0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : do_CVC4 %s 0.02/0.24 % Computer : n117.star.cs.uiowa.edu 0.02/0.24 % Model : x86_64 x86_64 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.24 % Memory : 32218.625MB 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.24 % CPULimit : 300 0.02/0.24 % DateTime : Sat Jul 14 06:00:09 CDT 2018 0.02/0.24 % CPUTime : 0.80/1.02 %----Proving without arithmetic mode 0.80/1.02 ------- cvc4-fof casc j9 : /export/starexec/sandbox/benchmark/theBenchmark.p at ... 0.80/1.03 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 5.21/5.45 % SZS status Theorem for theBenchmark 5.21/5.45 % SZS output start Proof for theBenchmark 5.21/5.45 (skolem (forall ((B_Z $$unsorted)) (or (not (v_P B_Z v_s0)) (and (not (hBOOL (hAPP v_b v_s2))) (v_P B_Z v_s2))) ) 5.21/5.45 ( skv_1 ) 5.21/5.45 ) 5.21/5.45 (skolem (forall ((V_h_2 $$unsorted) (V_g_2 $$unsorted) (T_g $$unsorted) (V_f_2 $$unsorted) (T_d $$unsorted) (T_e $$unsorted) (T_f $$unsorted)) (= (hAPP (c_Fun_Ocomp T_f T_e T_d V_f_2) (hAPP (c_Fun_Ocomp T_g T_f T_d V_g_2) V_h_2)) (hAPP (c_Fun_Ocomp T_g T_e T_d (hAPP (c_Fun_Ocomp T_f T_e T_g V_f_2) V_g_2)) V_h_2)) ) 5.21/5.45 ( skv_2 skv_3 skv_4 skv_5 skv_6 skv_7 skv_8 ) 5.21/5.45 ) 5.21/5.45 (skolem (let ((_let_0 (tc_prod tc_Com_Opname tc_Com_Ocom))) (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_0) B_x) (hAPP (c_List_Oset _let_0) c_Com_Obodies)))) (hBOOL (hAPP (hAPP (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool) (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT)) B_x))) )) 5.21/5.45 ( skv_9 ) 5.21/5.45 ) 5.21/5.45 (skolem (forall ((V_b $$unsorted) (V_pn $$unsorted)) (or (not (= (hAPP c_Com_Obody V_pn) (hAPP (c_Option_Ooption_OSome tc_Com_Ocom) V_b))) (hBOOL (hAPP c_Com_OWT V_b))) ) 5.21/5.48 ( skv_10 skv_11 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_Z $$unsorted)) (or (not (v_P B_Z v_s0)) (and (v_P B_Z v_s1) (not (hBOOL (hAPP v_b v_s1))))) ) 5.21/5.48 ( skv_12 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_n $$unsorted)) (or (not (= (c_Groups_Oone__class_Oone tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) B_n)))) ) 5.21/5.48 ( skv_13 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_y $$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 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) (hAPP c_Int_OAbs__Integ B_y)))) ) 5.21/5.48 ( skv_14 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) B_y) c_Int_OInteg))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) (hAPP c_Int_OAbs__Integ B_y)))) ) 5.21/5.48 ( skv_15 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_y $$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 c_Nat__Numeral_Oneg (hAPP c_Int_OAbs__Integ B_y)))) ) 5.21/5.48 ( skv_16 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) B_y) c_Int_OInteg))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) (hAPP c_Int_OAbs__Integ B_y)))) ) 5.21/5.48 ( skv_17 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_y $$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 (c_Finite__Set_Ofinite tc_Int_Oint) (hAPP c_Int_OAbs__Integ B_y)))) ) 5.21/5.48 ( skv_18 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) B_y) c_Int_OInteg))) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ) 5.21/5.48 ( skv_19 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_n $$unsorted)) (not (= c_Int_OMin (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))))) ) 5.21/5.48 ( skv_20 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_n $$unsorted)) (not (= (c_Groups_Oone__class_Oone tc_Int_Oint) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Nat_OSuc B_n))))) ) 5.21/5.48 ( skv_21 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_n $$unsorted)) (not (= (c_Groups_Ozero__class_Ozero tc_Int_Oint) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) c_Int_OMin) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Nat_OSuc B_n))))) ) 5.21/5.48 ( skv_22 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_n $$unsorted) (B_f $$unsorted)) (not (= (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody) (hAPP (c_Set_Oimage tc_Nat_Onat tc_Com_Opname 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))))) ) 5.21/5.48 ( skv_23 skv_24 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_n $$unsorted)) (not (= (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) ) 5.21/5.48 ( skv_25 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_n $$unsorted)) (not (= (c_Groups_Oone__class_Oone tc_Int_Oint) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) ) 5.21/5.48 ( skv_26 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_n $$unsorted)) (not (= c_Int_OPls (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) c_Int_OMin) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) ) 5.21/5.48 ( skv_27 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_n $$unsorted)) (not (= c_Int_OMin (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) c_Int_OMin) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) ) 5.21/5.48 ( skv_28 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_n $$unsorted)) (not (= (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) ) 5.21/5.48 ( skv_29 ) 5.21/5.48 ) 5.21/5.48 (skolem (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((B_n $$unsorted)) (not (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) _let_0) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) )) 5.21/5.48 ( skv_30 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member tc_HOL_Obool) B_x) (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool))))) ) 5.21/5.48 ( skv_31 ) 5.21/5.48 ) 5.21/5.48 (skolem (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member tc_Product__Type_Ounit) B_x) (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool))))) ) 5.21/5.48 ( skv_32 ) 5.21/5.48 ) 5.21/5.48 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Orefl__on T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) (c_Relation_OId T_b)) ) 5.21/5.48 ( tc_Com_Ocom ) 5.21/5.48 ( tc_Nat_Onat ) 5.21/5.48 ( tc_HOL_Obool ) 5.21/5.48 ( tc_Int_Oint ) 5.21/5.48 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.21/5.48 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.21/5.48 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.21/5.48 ( tc_Product__Type_Ounit ) 5.21/5.48 ) 5.21/5.48 (instantiation (forall ((V_z_2 $$unsorted) (V_m_2 $$unsorted)) (= (= V_z_2 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2)) (and (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_2)) (= V_m_2 (hAPP c_Int_Onat V_z_2)))) ) 5.21/5.48 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.48 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.48 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.48 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.48 ) 5.21/5.48 (instantiation (forall ((V_xs_2 $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) (hAPP (c_List_Oset T_b) V_xs_2))) (hAPP (c_Nat_Osize__class_Osize (tc_List_Olist T_b)) V_xs_2))) ) 5.21/5.48 ( c_Com_Obodies, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.21/5.48 ) 5.21/5.48 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit0 V_k_2)) (c_Int_OBit1 V_l_2))) (hBOOL (hAPP (hAPP _let_0 V_k_2) V_l_2))) )) 5.21/5.48 ( c_Int_OMin, c_Int_OPls ) 5.21/5.48 ) 5.21/5.48 (instantiation (let ((_let_0 (tc_Option_Ooption T_b))) (forall ((V_xys_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (c_Finite__Set_Ofinite _let_0) (hAPP (c_Set_Oimage T_c _let_0 (c_Map_Omap__of T_c T_b V_xys_2)) (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool))))) )) 5.21/5.48 ( c_Com_Obodies, tc_Com_Opname, tc_Com_Ocom ) 5.21/5.48 ) 5.21/5.48 (instantiation (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (tc_fun (tc_fun _let_0 tc_HOL_Obool) tc_HOL_Obool))) (let ((_let_3 (tc_fun T_b _let_2))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun _let_0 tc_HOL_Obool))) (= (c_Wellfounded_OwfP T_b (hAPP (hAPP (c_COMBC T_b _let_0 _let_1) (hAPP (hAPP (c_COMBB _let_3 (tc_fun _let_0 _let_1) T_b) (c_COMBC T_b _let_0 tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun T_b _let_0) _let_3 T_b) (hAPP (c_COMBB _let_0 _let_2 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))) ))))) 5.21/5.48 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.21/5.48 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.21/5.48 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 5.21/5.48 ( (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 ) 5.21/5.48 ) 5.21/5.48 (instantiation (forall ((V_z $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_z))) ) 5.21/5.48 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.48 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.48 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.48 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.48 ) 5.21/5.48 (instantiation (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (= (c_Wellfounded_Owf T_b (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP _let_1 V_y_2) V_x_2)) V_r_2)) (and (c_Wellfounded_Owf T_b V_r_2) (not (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP _let_1 V_x_2) V_y_2)) (c_Transitive__Closure_Ortrancl T_b V_r_2)))))) ))) 5.21/5.48 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.21/5.48 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.21/5.48 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.21/5.48 ) 5.21/5.48 (instantiation (forall ((V_ca_2 $$unsorted) (T_b $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_ca_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 5.21/5.48 ( skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.21/5.48 ) 5.21/5.48 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) ) 5.21/5.48 ( skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.21/5.48 ) 5.21/5.48 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 V_k_2) c_Int_OPls)) (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k_2)) c_Int_OPls))) )) 5.21/5.48 ( c_Int_OPls ) 5.21/5.48 ( (c_Int_OBit1 c_Int_OPls) ) 5.21/5.48 ( c_Int_OMin ) 5.21/5.48 ) 5.21/5.48 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite (tc_prod T_b T_b)))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP _let_0 V_r_2)) (hBOOL (hAPP _let_0 (c_Transitive__Closure_Otrancl T_b V_r_2)))) )) 5.21/5.48 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.21/5.48 ) 5.21/5.48 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_prod T_b T_b))) (let ((_let_2 (tc_fun (tc_fun _let_1 tc_HOL_Obool) tc_HOL_Obool))) (let ((_let_3 (tc_fun T_b _let_2))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun _let_1 tc_HOL_Obool))) (= (c_Equiv__Relations_Oequiv T_b (c_Orderings_Otop__class_Otop _let_0) V_A_2) (c_Equiv__Relations_Oequivp T_b (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (hAPP (hAPP (c_COMBB _let_3 (tc_fun _let_0 _let_0) T_b) (c_COMBC T_b _let_0 tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun T_b _let_1) _let_3 T_b) (hAPP (c_COMBB _let_1 _let_2 T_b) (c_member _let_1))) (c_Product__Type_OPair T_b T_b)))) V_A_2)))) ))))) 5.21/5.48 ( c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.21/5.48 ) 5.21/5.48 (instantiation (forall ((V_n $$unsorted)) (= V_n (hAPP (c_Nat_Osize__class_Osize tc_Nat_Onat) V_n)) ) 5.21/5.48 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.48 ) 5.21/5.48 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 V_k_2) V_l_2)) (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit0 V_k_2)) (c_Int_OBit0 V_l_2)))) )) 5.21/5.49 ( c_Int_OPls, c_Int_OPls ) 5.21/5.49 ) 5.21/5.49 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) _let_0)) (hBOOL (hAPP _let_0 V_x_2))) )) 5.21/5.49 ( skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.21/5.49 ) 5.21/5.49 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (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))) )) 5.21/5.49 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.21/5.49 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.21/5.49 ( (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)) ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_v_2 $$unsorted)) (= (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred V_v_2)))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v_2))) ) 5.21/5.49 ( c_Int_OPls ) 5.21/5.49 ( (c_Int_OBit1 c_Int_OPls) ) 5.21/5.49 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.21/5.49 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.21/5.49 ( c_Int_OMin ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) V_A_2))) ) 5.21/5.49 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.21/5.49 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 5.21/5.49 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 5.21/5.49 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.21/5.49 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_B_2))) ) 5.21/5.49 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.21/5.49 ( (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) ) 5.21/5.49 ( (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) ) 5.21/5.49 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.21/5.49 ) 5.21/5.49 (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))) ) 5.21/5.49 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_A_2 $$unsorted)) (= V_A_2 (hAPP (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) (hAPP (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) V_A_2))) ) 5.21/5.49 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 5.21/5.49 ) 5.21/5.49 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (forall ((V_w_2 $$unsorted)) (= (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP _let_0 V_w_2))) (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP _let_0 (c_Int_OBit0 V_w_2))))) )) 5.21/5.49 ( c_Int_OPls ) 5.21/5.49 ( (c_Int_OBit1 c_Int_OPls) ) 5.21/5.49 ( c_Int_OMin ) 5.21/5.49 ) 5.21/5.49 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2))) (hBOOL (hAPP _let_0 V_A_2))) )) 5.21/5.49 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.21/5.49 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.21/5.49 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.21/5.49 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.21/5.49 ) 5.21/5.49 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 V_k_2)) (hBOOL (hAPP _let_0 (c_Int_OBit0 V_k_2)))) )) 5.21/5.49 ( c_Int_OPls ) 5.21/5.49 ( (c_Int_OBit1 c_Int_OPls) ) 5.21/5.49 ( c_Int_OMin ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_w $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_w) V_w)) ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.49 ( c_Int_OMin ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) V_k_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) (c_Int_OBit0 V_k_2)))) ) 5.21/5.49 ( c_Int_OPls ) 5.21/5.49 ( (c_Int_OBit1 c_Int_OPls) ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.49 ( c_Int_OMin ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_n) (hAPP c_Nat_OSuc V_n))) ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.21/5.49 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((T_b $$unsorted)) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 5.21/5.49 ( tc_Com_Ocom ) 5.21/5.49 ( tc_Nat_Onat ) 5.21/5.49 ( tc_HOL_Obool ) 5.21/5.49 ( tc_Int_Oint ) 5.21/5.49 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.21/5.49 