (tc_Hoare__Mirabelle_Otriple t_a) ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (c_Set_Oimage T_c T_b V_f_2))) (= (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_c) V_a_2) V_B_2)) (hAPP (hAPP (c_Set_Oinsert T_b) (hAPP V_f_2 V_a_2)) (hAPP _let_0 V_B_2)))) ) 6.52/6.74 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= V_a_2 (c_Complete__Lattice_OSup__class_OSup T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 6.52/6.74 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 6.52/6.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_0 tc_HOL_Obool)) _let_1) _let_1))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.74 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.74 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__inf__class_Oinf T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Lattices_Osemilattice__inf__class_Oinf _let_1))) (let ((_let_3 (hAPP _let_2 V_A_2))) (let ((_let_4 (hAPP _let_3 V_B_2))) (let ((_let_5 (c_Finite__Set_Ofinite T_b))) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP _let_5 V_A_2))) (not (hBOOL (hAPP _let_5 V_B_2))) (= _let_4 (c_Orderings_Obot__class_Obot _let_1)) (= (hAPP (hAPP _let_0 (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2))) (c_Big__Operators_Olattice__class_OInf__fin T_b _let_4)) (hAPP (hAPP _let_0 (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OInf__fin T_b V_B_2)))))))))) ) 6.52/6.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tc_prod _let_1 _let_1))) (hAPP (hAPP (c_Set_Oinsert _let_3) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) _let_2) _let_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_3 tc_HOL_Obool))))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.74 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2))) (= (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2))) (= V_y_2 V_x_2))) ) 6.52/6.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 6.52/6.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 6.52/6.74 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 6.52/6.74 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 6.52/6.74 ( v_Ga, v_G, (tc_fun (tc_Hoare__Mirabelle_Otriple t_a) tc_HOL_Obool) ) 6.52/6.74 ) 6.52/6.74 (instantiation (forall ((T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (not (= (c_Orderings_Otop__class_Otop _let_0) (c_Orderings_Obot__class_Obot _let_0)))) ) 6.52/6.74 ( tc_HOL_Obool ) 6.52/6.74 ( tc_Nat_Onat ) 6.52/6.74 ( tc_Int_Oint ) 6.52/6.74 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 6.52/6.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_prod _let_1 _let_1))) ) 6.52/6.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 6.52/6.74 ( tc_Product__Type_Ounit ) 6.52/6.74 ( (tc_Hoare__Mirabelle_Otriple t_a) ) 6.52/6.74 ) 6.52/6.74 % SZS output end Proof for theBenchmark 6.52/6.76 EOF