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.21/5.49 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.21/5.49 ( tc_Com_Opname ) 5.21/5.49 ( tc_Product__Type_Ounit ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Nat_OSuc V_n)))) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.21/5.49 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_n))) ) 5.21/5.49 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_k $$unsorted)) (not (= c_Int_OMin (c_Int_OBit0 V_k))) ) 5.21/5.49 ( c_Int_OPls ) 5.21/5.49 ( (c_Int_OBit1 c_Int_OPls) ) 5.21/5.49 ( c_Int_OMin ) 5.21/5.49 ) 5.21/5.49 (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))) ) 5.21/5.49 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_nat_H_1 $$unsorted)) (not (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP c_Nat_OSuc V_nat_H_1))) ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.21/5.49 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_z_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2)) V_z_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) (hAPP c_Int_Onat V_z_2)))) ) 5.21/5.49 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_n $$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))) ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.21/5.49 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((T_a $$unsorted)) (hBOOL (hAPP (c_List_Odistinct T_a) (c_List_Olist_ONil T_a))) ) 5.21/5.49 ( tc_Nat_Onat ) 5.21/5.49 ( tc_Int_Oint ) 5.21/5.49 ) 5.21/5.49 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP _let_0 V_n))) (hAPP _let_0 V_m))) )) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.49 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ) 5.21/5.49 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k1_2)) (c_Int_OBit1 V_k2_2))) (hBOOL (hAPP (hAPP _let_0 V_k1_2) V_k2_2))) )) 5.21/5.49 ( c_Int_OMin, c_Int_OMin ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_k_2 $$unsorted)) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) V_k_2))) ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ) 5.21/5.49 (instantiation (let ((_let_0 (c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted)) (= _let_0 (hAPP (c_List_Otl T_a) _let_0)) )) 5.21/5.49 ( tc_Nat_Onat ) 5.21/5.49 ( tc_Int_Oint ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_v_2 $$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))) ) 5.21/5.49 ( c_Int_OPls ) 5.21/5.49 ( (c_Int_OBit1 c_Int_OPls) ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.49 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.21/5.49 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.21/5.49 ( c_Int_OMin ) 5.21/5.49 ) 5.21/5.49 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (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))) )) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_n_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_n_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n_2)))) ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.49 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.49 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.49 ) 5.21/5.49 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) V_n_2)) (hBOOL (hAPP (hAPP (c_member (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_m_2) V_n_2)) (c_Transitive__Closure_Otrancl tc_Nat_Onat c_Wellfounded_Opred__nat)))) ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.49 ) 5.21/5.49 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Obot__class_Obot (tc_fun T_b (tc_fun T_c tc_HOL_Obool))) V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_x_2) V_y_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))) )) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.21/5.49 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.21/5.49 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.21/5.49 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.21/5.50 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_n $$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)))))) ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.50 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.21/5.50 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.21/5.50 ) 5.21/5.50 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (forall ((V_Ga_2 $$unsorted) (V_F_2 $$unsorted) (T_b $$unsorted)) (= (and (hBOOL (hAPP _let_0 V_F_2)) (hBOOL (hAPP _let_0 V_Ga_2))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_F_2) V_Ga_2)))) )) 5.21/5.50 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.21/5.50 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.21/5.50 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (= V_x (hAPP (c_Option_Othe T_a) (hAPP (c_Option_Ooption_OSome T_a) V_x))) ) 5.21/5.50 ( skv_10, tc_Com_Ocom ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_k_2) V_l_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Int_OBit1 V_k_2)) (c_Int_OBit0 V_l_2)))) ) 5.21/5.50 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( c_Int_OPls, c_Int_OMin ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( c_Int_OMin, c_Int_OMin ) 5.21/5.50 ) 5.21/5.50 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m_2) V_n_2))) (or (hBOOL (hAPP _let_0 V_m_2)) (hBOOL (hAPP _let_0 V_n_2)))) )) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_j) V_i)) V_i))) ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.50 ) 5.21/5.50 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_w_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_1 (c_Int_OBit0 V_w_2)) _let_0)) (hBOOL (hAPP (hAPP _let_1 V_w_2) _let_0))) ))) 5.21/5.50 ( c_Int_OPls ) 5.21/5.50 ( (c_Int_OBit1 c_Int_OPls) ) 5.21/5.50 ( c_Int_OMin ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_z_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_z_2))) ) 5.21/5.50 ( c_Int_OPls ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.21/5.50 ( c_Int_OMin ) 5.21/5.50 ) 5.21/5.50 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (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))) )) 5.21/5.50 ( 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)) ) 5.21/5.50 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.21/5.50 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.21/5.50 ) 5.21/5.50 (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))) ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.50 ) 5.21/5.50 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (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)))) )) 5.21/5.50 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( c_Int_OMin, c_Int_OMin ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((T_b $$unsorted)) (c_Wellfounded_Owf (tc_fun T_b tc_HOL_Obool) (c_Wellfounded_Ofinite__psubset T_b)) ) 5.21/5.50 ( tc_Com_Ocom ) 5.21/5.50 ( tc_Nat_Onat ) 5.21/5.50 ( tc_HOL_Obool ) 5.21/5.50 ( tc_Int_Oint ) 5.21/5.50 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.21/5.50 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.21/5.50 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.21/5.50 ( tc_Product__Type_Ounit ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_z_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_z_2)) (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)))) ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.21/5.50 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.50 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_x_2 $$unsorted)) (= (c_Nat__Transfer_Ois__nat V_x_2) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_x_2))) ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.21/5.50 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.50 ( c_Int_OMin ) 5.21/5.50 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.50 ) 5.21/5.50 (instantiation (let ((_let_0 (c_List_Odistinct T_b))) (forall ((V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP _let_0 (hAPP (hAPP (c_List_Olist_OCons T_b) V_x_2) V_xs_2))) (and (hBOOL (hAPP _let_0 V_xs_2)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) (hAPP (c_List_Oset T_b) V_xs_2)))))) )) 5.21/5.50 ( c_Com_Obodies, skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_m $$unsorted)) (= V_m (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_m)) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))))) ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.50 ) 5.21/5.50 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit0 V_k_2)) (c_Int_OBit0 V_l_2))) (hBOOL (hAPP (hAPP _let_0 V_k_2) V_l_2))) )) 5.21/5.50 ( c_Int_OPls, c_Int_OPls ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_k_2 $$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))) ) 5.21/5.50 ( c_Int_OPls ) 5.21/5.50 ( (c_Int_OBit1 c_Int_OPls) ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( c_Int_OMin ) 5.21/5.50 ) 5.21/5.50 (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)))) ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.50 ) 5.21/5.50 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k1_2)) (c_Int_OBit1 V_k2_2))) (hBOOL (hAPP (hAPP _let_0 V_k1_2) V_k2_2))) )) 5.21/5.50 ( c_Int_OMin, c_Int_OMin ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_k1_2) V_k2_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_OBit0 V_k1_2)) (c_Int_OBit1 V_k2_2)))) ) 5.21/5.50 ( c_Int_OPls, c_Int_OMin ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( (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) ) 5.21/5.50 ( c_Int_OMin, c_Int_OPls ) 5.21/5.50 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( c_Int_OMin, c_Int_OMin ) 5.21/5.50 ( (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) ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((T_a $$unsorted)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Nat_Osize__class_Osize (tc_List_Olist T_a)) (c_List_Olist_ONil T_a))) ) 5.21/5.50 ( tc_Nat_Onat ) 5.21/5.50 ( tc_Int_Oint ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Osingle__valued T_b T_b (c_Relation_OId T_b)) ) 5.21/5.50 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.21/5.50 ) 5.21/5.50 (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) V_z_2)) (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))))) ) 5.21/5.50 ( c_Int_OPls, c_Int_OMin ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( (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) ) 5.21/5.50 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.21/5.50 ( c_Int_OMin, c_Int_OMin ) 5.21/5.50 ( (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) ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_n $$unsorted)) (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n)))) ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.50 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.50 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_a_2 $$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))) ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.21/5.50 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.21/5.50 ( (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) ) 5.21/5.50 ( (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) ) 5.21/5.50 ) 5.21/5.50 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) (hAPP (c_COMBK _let_0 T_c) _let_1))) ))) 5.21/5.50 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_a_2)) (c_Relation_OId T_b))) ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.21/5.50 ( c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.21/5.50 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.21/5.50 ( c_FunDef_Omax__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP V_A_2 V_x_2)) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) ) 5.21/5.50 ( (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((T_b $$unsorted)) (c_Wellfounded_Owf T_b (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) ) 5.21/5.50 ( tc_Nat_Onat ) 5.21/5.50 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.21/5.50 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.21/5.50 ) 5.21/5.50 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_k_2 $$unsorted)) (= (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))) )) 5.21/5.50 ( c_Int_OPls ) 5.21/5.50 ( (c_Int_OBit1 c_Int_OPls) ) 5.21/5.50 ( c_Int_OMin ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_xs_2 $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (hAPP (c_List_Oset T_b) V_xs_2))) ) 5.21/5.50 ( c_Com_Obodies, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.21/5.50 ) 5.21/5.50 (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)))) ) 5.21/5.50 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 5.21/5.50 ( (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 ) 5.21/5.50 ( (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 ) 5.21/5.50 ) 5.21/5.50 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n))) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 5.21/5.50 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.21/5.50 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.50 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.21/5.50 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.21/5.50 ) 5.21/5.50 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_k_2 $$unsorted)) (= (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))) )) 5.21/5.50 ( c_Int_OPls ) 5.21/5.50 ( (c_Int_OBit1 c_Int_OPls) ) 5.21/5.50 ( c_Int_OMin ) 5.21/5.50 ) 5.21/5.50 (instantiation (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))) (forall ((T_c $$unsorted) (T_b $$unsorted)) (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))) ))))) 5.21/5.50 ( tc_Com_Ocom, tc_Com_Opname ) 5.21/5.50 ( tc_Nat_Onat, tc_Nat_Onat ) 5.21/5.50 ( tc_HOL_Obool, tc_Int_Oint ) 5.21/5.50 ( tc_Int_Oint, tc_Int_Oint ) 5.21/5.50 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.21/5.50 ( (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) ) 5.21/5.50 ) 5.21/5.50 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$unsorted)) (c_Finite__Set_Ofun__left__comm__idem T_b _let_0 (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_0 _let_0) T_b) (hAPP (c_COMBC _let_0 _let_0 _let_0) (c_Groups_Ominus__class_Ominus _let_0))) (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (c_Set_Oinsert T_b)) (c_Orderings_Obot__class_Obot _let_0)))) )) 5.21/5.50 ( tc_Com_Ocom ) 5.21/5.50 ( tc_Nat_Onat ) 5.21/5.50 ( tc_HOL_Obool ) 5.21/5.50 ( tc_Int_Oint ) 5.21/5.50 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.21/5.50 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.50 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.50 ( tc_Product__Type_Ounit ) 5.29/5.50 ) 5.29/5.50 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_1 V_k_2) V_l_2)) (hBOOL (hAPP (hAPP _let_1 (hAPP _let_0 V_k_2)) (hAPP _let_0 V_l_2)))) ))) 5.29/5.50 ( c_Int_OPls, c_Int_OPls ) 5.29/5.50 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls ) 5.29/5.50 ) 5.29/5.50 (instantiation (forall ((V_a1_2 $$unsorted) (V_a2_2 $$unsorted)) (= (hBOOL (hAPP c_Com_OWT V_a1_2)) (hBOOL (hAPP c_Com_OWT (c_Com_Ocom_OWhile V_a2_2 V_a1_2)))) ) 5.29/5.50 ( v_c, v_b ) 5.29/5.50 ) 5.29/5.50 (instantiation (forall ((V_C_2 $$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)) ) 5.29/5.50 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 5.29/5.50 ) 5.29/5.50 (instantiation (let ((_let_0 (hAPP (c_Product__Type_Ofst (tc_fun (tc_prod T_b T_b) tc_HOL_Obool) (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_Pa_2))) (forall ((V_Pa_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) (= (and (c_Wellfounded_Owf T_b _let_0) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) _let_0) (hAPP (c_Product__Type_Osnd _let_0 _let_0) V_Pa_2))) _let_0))) (c_FunDef_Oreduction__pair T_b V_Pa_2))) )) 5.29/5.50 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) c_FunDef_Omin__strict) c_FunDef_Omin__weak)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.29/5.50 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) c_FunDef_Omax__strict) c_FunDef_Omax__weak)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.29/5.50 ) 5.29/5.50 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 V_k_2) c_Int_OMin)) (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k_2)) c_Int_OMin))) )) 5.29/5.50 ( c_Int_OPls ) 5.29/5.50 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.50 ( c_Int_OMin ) 5.29/5.50 ) 5.29/5.50 (instantiation (forall ((T_b $$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))) ) 5.29/5.50 ( tc_Nat_Onat ) 5.29/5.50 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.50 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.29/5.50 ) 5.29/5.50 (instantiation (forall ((V_z_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP c_Int_Onat V_z_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_2))) ) 5.29/5.50 ( c_Int_OPls ) 5.29/5.50 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.50 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.50 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.50 ( c_Int_OMin ) 5.29/5.50 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.50 ) 5.29/5.50 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_k_2 $$unsorted)) (= (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))) )) 5.29/5.50 ( c_Int_OPls ) 5.29/5.50 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.50 ( c_Int_OMin ) 5.29/5.50 ) 5.29/5.50 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (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))) )) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_l_2 $$unsorted)) (= (= c_Int_OPls (c_Int_OBit0 V_l_2)) (= c_Int_OPls V_l_2)) ) 5.29/5.51 ( c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (= (c_Wellfounded_Oacyclic T_b (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP _let_1 V_y_2) V_x_2)) V_r_2)) (and (c_Wellfounded_Oacyclic T_b V_r_2) (not (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP _let_1 V_x_2) V_y_2)) (c_Transitive__Closure_Ortrancl T_b V_r_2)))))) ))) 5.29/5.51 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.51 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.51 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$unsorted)) (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)) )) 5.29/5.51 ( tc_Com_Ocom ) 5.29/5.51 ( tc_Nat_Onat ) 5.29/5.51 ( tc_HOL_Obool ) 5.29/5.51 ( tc_Int_Oint ) 5.29/5.51 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.51 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ( tc_Product__Type_Ounit ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq 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_Ortrancl tc_Nat_Onat c_Wellfounded_Opred__nat)))) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (hAPP (c_Rings_Odvd__class_Odvd tc_Nat_Onat) V_k_2))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 V_n_2)) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n_2) V_k_2)))) )) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (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__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))) ) 5.29/5.51 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.51 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.51 ( c_Int_OMin, c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (hAPP (c_Relation_OField T_b) V_r_2))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (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_0) (hAPP (c_COMBK (tc_fun T_b tc_HOL_Obool) T_b) _let_0)))) )) 5.29/5.51 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.29/5.51 ) 5.29/5.51 (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 (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_Oreflp T_b V_r_2)) ) 5.29/5.51 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.51 ( (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 ) 5.29/5.51 ( (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 ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (forall ((V_w_2 $$unsorted)) (= (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP _let_0 V_w_2))) (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP _let_0 (c_Int_OBit1 V_w_2))))) )) 5.29/5.51 ( c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_m $$unsorted)) (= V_m (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP c_Nat_OSuc V_n))) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.29/5.51 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_n $$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))))) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.29/5.51 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted)) (= _let_0 (c_List_Obutlast T_a _let_0)) )) 5.29/5.51 ( tc_Nat_Onat ) 5.29/5.51 ( tc_Int_Oint ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((T_b $$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))) ) 5.29/5.51 ( tc_Com_Ocom ) 5.29/5.51 ( tc_Nat_Onat ) 5.29/5.51 ( tc_HOL_Obool ) 5.29/5.51 ( tc_Int_Oint ) 5.29/5.51 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.51 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ( tc_Product__Type_Ounit ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 V_k_2)) (hBOOL (hAPP _let_0 (c_Int_OBit1 V_k_2)))) )) 5.29/5.51 ( c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_w_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_1 (c_Int_OBit1 V_w_2)) _let_0)) (hBOOL (hAPP (hAPP _let_1 V_w_2) _let_0))) ))) 5.29/5.51 ( c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_l_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (c_Map_Odom T_b T_c (c_Map_Omap__of T_b T_c V_l_2)))) ) 5.29/5.51 ( c_Com_Obodies, tc_Com_Ocom, tc_Com_Opname ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_n_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP _let_0 V_m_2)) (hAPP _let_0 V_n_2)))) )) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_n $$unsorted)) (= V_n (hAPP c_Int_Onat (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n))) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_z $$unsorted)) (c_Nat__Transfer_Ois__nat (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_z)) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 V_k_2)) (hBOOL (hAPP _let_0 (c_Int_OBit1 V_k_2)))) )) 5.29/5.51 ( c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (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))))) )) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_n $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Nat_OSuc V_n)) V_n))) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.29/5.51 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k1_2)) (c_Int_OBit0 V_k2_2))) (hBOOL (hAPP (hAPP _let_0 V_k1_2) V_k2_2))) )) 5.29/5.51 ( c_Int_OPls, c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_A_2 $$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)))) ) 5.29/5.51 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 5.29/5.51 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (c_Transitive__Closure_Otrancl T_b V_r_2))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= _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))) )) 5.29/5.51 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.51 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.29/5.51 ( (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) ) 5.29/5.51 ( (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) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_k_2 $$unsorted)) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_k_2))) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_Z_2 $$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)))) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_OBit0 V_k_2)) c_Int_OMin)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_k_2) c_Int_OMin))) ) 5.29/5.51 ( c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_x_2 $$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)))) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_x $$unsorted) (T_b $$unsorted)) (not (c_Option_Ois__none T_b (hAPP (c_Option_Ooption_OSome T_b) V_x))) ) 5.29/5.51 ( skv_10, tc_Com_Ocom ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) V_k_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) (c_Int_OBit1 V_k_2)))) ) 5.29/5.51 ( c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_m $$unsorted) (V_i $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_i) (hAPP c_Nat_OSuc (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_i)))) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_n_2 $$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)))) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 (c_Int_OBit0 V_k_2))) (hBOOL (hAPP _let_0 V_k_2))) )) 5.29/5.51 ( c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_2 (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat))) (let ((_let_3 (c_Set_Oinsert _let_1))) (let ((_let_4 (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))) (let ((_let_5 (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel))) (forall ((V_v_2 $$unsorted) (V_u_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP (hAPP _let_0 V_x_2) V_v_2)) (hAPP (hAPP _let_0 V_u_2) V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP c_Int_OAbs__Integ (hAPP _let_5 (hAPP (hAPP _let_3 (hAPP (hAPP _let_2 V_x_2) V_y_2)) _let_4)))) (hAPP c_Int_OAbs__Integ (hAPP _let_5 (hAPP (hAPP _let_3 (hAPP (hAPP _let_2 V_u_2) V_v_2)) _let_4)))))) ))))))) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_k $$unsorted)) (= V_k (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_k)) ) 5.29/5.51 ( c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.51 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.51 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (hBOOL (hAPP (hAPP _let_0 V_z) V_w)) (hBOOL (hAPP (hAPP _let_0 V_w) V_z))) )) 5.29/5.51 ( c_Int_OPls, c_Int_OMin ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.51 ( (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))) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.29/5.51 ( (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))) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.51 ( (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) ) 5.29/5.51 ( c_Int_OMin, c_Int_OPls ) 5.29/5.51 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.51 ( c_Int_OMin, c_Int_OMin ) 5.29/5.51 ( (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) ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 (c_Int_OBit1 V_k_2))) (hBOOL (hAPP _let_0 V_k_2))) )) 5.29/5.51 ( c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Nat_Osize__class_Osize (tc_Option_Ooption T_a)) (hAPP (c_Option_Ooption_OSome T_a) V_a))) ) 5.29/5.51 ( skv_10, tc_Com_Ocom ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_v_2 $$unsorted)) (= (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))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) V_v_2))) ) 5.29/5.51 ( c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.51 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.51 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member (tc_prod _let_0 _let_0)) (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) V_A_2) V_B_2)) (c_Wellfounded_Ofinite__psubset T_b))) (and (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_A_2) V_B_2)))) )) 5.29/5.51 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.51 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) V_m))) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_k $$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)))) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.51 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 V_k_2)) (hBOOL (hAPP _let_0 (c_Int_OBit0 V_k_2)))) )) 5.29/5.51 ( c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.51 ( c_Int_OMin ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= V_A_2 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (c_Set_Oinsert T_b)) (c_Orderings_Obot__class_Obot _let_0)))) )) 5.29/5.51 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (c_Relation_Orefl__on T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (c_Relation_OId T_b))) ) 5.29/5.51 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.51 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.29/5.51 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((T_b $$unsorted)) (c_Finite__Set_Ofun__left__comm__idem T_b (tc_fun T_b tc_HOL_Obool) (c_Set_Oinsert T_b)) ) 5.29/5.51 ( tc_Com_Ocom ) 5.29/5.51 ( tc_Nat_Onat ) 5.29/5.51 ( tc_HOL_Obool ) 5.29/5.51 ( tc_Int_Oint ) 5.29/5.51 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.51 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ( tc_Product__Type_Ounit ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Otop__class_Otop _let_0))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) _let_1)) ))) 5.29/5.51 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_k_2)) (hAPP _let_1 V_l_2))) (hBOOL (hAPP (hAPP _let_0 V_k_2) V_l_2))) ))) 5.29/5.51 ( c_Int_OPls, c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls ) 5.29/5.51 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls ) 5.29/5.51 ) 5.29/5.51 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2))) )) 5.29/5.51 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.51 ) 5.29/5.51 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_w_2) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_z_2) (c_Groups_Oone__class_Oone tc_Int_Oint)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w_2) V_z_2))) ) 5.29/5.51 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.51 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.29/5.51 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.52 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.52 ( c_Int_OMin, c_Int_OMin ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_Opred V_k_2)) V_l_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_k_2) V_l_2))) ) 5.29/5.52 ( c_Int_OPls, c_Int_OMin ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.52 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.52 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.52 ( c_Int_OMin, c_Int_OPls ) 5.29/5.52 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.52 ( c_Int_OMin, c_Int_OMin ) 5.29/5.52 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.52 ) 5.29/5.52 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_k_2 $$unsorted)) (= (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))) )) 5.29/5.52 ( c_Int_OPls ) 5.29/5.52 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.52 ( c_Int_OMin ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (forall ((B_x $$unsorted)) (hBOOL (hAPP (hAPP (c_member T_b) B_x) (c_Wellfounded_Oacc T_b V_r_2))) ) (c_Wellfounded_Owf T_b V_r_2)) ) 5.29/5.52 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.52 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.29/5.52 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 5.29/5.52 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 5.29/5.52 ) 5.29/5.52 (instantiation (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (forall ((V_X_2 $$unsorted)) (hBOOL (hAPP (hAPP (c_member (tc_prod _let_0 _let_0)) (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) V_X_2) (c_Orderings_Obot__class_Obot _let_0))) c_FunDef_Omin__weak)) )) 5.29/5.52 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 5.29/5.52 ) 5.29/5.52 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_2 (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat))) (let ((_let_3 (c_Set_Oinsert _let_1))) (let ((_let_4 (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))) (let ((_let_5 (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel))) (forall ((V_v_2 $$unsorted) (V_u_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP c_Int_OAbs__Integ (hAPP _let_5 (hAPP (hAPP _let_3 (hAPP (hAPP _let_2 V_x_2) V_y_2)) _let_4)))) (hAPP c_Int_OAbs__Integ (hAPP _let_5 (hAPP (hAPP _let_3 (hAPP (hAPP _let_2 V_u_2) V_v_2)) _let_4))))) (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)))) ))))))) 5.29/5.52 ( (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) ) 5.29/5.52 ( (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) ) 5.29/5.52 ) 5.29/5.52 (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))) ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.52 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.52 ( (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) ) 5.29/5.52 ( (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) ) 5.29/5.52 ) 5.29/5.52 (instantiation (let ((_let_0 (c_member T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (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)) (not (= (hAPP V_f_2 V_y_2) (hAPP V_f_2 V_x_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)) )) 5.29/5.52 ( (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_OBit0 (c_Int_OBit1 c_Int_OPls))), (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 ) 5.29/5.52 ( (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))), (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 ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.52 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.52 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.52 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.52 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.52 ) 5.29/5.52 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (c_Groups_Ouminus__class_Ouminus _let_0) (c_Orderings_Otop__class_Otop _let_0))) )) 5.29/5.52 ( tc_Com_Ocom ) 5.29/5.52 ( tc_Nat_Onat ) 5.29/5.52 ( tc_HOL_Obool ) 5.29/5.52 ( tc_Int_Oint ) 5.29/5.52 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.52 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.52 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.52 ( tc_Product__Type_Ounit ) 5.29/5.52 ) 5.29/5.52 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless T_a) V_z))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (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_0 V_y))) (hBOOL (hAPP _let_0 V_x))) )) 5.29/5.52 ( c_Int_OPls, c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.29/5.52 ( (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 ) 5.29/5.52 ( c_Int_OMin, (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 ) 5.29/5.52 ) 5.29/5.52 (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))) ) 5.29/5.52 ( 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)) ) 5.29/5.52 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.52 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)) (or (= V_y_2 V_x_2) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2))))) ) 5.29/5.52 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.29/5.52 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.29/5.52 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.52 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OPls), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Complete__Lattice_OInf__class_OInf T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))) (c_Orderings_Obot__class_Obot T_b))) ) 5.29/5.52 ( tc_Com_Ocom ) 5.29/5.52 ( tc_Nat_Onat ) 5.29/5.52 ( tc_HOL_Obool ) 5.29/5.52 ( tc_Int_Oint ) 5.29/5.52 ( (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 5.29/5.52 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.52 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.29/5.52 ( (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.29/5.52 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.52 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.52 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.52 ( tc_Product__Type_Ounit ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((V_v $$unsorted)) (= (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v) (hAPP c_Int_Onat (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v))) ) 5.29/5.52 ( c_Int_OPls ) 5.29/5.52 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.52 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.52 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.52 ( c_Int_OMin ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_x) V_y) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_y)))) ) 5.29/5.52 ( (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 ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((V_com_H_2 $$unsorted) (V_fun_H_2 $$unsorted) (V_com_2 $$unsorted) (V_fun_2 $$unsorted)) (= (and (= V_com_H_2 V_com_2) (= V_fun_H_2 V_fun_2)) (= (c_Com_Ocom_OWhile V_fun_H_2 V_com_H_2) (c_Com_Ocom_OWhile V_fun_2 V_com_2))) ) 5.29/5.52 ( v_c, v_b, v_c, v_b ) 5.29/5.52 ( v_c, v_b, v_ca, v_ba ) 5.29/5.52 ( v_ca, v_ba, v_c, v_b ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_y_2) V_x_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2))))) ) 5.29/5.52 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.52 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ) 5.29/5.52 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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)))) )) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.52 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.52 ( (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) ) 5.29/5.52 ( (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) ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Ozero__class_Ozero T_a)) (c_Groups_Oone__class_Oone T_a)))) ) 5.29/5.52 ( tc_Nat_Onat ) 5.29/5.52 ( tc_Int_Oint ) 5.29/5.52 ( tc_Code__Numeral_Ocode__numeral ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((V_a_2 $$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))) ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.52 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.52 ( (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) ) 5.29/5.52 ( (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) ) 5.29/5.52 ) 5.29/5.52 (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))) ) 5.29/5.52 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.52 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.29/5.52 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.29/5.52 ) 5.29/5.52 (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)))) ) 5.29/5.52 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.29/5.52 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 5.29/5.52 ( (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 ) 5.29/5.52 ) 5.29/5.52 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (hBOOL (hAPP (hAPP _let_0 V_y) V_x)) (hBOOL (hAPP (hAPP _let_0 V_x) V_y))) )) 5.29/5.52 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.29/5.52 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.29/5.52 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.52 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.52 ) 5.29/5.52 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint))) (let ((_let_2 (c_Divides_OposDivAlg V_a_2 V_ba_2))) (let ((_let_3 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_ba_2) _let_0)))) (let ((_let_4 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_a_2) V_ba_2)))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Divides_OposDivAlg__rel) (hAPP (hAPP _let_1 V_a_2) V_ba_2)))) (and (or _let_3 _let_4 (= (hAPP (c_Divides_Oadjust V_ba_2) (c_Divides_OposDivAlg V_a_2 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) V_ba_2))) _let_2)) (or (and (not _let_3) (not _let_4)) (= _let_2 (hAPP (hAPP _let_1 _let_0) V_a_2))))) )))))) 5.29/5.52 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.52 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.29/5.52 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.52 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.52 ( c_Int_OMin, c_Int_OMin ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (forall ((B_f $$unsorted)) (not (forall ((B_i $$unsorted)) (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) (hAPP B_f (hAPP c_Nat_OSuc B_i))) (hAPP B_f B_i))) V_r_2)) )) ) (c_Wellfounded_Owf T_b V_r_2)) ) 5.29/5.52 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.52 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.29/5.52 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 5.29/5.52 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 5.29/5.52 ) 5.29/5.52 (instantiation (let ((_let_0 (c_Relation_ODomain T_b T_c))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (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_ba_2)) V_r_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (hAPP _let_0 V_r_2))) )) 5.29/5.52 ( (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 ) 5.29/5.52 ( (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 ) 5.29/5.52 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) 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) ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)) (c_Groups_Oone__class_Oone T_a)))) ) 5.29/5.52 ( tc_Nat_Onat ) 5.29/5.52 ( tc_Int_Oint ) 5.29/5.52 ( tc_Code__Numeral_Ocode__numeral ) 5.29/5.52 ) 5.29/5.52 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$unsorted)) (= (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)) )) 5.29/5.52 ( tc_Nat_Onat ) 5.29/5.52 ( tc_Int_Oint ) 5.29/5.52 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.52 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.52 ) 5.29/5.52 (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)))) ) 5.29/5.52 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.52 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.29/5.52 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.29/5.52 ) 5.29/5.52 (instantiation (forall ((V_Pa_2 $$unsorted) (T_b $$unsorted) (B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) (hBOOL (hAPP V_Pa_2 B_x))) ) 5.29/5.52 ( (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)), (tc_prod tc_Com_Opname tc_Com_Ocom), skv_9 ) 5.29/5.52 ) 5.29/5.52 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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) (= (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)) (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)))) ))))) 5.29/5.52 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.52 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.52 ( (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)) ) 5.29/5.53 ) 5.29/5.53 (instantiation (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))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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))) (= (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)) (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)))) )))) 5.29/5.53 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.53 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.53 ( (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)) ) 5.29/5.53 ) 5.29/5.53 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Int_OBit1 c_Int_OPls)) V_w)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (c_Groups_Oone__class_Oone T_a)) (hAPP _let_0 V_w)))) )) 5.29/5.53 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.29/5.53 ) 5.29/5.53 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 _let_1) V_a_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) _let_1)))) ))) 5.29/5.53 ( c_Int_OPls, tc_Int_Oint ) 5.29/5.53 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.53 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.53 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.29/5.53 ( c_Int_OMin, tc_Int_Oint ) 5.29/5.53 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.29/5.53 ) 5.29/5.53 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_Opred V_k) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_k) c_Int_OMin)) ) 5.29/5.53 ( c_Int_OPls ) 5.29/5.53 ( c_Int_OMin ) 5.29/5.53 ) 5.29/5.53 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (hAPP (c_Set_Oinsert T_b) V_x_2))) (let ((_let_3 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_4 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP _let_2 _let_3)))) (let ((_let_5 (c_Big__Operators_Olattice_OSup__fin T_b _let_0 (hAPP _let_2 V_A_2)))) (let ((_let_6 (= _let_3 _let_4))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or _let_6 (= _let_5 (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 _let_4)))) (or (not _let_6) (= V_x_2 _let_5)))) )))))))) 5.29/5.53 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.53 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.53 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.53 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.53 ) 5.29/5.53 (instantiation (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ogroup__add T_b)) (= (= (c_Groups_Ozero__class_Ozero T_b) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_ba_2)) (= V_ba_2 V_a_2))) ) 5.29/5.53 ( (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 ) 5.29/5.53 ) 5.29/5.53 (instantiation (forall ((V_Pa_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_Pa_2 (hAPP c_Int_ORep__Integ B_x))) )) (hBOOL (hAPP V_Pa_2 V_y_2))) ) 5.29/5.53 ( (c_Nat_Osize__class_Osize tc_Com_Ocom), c_Com_Ocom_OSKIP ) 5.29/5.53 ( c_Nat_OSuc, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.53 ( c_Nat_OSuc, (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.29/5.53 ( c_Nat_OSuc, (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.29/5.53 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), c_Int_OPls ) 5.29/5.53 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit1 c_Int_OPls) ) 5.29/5.53 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.53 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.53 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.53 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin ) 5.29/5.53 ( (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) ) 5.29/5.53 ( (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) ) 5.29/5.53 ( (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))) ) 5.29/5.53 ( (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))) ) 5.29/5.53 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_OPls ) 5.29/5.53 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 c_Int_OPls) ) 5.29/5.53 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.53 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.53 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_OMin ) 5.29/5.53 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.53 ( c_Int_Onat, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.53 ( c_Int_Onat, (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.53 ( c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.53 ( c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.53 ( (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral), c_Int_OPls ) 5.29/5.53 ( (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral), (c_Int_OBit1 c_Int_OPls) ) 5.29/5.53 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.53 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin ) 5.29/5.53 ( (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) ) 5.29/5.53 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.53 ( (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))) ) 5.29/5.53 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.53 ( (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))) ) 5.29/5.53 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), c_Int_OPls ) 5.29/5.53 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.53 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), c_Int_OMin ) 5.29/5.53 ( (c_Nat_Osize__class_Osize tc_HOL_Obool), c_fTrue ) 5.29/5.53 ( (c_Nat_Osize__class_Osize tc_HOL_Obool), c_fFalse ) 5.29/5.53 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.53 ( (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool), c_fequal ) 5.29/5.53 ( c_Nat__Numeral_Oneg, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.53 ( c_Nat__Numeral_Oneg, (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.53 ( c_Nat__Numeral_Oneg, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin) ) 5.29/5.53 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.53 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.53 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.53 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin), c_Int_OMin ) 5.29/5.53 ( c_Com_OWT, c_Com_Ocom_OSKIP ) 5.29/5.53 ( c_Com_OWT, skv_10 ) 5.29/5.53 ( (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 5.29/5.53 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.53 ( c_Code__Numeral_Oof__nat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.53 ( c_Code__Numeral_Oof__nat, (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.53 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (c_Nat_Osize__class_Osize tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (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))) ) 5.29/5.53 ( (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint), c_fconj ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (c_Set_Oinsert tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( v_ba, v_s0 ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (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) ) 5.29/5.53 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (c_Finite__Set_Ofinite tc_Int_Oint), (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 5.29/5.53 ( (c_Finite__Set_Ofinite tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 5.29/5.53 ( (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) ) 5.29/5.53 ( v_b, v_s2 ) 5.29/5.53 ( v_b, v_s1 ) 5.29/5.53 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 5.29/5.53 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 5.29/5.53 ( (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_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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))) ) 5.29/5.53 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_0 _let_0))), (let ((_let_0 (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_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_0) _let_0)) ) 5.29/5.53 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Orderings_Obot__class_Obot _let_0))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 5.29/5.53 ( (let ((_let_0 (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_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))) (hAPP (hAPP (c_Product__Type_OPair (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_0) _let_0))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))) ) 5.29/5.53 ( (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_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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))) ) 5.29/5.53 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls), c_Int_OPls ) 5.29/5.53 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls), c_Int_OMin ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (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) ) 5.29/5.53 ( (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) ) 5.29/5.53 ( (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) ) 5.29/5.53 ( c_Com_Obody, skv_11 ) 5.29/5.53 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.53 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin), c_Int_OPls ) 5.29/5.53 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin), c_Int_OMin ) 5.29/5.53 ( c_Code__Numeral_Oint__of, (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 5.29/5.53 ( (c_Product__Type_Oprod_Oprod__case 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))) (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))))) ) 5.29/5.53 ( (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) ) 5.29/5.53 ( 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))))) ) 5.29/5.53 ( 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)))))) ) 5.29/5.53 ( (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)))) ) 5.29/5.53 ( (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))))) ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (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 ) 5.29/5.53 ( (c_Option_Ooption_OSome tc_Com_Ocom), skv_10 ) 5.29/5.53 ( (hAPP (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) ) 5.29/5.53 ( (c_Finite__Set_Ocard tc_HOL_Obool), (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)) ) 5.29/5.53 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls), c_Int_OMin ) 5.29/5.53 ( (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 5.29/5.53 ( (c_Finite__Set_Ocard tc_Product__Type_Ounit), (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)) ) 5.29/5.53 ( (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) ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omin__strict ) 5.29/5.53 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omax__strict ) 5.29/5.53 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_0 _let_0) c_FunDef_Omin__strict)), c_FunDef_Omin__weak ) 5.29/5.53 ( (c_Finite__Set_Ofinite tc_Com_Opname), (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody) ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool), (c_Orderings_Oord__class_Oless tc_Nat_Onat) ) 5.29/5.53 ( (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) ) 5.29/5.53 ( (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) ) 5.29/5.53 ( (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 ) 5.29/5.53 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat), c_Int_Onat ) 5.29/5.53 ( (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)))) ) 5.29/5.53 ( (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)))))), (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)))) ) 5.29/5.53 ( (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)))) ) 5.29/5.53 ( (let ((_let_0 (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)))) (c_COMBB _let_0 _let_0 tc_Int_Oint)), (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool) ) 5.29/5.53 ( (let ((_let_0 (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)))) (hAPP (c_COMBB _let_0 _let_0 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)) ) 5.29/5.53 ( (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) ) 5.29/5.53 ( (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint), c_fequal ) 5.29/5.53 ( (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 ) 5.29/5.53 ( (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) ) 5.29/5.53 ( (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool), (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT) ) 5.29/5.53 ( (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname), c_Com_OWT ) 5.29/5.53 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool) (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT)), skv_9 ) 5.29/5.53 ( (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)), skv_9 ) 5.29/5.53 ( (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)), c_Com_Obodies ) 5.29/5.53 ( (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 ) 5.29/5.53 ( (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)) ) 5.29/5.53 ( (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 ) 5.29/5.53 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_0 _let_0) c_FunDef_Omax__strict)), c_FunDef_Omax__weak ) 5.29/5.53 ( (c_COMBK tc_HOL_Obool tc_Nat_Onat), c_fTrue ) 5.29/5.53 ( (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)) ) 5.29/5.54 ( (c_Fun_Ocomp skv_8 skv_7 skv_6 skv_5), (hAPP (c_Fun_Ocomp skv_4 skv_8 skv_6 skv_3) skv_2) ) 5.29/5.54 ( (c_Fun_Ocomp skv_4 skv_8 skv_6 skv_3), skv_2 ) 5.29/5.54 ( (c_Fun_Ocomp skv_8 skv_7 skv_4 skv_5), skv_3 ) 5.29/5.54 ( (c_Fun_Ocomp skv_4 skv_7 skv_6 (hAPP (c_Fun_Ocomp skv_8 skv_7 skv_4 skv_5) skv_3)), skv_2 ) 5.29/5.54 ( (hAPP (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)) skv_9), (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies) ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2))) (let ((_let_2 (c_Orderings_Oord__class_Omax T_b))) (let ((_let_3 (c_Finite__Set_Ofinite T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_3 V_A_2))) (not (hBOOL (hAPP _let_3 V_B_2))) (= (c_Orderings_Obot__class_Obot _let_0) _let_1) (= (hAPP (hAPP _let_2 (c_Big__Operators_Olattice_OSup__fin T_b _let_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2))) (c_Big__Operators_Olattice_OSup__fin T_b _let_2 _let_1)) (hAPP (hAPP _let_2 (c_Big__Operators_Olattice_OSup__fin T_b _let_2 V_A_2)) (c_Big__Operators_Olattice_OSup__fin T_b _let_2 V_B_2)))) ))))) 5.29/5.54 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.54 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.54 ( (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)) ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (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))) )) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.54 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted)) (= _let_0 (hAPP (c_List_Orev T_a) _let_0)) )) 5.29/5.54 ( tc_Nat_Onat ) 5.29/5.54 ( tc_Int_Oint ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_x_2))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_3 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP _let_1 _let_2)))) (let ((_let_4 (c_Big__Operators_Olinorder__class_OMax T_b (hAPP _let_1 V_A_2)))) (let ((_let_5 (= _let_2 _let_3))) (forall ((V_x_2 $$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))) (and (or _let_5 (= _let_4 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMax T_b _let_3)))) (or (not _let_5) (= V_x_2 _let_4)))) ))))))) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.54 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.54 ( (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) ) 5.29/5.54 ( (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) ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_Product__Type_OPair T_a T_b))) (forall ((V_b_H $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (hAPP (hAPP _let_0 V_a_H) V_b_H) (hAPP (hAPP _let_0 V_a) V_b))) (and (= V_a_H V_a) (= V_b_H V_b))) )) 5.29/5.54 ( (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 ) 5.29/5.54 ( (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 ) 5.29/5.54 ( (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_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.29/5.54 ( (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) ) 5.29/5.54 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.54 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.54 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (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 _let_2) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) B_x) B_y)) (hAPP (hAPP _let_1 B_x) (hAPP (hAPP _let_1 B_y) _let_2)))) )) (hBOOL (hAPP (hAPP _let_0 (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) V_A_2))) )))) 5.29/5.54 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.54 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.29/5.54 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Nat_Onat _let_0))) (let ((_let_3 (tc_fun tc_Nat_Onat T_b))) (forall ((V_xs_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (c_List_Oset T_b) V_xs_2) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBB _let_1 tc_HOL_Obool T_b) (c_HOL_OEx tc_Nat_Onat)) (hAPP (hAPP (c_COMBC T_b _let_1 _let_1) (hAPP (hAPP (c_COMBB _let_2 (tc_fun _let_1 _let_1) T_b) (c_COMBS tc_Nat_Onat tc_HOL_Obool tc_HOL_Obool)) (hAPP (hAPP (c_COMBB _let_1 _let_2 T_b) (hAPP (c_COMBB tc_HOL_Obool _let_0 tc_Nat_Onat) c_fconj)) (hAPP (hAPP (c_COMBC T_b _let_3 _let_1) (hAPP (hAPP (c_COMBB (tc_fun T_b tc_HOL_Obool) (tc_fun _let_3 _let_1) T_b) (c_COMBB T_b tc_HOL_Obool tc_Nat_Onat)) c_fequal)) (hAPP (c_List_Onth T_b) V_xs_2))))) (hAPP (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat)) (hAPP (c_Nat_Osize__class_Osize (tc_List_Olist T_b)) V_xs_2)))))) ))))) 5.29/5.54 ( c_Com_Obodies, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_k_2 $$unsorted) (V_f_2 $$unsorted) (V_n_2 $$unsorted)) (or (not (forall ((B_i $$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 $$unsorted)) (or (not (= V_k_2 (hAPP V_f_2 B_i))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) B_i) V_n_2)))) ))) )) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 c_Int_OPls) ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OAbs__Integ, (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))) ) 5.29/5.54 ( c_Int_OMin, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.54 ( c_Int_OMin, c_Int_OAbs__Integ, (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))) ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_member (tc_prod T_b T_b)))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (let ((_let_2 (hAPP _let_1 V_a_2))) (let ((_let_3 (c_Transitive__Closure_Otrancl T_b V_r_2))) (forall ((V_ca_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ba_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_ca_2)) (c_Transitive__Closure_Ortrancl T_b V_r_2)))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ca_2)) _let_3))) ))))) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Wellfounded_Opred__nat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.54 ) 5.29/5.54 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (= V_a_2 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_a_2) (c_Big__Operators_Olattice_OInf__fin T_b (c_Orderings_Oord__class_Omin T_b) V_A_2)))) ) 5.29/5.54 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hAPP (c_Set_Oimage T_b T_b _let_0) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_x_2)) (hAPP (c_SetInterval_Oord__class_OatMost T_b) (hAPP _let_0 V_x_2)))) )) 5.29/5.54 ( c_Int_OPls, tc_Int_Oint ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.54 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.54 ( c_Int_OMin, tc_Int_Oint ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (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))) ))) 5.29/5.54 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m) V_n))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (hAPP _let_0 V_m)) (hAPP _let_0 V_n)))) )) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.29/5.54 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.29/5.54 ) 5.29/5.54 (instantiation (forall ((V_k $$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))) ) 5.29/5.54 ( c_Int_OPls ) 5.29/5.54 ( c_Int_OMin ) 5.29/5.54 ) 5.29/5.54 (instantiation (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))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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)))) )))) 5.29/5.54 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.54 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.54 ( (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)) ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_1 (c_Big__Operators_Olattice_OInf__fin T_b _let_0 V_A_2))) (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))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= _let_1 (hAPP (hAPP _let_0 V_x_2) _let_1))) ))) 5.29/5.54 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (hBOOL (hAPP (hAPP _let_0 V_x) V_y)) (hBOOL (hAPP (hAPP _let_0 V_y) V_x)) (= V_y V_x)) )) 5.29/5.54 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.29/5.54 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.54 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.54 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.54 ) 5.29/5.54 (instantiation (forall ((V_l $$unsorted) (V_k $$unsorted)) (not (= (c_Int_OBit1 V_k) (c_Int_OBit0 V_l))) ) 5.29/5.54 ( c_Int_OPls, c_Int_OMin ) 5.29/5.54 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls ) 5.29/5.54 ( c_Int_OMin, (c_Int_OBit1 c_Int_OPls) ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_c))) (forall ((V_B_2 $$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 _let_0 (hAPP V_B_2 B_a)))) )) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tc_fun T_c tc_HOL_Obool)) V_A_2) V_B_2)))) )) 5.29/5.54 ( (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 ) 5.29/5.54 ( (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 ) 5.29/5.54 ( (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 ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_1))))) (let ((_let_3 (= (c_Orderings_Obot__class_Obot _let_1) _let_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (and (or (not _let_3) (= V_x_2 _let_0)) (or _let_3 (= _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_x_2) (c_Big__Operators_Olattice__class_OInf__fin T_b _let_2)))))) ))))) 5.29/5.54 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.54 ) 5.29/5.54 (instantiation (forall ((V_n_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Osemiring__1 T_b)) (= (c_Nat_Osemiring__1__class_Oof__nat__aux T_b (hAPP (hAPP (c_COMBC T_b T_b T_b) (c_Groups_Oplus__class_Oplus T_b)) (c_Groups_Oone__class_Oone T_b)) V_n_2 (c_Groups_Ozero__class_Ozero T_b)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_b) V_n_2))) ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.29/5.54 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.29/5.54 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 5.29/5.54 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.29/5.54 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hAPP (c_SetInterval_Oord__class_OatLeast T_b) (hAPP _let_0 V_x_2)) (hAPP (c_Set_Oimage T_b T_b _let_0) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_x_2)))) )) 5.29/5.54 ( c_Int_OPls, tc_Int_Oint ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.54 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.54 ( c_Int_OMin, tc_Int_Oint ) 5.29/5.54 ) 5.29/5.54 (instantiation (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) (c_Complete__Lattice_OSup__class_OSup T_b V_A_2)))) ) 5.29/5.54 ( (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.54 ) 5.29/5.54 (instantiation (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (forall ((V_xs_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Oab__semigroup__idem__mult T_b)) (= V_xs_2 (c_List_Olist_ONil T_b)) (= (hAPP (c_List_Ofoldl T_b T_b _let_0 (hAPP (c_List_Ohd T_b) V_xs_2)) (hAPP (c_List_Otl T_b) V_xs_2)) (hAPP (c_Finite__Set_Ofold1 T_b _let_0) (hAPP (c_List_Oset T_b) V_xs_2)))) )) 5.29/5.54 ( c_Com_Obodies, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.54 ) 5.29/5.54 (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)))) ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.54 ( c_Int_OMin, tc_Int_Oint ) 5.29/5.54 ) 5.29/5.54 (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))) ) 5.29/5.54 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.29/5.54 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.54 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.54 ( (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 ) 5.29/5.55 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.55 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.55 ( (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 ) 5.29/5.55 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.55 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.55 ( (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)) ) 5.29/5.55 ) 5.29/5.55 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (let ((_let_1 (hAPP (c_Int_Oring__1__class_Oof__int T_a) V_k))) (let ((_let_2 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_k) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (forall ((V_k $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (and (or (not _let_2) (= _let_1 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (hAPP _let_0 (hAPP c_Int_Onat (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_k)))))) (or _let_2 (= _let_1 (hAPP _let_0 (hAPP c_Int_Onat V_k)))))) )))) 5.29/5.55 ( c_Int_OPls, tc_Int_Oint ) 5.29/5.55 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.29/5.55 ) 5.29/5.55 (instantiation (forall ((V_k $$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 $$unsorted)) (or (not (= V_k (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) B_n)))) ))) ) 5.29/5.55 ( c_Int_OPls ) 5.29/5.55 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.55 ( c_Int_OMin ) 5.29/5.55 ) 5.29/5.55 (instantiation (forall ((V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) (hAPP (c_List_Oset T_b) V_xs_2)))) (= V_xs_2 (c_List_Olinorder__class_Oinsort__insert__key T_b T_b (c_COMBI T_b) V_x_2 V_xs_2))) ) 5.29/5.55 ( c_Com_Obodies, skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.55 ) 5.29/5.55 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (c_Orderings_Oord_Omin T_b (hAPP (c_COMBC T_b T_b tc_HOL_Obool) (c_Orderings_Oord__class_Oless__eq T_b))) (c_Orderings_Oord__class_Omax T_b))) ) 5.29/5.55 ( tc_Nat_Onat ) 5.29/5.55 ( tc_Int_Oint ) 5.29/5.55 ( tc_Code__Numeral_Ocode__numeral ) 5.29/5.55 ) 5.29/5.55 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (= (hAPP (c_Finite__Set_Ocard T_c) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)) (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2))) ) 5.29/5.55 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.55 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.29/5.55 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.55 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.55 ) 5.29/5.55 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) V_B_2) (c_Complete__Lattice_OSup__class_OSup _let_0 (hAPP (c_Set_Oimage T_c _let_0 V_B_2) V_A_2))) )) 5.29/5.55 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 5.29/5.55 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 5.29/5.55 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 5.29/5.55 ) 5.29/5.55 (instantiation (forall ((T_a $$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)))) ) 5.29/5.55 ( tc_Nat_Onat ) 5.29/5.55 ( tc_Int_Oint ) 5.29/5.55 ( tc_Code__Numeral_Ocode__numeral ) 5.29/5.55 ) 5.29/5.55 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2) (hAPP (hAPP (c_Finite__Set_Ofold T_b _let_0 (c_Set_Oinsert T_b)) V_B_2) V_A_2))) )) 5.29/5.55 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.55 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.55 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.55 ) 5.29/5.55 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hAPP (c_Set_Oimage T_b T_b _let_0) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_x_2)) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) (hAPP _let_0 V_x_2)))) )) 5.29/5.55 ( c_Int_OPls, tc_Int_Oint ) 5.29/5.55 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.55 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.55 ( c_Int_OMin, tc_Int_Oint ) 5.29/5.55 ) 5.29/5.55 (instantiation (forall ((V_a $$unsorted)) (= (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)) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_a)) ) 5.29/5.55 ( c_Int_OPls ) 5.29/5.55 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.55 ( c_Int_OMin ) 5.29/5.55 ) 5.29/5.55 (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))) ) 5.29/5.55 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.55 ) 5.29/5.55 (instantiation (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))) (forall ((V_ca_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ba_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_ca_2)) V_r_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ca_2)) _let_3))) ))))) 5.29/5.55 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Wellfounded_Opred__nat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.55 ) 5.29/5.55 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_k $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (c_Groups_Oone__class_Oone T_a)) (hAPP _let_0 V_k)) (hAPP _let_0 (c_Int_Osucc V_k)))) )) 5.29/5.55 ( c_Int_OPls, tc_Nat_Onat ) 5.29/5.55 ( c_Int_OPls, tc_Int_Oint ) 5.29/5.55 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.29/5.55 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.29/5.55 ( c_Int_OMin, tc_Nat_Onat ) 5.29/5.55 ( c_Int_OMin, tc_Int_Oint ) 5.29/5.55 ( c_Int_OMin, tc_Code__Numeral_Ocode__numeral ) 5.29/5.55 ) 5.29/5.55 (instantiation (let ((_let_0 (c_Relation_OImage T_b T_b V_r_2))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (let ((_let_3 (c_member T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (= (and (= (hAPP _let_0 (hAPP (hAPP _let_1 V_x_2) _let_2)) (hAPP _let_0 (hAPP (hAPP _let_1 V_y_2) _let_2))) (hBOOL (hAPP (hAPP _let_3 V_y_2) V_A_2)) (hBOOL (hAPP (hAPP _let_3 V_x_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_x_2) V_y_2)) V_r_2)))) ))))) 5.29/5.55 ( (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)), 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) ) 5.29/5.55 ) 5.29/5.55 (instantiation (forall ((T_b $$unsorted)) (= (c_Transitive__Closure_Ortrancl T_b (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) (c_Relation_OId T_b)) ) 5.29/5.55 ( tc_Nat_Onat ) 5.29/5.55 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.55 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.29/5.55 ) 5.29/5.55 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (c_List_Olist_ONil T_b) (c_List_Olinorder__class_Osorted__list__of__set T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 5.29/5.55 ( tc_Com_Ocom ) 5.29/5.55 ( tc_Nat_Onat ) 5.29/5.55 ( tc_HOL_Obool ) 5.29/5.55 ( tc_Int_Oint ) 5.29/5.55 ( tc_Code__Numeral_Ocode__numeral ) 5.29/5.55 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.55 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.55 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.55 ( tc_Product__Type_Ounit ) 5.29/5.55 ) 5.29/5.55 (instantiation (let ((_let_0 (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (let ((_let_2 (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Nitpick_Onorm__frac__rel))) (forall ((V_Pa_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP _let_2 (hAPP (hAPP _let_0 V_a0_2) V_a1_2)))) (not (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (not (hBOOL (hAPP _let_2 (hAPP (hAPP _let_0 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_Pa_2 (hAPP _let_1 B_a)) (hAPP _let_1 B_b))))) (hBOOL (hAPP (hAPP V_Pa_2 B_a) B_b))) )) (hBOOL (hAPP (hAPP V_Pa_2 V_a0_2) V_a1_2))) )))) 5.29/5.55 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OPls, c_Int_OMin ) 5.29/5.55 ( (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) ) 5.29/5.55 ( (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) ) 5.29/5.55 ( (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) ) 5.29/5.55 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.55 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 5.29/5.55 ( (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) ) 5.29/5.55 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.55 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.55 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.29/5.55 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.55 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.55 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 5.29/5.55 ( (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) ) 5.29/5.55 ( (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) ) 5.29/5.55 ( (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) ) 5.29/5.55 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), (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)) ) 5.29/5.55 ( (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)) ) 5.29/5.55 ( (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)) ) 5.29/5.55 ( (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 ) 5.29/5.55 ( (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) ) 5.29/5.55 ( (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)) ) 5.29/5.55 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 5.29/5.55 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 5.29/5.55 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_0 _let_0))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (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_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_0) _let_0)) ) 5.29/5.55 ( (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)) ) 5.29/5.55 ( (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)) ) 5.29/5.55 ( (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)) ) 5.29/5.55 ( (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)) ) 5.29/5.55 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omax__weak, c_FunDef_Omax__strict ) 5.29/5.55 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omin__weak, c_FunDef_Omin__strict ) 5.29/5.55 ( (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) ) 5.29/5.55 ( (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 ) 5.29/5.55 ( (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 ) 5.29/5.55 ( (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)))) ) 5.29/5.55 ( (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)))) ) 5.29/5.55 ( (let ((_let_0 (tc_fun tc_Int_Oint (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))) (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) ) 5.29/5.55 ( (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) ) 5.29/5.55 ( (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool), skv_9, (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT) ) 5.29/5.55 ( (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)), (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9 ) 5.29/5.55 ( (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 ) 5.29/5.55 ( (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 ) 5.29/5.55 ) 5.29/5.55 (instantiation (let ((_let_0 (tc_fun T_c tc_HOL_Obool))) (forall ((V_ca_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_0) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hAPP (c_COMBK _let_0 T_b) V_ca_2))) )) 5.29/5.55 ( c_Com_OWT, tc_Com_Ocom, tc_Com_Opname ) 5.29/5.55 ) 5.29/5.55 (instantiation (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (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)))) (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_x_2) V_y_2)) ))) 5.29/5.55 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.29/5.55 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.29/5.55 ( (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) ) 5.29/5.55 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.55 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.55 ) 5.29/5.55 (instantiation (forall ((V_z $$unsorted)) (or (hBOOL (hAPP c_Nat__Numeral_Oneg V_z)) (= V_z (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Int_Onat V_z)))) ) 5.29/5.55 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.55 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.55 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.55 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.55 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin) ) 5.29/5.55 ) 5.29/5.55 (instantiation (forall ((V_k_2 $$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_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (c_SetInterval_Oord__class_OgreaterThanLessThan T_b V_k_2 V_l_2))) ) 5.29/5.55 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.29/5.55 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.55 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.55 ( (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 ) 5.29/5.55 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.55 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.55 ( (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 ) 5.29/5.55 ) 5.29/5.55 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (= V_A_2 (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2))) ) 5.29/5.55 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.55 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.55 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.55 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.56 ( (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.56 ) 5.29/5.56 (instantiation (forall ((V_i $$unsorted) (V_j $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_j) V_i))) (= (c_List_Oupto V_i V_j) (c_List_Olist_ONil tc_Int_Oint))) ) 5.29/5.56 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.29/5.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.56 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.56 ( c_Int_OMin, c_Int_OMin ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (c_Nat_Osize__class_Osize tc_Nat_Onat))) (forall ((V_nat $$unsorted)) (= (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)))) )) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.56 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.29/5.56 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.29/5.56 ) 5.29/5.56 (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_Osgn__class_Osgn T_a V_a) (c_Groups_Oone__class_Oone T_a))) ) 5.29/5.56 ( c_Int_OPls, tc_Int_Oint ) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.56 ( c_Int_OMin, tc_Int_Oint ) 5.29/5.56 ) 5.29/5.56 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (class_Lattices_Osemilattice__sup T_b)) (= (c_Orderings_Oord__class_Omax T_b) (c_Lattices_Osemilattice__sup__class_Osup T_b))) ) 5.29/5.56 ( tc_Nat_Onat ) 5.29/5.56 ( tc_HOL_Obool ) 5.29/5.56 ( tc_Int_Oint ) 5.29/5.56 ( tc_Code__Numeral_Ocode__numeral ) 5.29/5.56 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (tc_prod T_c T_b))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (c_Relation_OImage T_c T_b V_r_2) (hAPP (hAPP (c_Set_Oinsert T_c) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool)))) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBC T_b _let_1 tc_HOL_Obool) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_1 tc_HOL_Obool) T_b) (c_member _let_0)) (hAPP (c_Product__Type_OPair T_c T_b) V_a_2))) V_r_2))) ))) 5.29/5.56 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.56 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (c_member T_b))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (hBOOL (hAPP _let_0 V_A_2)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) (not (forall ((B_x $$unsorted)) (or (hBOOL (hAPP _let_0 (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_1) 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_1 B_x) V_A_2)))) ))) ))) 5.29/5.56 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.56 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.29/5.56 ( (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 ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_c tc_HOL_Obool))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2) (hAPP (hAPP (hAPP (c_Finite__Set_Ofold__image _let_0 T_b (c_Lattices_Osemilattice__sup__class_Osup _let_0)) (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (hAPP (hAPP (c_COMBB T_c (tc_fun _let_0 _let_0) T_b) (c_Set_Oinsert T_c)) V_f_2)) _let_0)) _let_0) V_A_2)))) )) 5.29/5.56 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.56 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.29/5.56 ( (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 ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin))) (forall ((V_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_b))) (= _let_0 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) _let_0) V_b))) )) 5.29/5.56 ( c_Int_OPls ) 5.29/5.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.56 ( c_Int_OMin ) 5.29/5.56 ) 5.29/5.56 (instantiation (forall ((T_a $$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)))) ) 5.29/5.56 ( tc_Nat_Onat ) 5.29/5.56 ( tc_Int_Oint ) 5.29/5.56 ( tc_Code__Numeral_Ocode__numeral ) 5.29/5.56 ) 5.29/5.56 (instantiation (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_d tc_HOL_Obool)))) (let ((_let_2 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (= _let_2 (hAPP (c_Set_Oimage T_c T_b V_f_2) _let_0))) (not (= _let_1 (hAPP (c_Set_Oimage T_b T_d V_g_2) _let_2))) (= (hAPP (c_Set_Oimage T_c T_d (hAPP (c_Fun_Ocomp T_b T_d T_c V_g_2) V_f_2)) _let_0) _let_1)) )))) 5.29/5.56 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, c_Code__Numeral_Onat__of, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral ) 5.29/5.56 ( c_Code__Numeral_Oof__nat, tc_Code__Numeral_Ocode__numeral, c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 5.29/5.56 ( skv_3, skv_8, skv_2, skv_4, skv_6 ) 5.29/5.56 ( skv_5, skv_7, skv_3, skv_8, skv_4 ) 5.29/5.56 ( skv_5, skv_7, (hAPP (c_Fun_Ocomp skv_4 skv_8 skv_6 skv_3) skv_2), skv_8, skv_6 ) 5.29/5.56 ( (hAPP (c_Fun_Ocomp skv_8 skv_7 skv_4 skv_5) skv_3), skv_7, skv_2, skv_4, skv_6 ) 5.29/5.56 ) 5.29/5.56 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_r_2)) (c_Wellfounded_Owf (tc_fun T_b tc_HOL_Obool) (c_Wellfounded_Omax__ext T_b V_r_2))) ) 5.29/5.56 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.56 ( c_FunDef_Opair__leq, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted)) (or (not (c_Nat__Transfer_Onat__set V_A_2)) (not (c_Nat__Transfer_Onat__set V_B_2)) (= (= V_B_2 V_A_2) (= (hAPP _let_0 V_A_2) (hAPP _let_0 V_B_2)))) )) 5.29/5.56 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 5.29/5.56 ) 5.29/5.56 (instantiation (forall ((V_a_2 $$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))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (= V_a_2 (hAPP (hAPP (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)))) ) 5.29/5.56 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.56 ) 5.29/5.56 (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))) ) 5.29/5.56 ( tc_Com_Ocom, tc_HOL_Obool ) 5.29/5.56 ( tc_Nat_Onat, tc_HOL_Obool ) 5.29/5.56 ( tc_HOL_Obool, tc_HOL_Obool ) 5.29/5.56 ( tc_Int_Oint, tc_HOL_Obool ) 5.29/5.56 ( tc_Int_Oint, tc_Int_Oint ) 5.29/5.56 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.29/5.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.29/5.56 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.29/5.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.29/5.56 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= V_y_2 V_x_2) (= (hAPP _let_0 V_y_2) (hAPP _let_0 V_x_2))) )) 5.29/5.56 ( (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))) ) 5.29/5.56 ( (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) ) 5.29/5.56 ( (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_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.56 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.56 ( (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_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.56 ( (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))) ) 5.29/5.56 ) 5.29/5.56 (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)))) ) 5.29/5.56 ( c_Int_OPls, tc_Int_Oint ) 5.29/5.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.56 ( c_Int_OMin, tc_Int_Oint ) 5.29/5.56 ) 5.29/5.56 (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)))) ) 5.29/5.56 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.56 ) 5.29/5.56 (instantiation (forall ((V_z $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z))) (= (hAPP c_Nat_OSuc (hAPP c_Int_Onat V_z)) (hAPP c_Int_Onat (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_z)))) ) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.56 ( c_Int_OMin ) 5.29/5.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.56 ) 5.29/5.56 (instantiation (forall ((T_b $$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))) ) 5.29/5.56 ( tc_Com_Ocom ) 5.29/5.56 ( tc_Nat_Onat ) 5.29/5.56 ( tc_HOL_Obool ) 5.29/5.56 ( tc_Int_Oint ) 5.29/5.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.56 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.56 ( tc_Product__Type_Ounit ) 5.29/5.56 ) 5.29/5.56 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) (= V_y (hAPP (hAPP (c_Orderings_Oord__class_Omin T_a) V_x) V_y))) ) 5.29/5.56 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.56 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.56 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.56 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_a_2 $$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))) (= (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)))) )) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.56 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.56 ( (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) ) 5.29/5.56 ( (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) ) 5.29/5.56 ) 5.29/5.56 (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))) ) 5.29/5.56 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.56 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.29/5.56 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_a_2))) (= (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_a_2) V_ba_2))) (and (hBOOL (hAPP (hAPP _let_0 V_ba_2) V_a_2)) (hBOOL (hAPP _let_1 V_ba_2))))) ))) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.56 ( (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))) ) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.29/5.56 ( (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))) ) 5.29/5.56 ( c_Int_OMin, c_Int_OPls ) 5.29/5.56 ( c_Int_OMin, c_Int_OMin ) 5.29/5.56 ) 5.29/5.56 (instantiation (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))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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) (= (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_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)))) )))) 5.29/5.56 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.56 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.56 ( (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)) ) 5.29/5.56 ) 5.29/5.56 (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))) ) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.56 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.56 ( (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) ) 5.29/5.56 ( (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) ) 5.29/5.56 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.56 ) 5.29/5.56 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Orderings_Obot__class_Obot T_b) (c_Complete__Lattice_OSup__class_OSup T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 5.29/5.56 ( tc_Com_Ocom ) 5.29/5.56 ( tc_Nat_Onat ) 5.29/5.56 ( tc_HOL_Obool ) 5.29/5.56 ( tc_Int_Oint ) 5.29/5.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.56 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.56 ( tc_Product__Type_Ounit ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OatLeast T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (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)))) )) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ogroup__add T_b)) (= (= V_a_2 _let_0) (= _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)))) )) 5.29/5.56 ( c_Int_OPls, tc_Int_Oint ) 5.29/5.56 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.56 ( c_Int_OMin, tc_Int_Oint ) 5.29/5.56 ) 5.29/5.56 (instantiation (forall ((T_b $$unsorted)) (= (hAPP (c_Relation_ORange T_b T_b) (c_Relation_OId T_b)) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))) ) 5.29/5.56 ( tc_Com_Ocom ) 5.29/5.56 ( tc_Nat_Onat ) 5.29/5.56 ( tc_HOL_Obool ) 5.29/5.56 ( tc_Int_Oint ) 5.29/5.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.56 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.56 ( tc_Product__Type_Ounit ) 5.29/5.56 ) 5.29/5.56 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Obot T_1)) (class_Orderings_Obot (tc_fun T_2 T_1))) ) 5.29/5.56 ( tc_Com_Ocom, tc_HOL_Obool ) 5.29/5.56 ( tc_Nat_Onat, tc_HOL_Obool ) 5.29/5.56 ( tc_HOL_Obool, tc_HOL_Obool ) 5.29/5.56 ( tc_Int_Oint, tc_HOL_Obool ) 5.29/5.56 ( tc_Int_Oint, tc_Int_Oint ) 5.29/5.56 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.29/5.56 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.29/5.56 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.29/5.56 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.29/5.56 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (let ((_let_1 (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat))) (forall ((V_k_2 $$unsorted)) (= (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))) ))) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.56 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.29/5.56 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OgreaterThan T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (= V_y_2 V_x_2) (= (hAPP _let_0 V_x_2) (hAPP _let_0 V_y_2)))) )) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat))) (forall ((V_n_2 $$unsorted)) (= (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))) )) 5.29/5.56 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.56 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.29/5.56 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.29/5.56 ) 5.29/5.56 (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_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b T_c) V_A_2) V_f_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))) ) 5.29/5.56 ( (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) ) 5.29/5.56 ( (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) ) 5.29/5.56 ( (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) ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (c_Com_Ocom_OWhile V_ba_2 V_ca_2))) (forall ((V_s2_2 $$unsorted) (V_s1_2 $$unsorted) (V_n_2 $$unsorted) (V_ca_2 $$unsorted) (V_s0_2 $$unsorted) (V_ba_2 $$unsorted)) (or (not (hBOOL (hAPP V_ba_2 V_s0_2))) (not (c_Natural_Oevaln V_ca_2 V_s0_2 V_n_2 V_s1_2)) (not (c_Natural_Oevaln _let_0 V_s1_2 V_n_2 V_s2_2)) (c_Natural_Oevaln _let_0 V_s0_2 V_n_2 V_s2_2)) )) 5.29/5.56 ( v_s2, v_s1, v_na, v_ca, v_s0, v_ba ) 5.29/5.56 ) 5.29/5.56 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_l_2) V_u_2))) (= (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_l_2) V_u_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP (hAPP (c_Set_Oinsert T_b) V_l_2) (c_Orderings_Obot__class_Obot _let_0))) (c_SetInterval_Oord__class_OgreaterThanLessThan T_b V_l_2 V_u_2)))) )) 5.29/5.57 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.29/5.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.57 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.57 ) 5.29/5.57 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (hAPP (c_Set_Oimage T_c T_b V_f_2) V_A_2)))) (not (c_Fun_Oinj__on T_c T_b V_f_2 V_A_2)) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) V_A_2))) ) 5.29/5.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.29/5.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 5.29/5.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 5.29/5.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 5.29/5.57 ) 5.29/5.57 (instantiation (forall ((T_b $$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)))) ) 5.29/5.57 ( tc_Nat_Onat ) 5.29/5.57 ( tc_Int_Oint ) 5.29/5.57 ( tc_Code__Numeral_Ocode__numeral ) 5.29/5.57 ) 5.29/5.57 (instantiation (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))) (forall ((T_b $$unsorted)) (= (c_Wellfounded_Ofinite__psubset T_b) (hAPP (c_Set_OCollect (tc_prod _let_1 _let_1)) (hAPP (c_Product__Type_Oprod_Oprod__case _let_1 _let_1 tc_HOL_Obool) (hAPP (hAPP (c_COMBC _let_1 _let_2 _let_2) (hAPP (hAPP (c_COMBB _let_3 (tc_fun _let_2 _let_2) _let_1) (c_COMBS _let_1 tc_HOL_Obool tc_HOL_Obool)) (hAPP (hAPP (c_COMBB _let_2 _let_3 _let_1) (hAPP (c_COMBB tc_HOL_Obool _let_0 _let_1) c_fconj)) (c_Orderings_Oord__class_Oless _let_1)))) (c_Finite__Set_Ofinite T_b))))) ))))) 5.29/5.57 ( tc_Nat_Onat ) 5.29/5.57 ( tc_Int_Oint ) 5.29/5.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.57 ( tc_Com_Opname ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (forall ((T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) _let_0))) )) 5.29/5.57 ( tc_Nat_Onat ) 5.29/5.57 ( tc_Int_Oint ) 5.29/5.57 ( tc_Code__Numeral_Ocode__numeral ) 5.29/5.57 ) 5.29/5.57 (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)))) ) 5.29/5.57 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (not (= V_y_2 V_x_2)) (or (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2)) (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2))))) )) 5.29/5.57 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.29/5.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.29/5.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.57 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.57 ) 5.29/5.57 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (not (= (c_Orderings_Obot__class_Obot T_a) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y))) (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))) ) 5.29/5.57 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.57 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.57 ( (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_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.57 ) 5.29/5.57 (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)))) ) 5.29/5.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (not (class_Int_Onumber__ring T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (hAPP _let_0 V_x_2)) (hAPP _let_0 V_y_2))))) )) 5.29/5.57 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.29/5.57 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Int_Oint ) 5.29/5.57 ) 5.29/5.57 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_a) (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a)))) ) 5.29/5.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.57 ( c_Int_OMin, tc_Int_Oint ) 5.29/5.57 ) 5.29/5.57 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Finite__Set_Ocard T_b) V_A_2))) (and (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2)) (not (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 5.29/5.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 5.29/5.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 5.29/5.57 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.29/5.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.29/5.57 ) 5.29/5.57 (instantiation (forall ((V_k_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_k_2) (hAPP (c_Groups_Ouminus__class_Ouminus (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_k_2)))) ) 5.29/5.57 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.57 ) 5.29/5.57 (instantiation (forall ((V_b $$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))) ) 5.29/5.57 ( c_Int_OPls ) 5.29/5.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.57 ( c_Int_OMin ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (c_Relation_Oconverse T_b T_b))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (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)))) )) 5.29/5.57 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= (hAPP _let_0 V_A_2) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_1))))))) ))) 5.29/5.57 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2))) (forall ((V_x_2 $$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))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_x_2) _let_0))) )) 5.29/5.57 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((T_b $$unsorted)) (= _let_0 (hAPP (c_Set_Oimage T_b T_b (c_Fun_Oid T_b)) _let_0)) )) 5.29/5.57 ( tc_Com_Ocom ) 5.29/5.57 ( tc_Nat_Onat ) 5.29/5.57 ( tc_HOL_Obool ) 5.29/5.57 ( tc_Int_Oint ) 5.29/5.57 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.57 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.57 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.57 ( tc_Product__Type_Ounit ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_u_2 $$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))) (= (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)))) )) 5.29/5.57 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.29/5.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.57 ( (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 ) 5.29/5.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.57 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.57 ( (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 ) 5.29/5.57 ) 5.29/5.57 (instantiation (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))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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)))) ))))) 5.29/5.57 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.57 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.57 ( (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)) ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (c_Set_Oimage T_c T_b V_f_2) V_A_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_c _let_0 _let_0) (hAPP (hAPP (c_COMBB T_b (tc_fun _let_0 _let_0) T_c) (c_Set_Oinsert T_b)) V_f_2)) (c_Orderings_Obot__class_Obot _let_0)))) )) 5.29/5.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.29/5.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 5.29/5.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (c_Set_Oimage T_c T_b V_f_2))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert T_b) (hAPP V_f_2 V_a_2)) (hAPP _let_0 V_B_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_c) V_a_2) V_B_2))) )) 5.29/5.57 ( (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 ) 5.29/5.57 ) 5.29/5.57 (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))) ) 5.29/5.57 ( c_Wellfounded_Oless__than, tc_Nat_Onat, c_Wellfounded_Oless__than, tc_Nat_Onat ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_d $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (c_Set_Oimage T_d T_b V_f_2) (hAPP (c_Set_Oimage T_c T_d V_g_2) _let_0)) (hAPP (c_Set_Oimage T_c T_b (hAPP (hAPP (c_COMBB T_d T_b T_c) V_f_2) V_g_2)) _let_0)) )) 5.29/5.57 ( c_Nat_OSuc, (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal), tc_Nat_Onat, (tc_fun tc_Nat_Onat tc_HOL_Obool), tc_Nat_Onat ) 5.29/5.57 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_fconj, tc_HOL_Obool, (tc_fun tc_HOL_Obool tc_HOL_Obool), tc_Int_Oint ) 5.29/5.57 ( c_Nitpick_Oint__gcd, (hAPP (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) c_fequal), (tc_fun tc_Int_Oint tc_Int_Oint), (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.29/5.57 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) (tc_fun tc_Int_Oint _let_0) tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd)), (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool), (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.29/5.57 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (tc_fun tc_Int_Oint tc_HOL_Obool), (tc_fun tc_Int_Oint tc_HOL_Obool), tc_Int_Oint ) 5.29/5.57 ) 5.29/5.57 (instantiation (forall ((V_b $$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))) ) 5.29/5.57 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.57 ) 5.29/5.57 (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))) ) 5.29/5.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.29/5.57 ( (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 ) 5.29/5.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 5.29/5.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v))) (forall ((V_v $$unsorted)) (or (hBOOL (hAPP c_Nat__Numeral_Oneg _let_0)) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v)) _let_0)) )) 5.29/5.57 ( c_Int_OPls ) 5.29/5.57 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.57 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.57 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.57 ( c_Int_OMin ) 5.29/5.57 ) 5.29/5.57 (instantiation (forall ((V_v $$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_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v)))) ) 5.29/5.57 ( c_Int_OPls ) 5.29/5.57 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.57 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.57 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.57 ( c_Int_OMin ) 5.29/5.57 ) 5.29/5.57 (instantiation (forall ((V_Pa_2 $$unsorted) (T_b $$unsorted)) (= V_Pa_2 (hAPP (c_Set_OCollect T_b) V_Pa_2)) ) 5.29/5.57 ( (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) ) 5.29/5.57 ( (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) ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (hBOOL (hAPP _let_1 V_x_2))) (not (hBOOL (hAPP _let_1 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))))) ))) 5.29/5.57 ( c_Int_OPls, c_Int_OMin ) 5.29/5.57 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.57 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.57 ( (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) ) 5.29/5.57 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.57 ( c_Int_OMin, c_Int_OMin ) 5.29/5.57 ( (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) ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (forall ((V_n $$unsorted)) (or (not (hBOOL (hAPP _let_0 (hAPP _let_1 V_n)))) (and (hBOOL (hAPP _let_0 (hAPP _let_1 (c_Int_OBit0 V_n)))) (hBOOL (hAPP _let_0 (hAPP _let_1 (c_Int_OBit1 V_n)))))) ))) 5.29/5.57 ( c_Int_OPls ) 5.29/5.57 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.57 ( c_Int_OMin ) 5.29/5.57 ) 5.29/5.57 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Complete__Lattice_OInf__class_OInf T_b V_A_2) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b)) (c_Orderings_Otop__class_Otop T_b)) V_A_2))) ) 5.29/5.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.57 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.29/5.57 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_a_2))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP _let_1 V_A_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP _let_1 (c_Orderings_Obot__class_Obot _let_0))) V_A_2)) ))) 5.29/5.57 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.57 ( (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) ) 5.29/5.57 ( (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) ) 5.29/5.57 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.57 ) 5.29/5.57 (instantiation (let ((_let_0 (hAPP (c_Set_Oinsert T_b) V_a_2))) (let ((_let_1 (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_A_2))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (hAPP _let_1 (hAPP _let_0 V_B_2)) (hAPP _let_0 (hAPP _let_1 V_B_2))) ))) 5.29/5.57 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (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_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_0) _let_0)), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.57 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (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_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_0) _let_0)), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.57 ) 5.29/5.57 (instantiation (forall ((T_c $$unsorted) (V_ba_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (not (hBOOL (hAPP (hAPP V_B_2 V_a_2) V_ba_2))) (hBOOL (hAPP (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tc_fun T_c tc_HOL_Obool)) V_A_2) V_B_2) V_ba_2))) ) 5.29/5.58 ( tc_Nat_Onat, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)), (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.58 ) 5.29/5.58 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) ) 5.29/5.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.29/5.58 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.58 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.58 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.58 ) 5.29/5.58 (instantiation (forall ((T_b $$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))) ) 5.29/5.58 ( tc_Nat_Onat ) 5.29/5.58 ( tc_HOL_Obool ) 5.29/5.58 ( tc_Int_Oint ) 5.29/5.58 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hAPP (c_SetInterval_Oord__class_OlessThan T_b) (hAPP _let_0 V_x_2)) (hAPP (c_Set_Oimage T_b T_b _let_0) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_x_2)))) )) 5.29/5.58 ( c_Int_OPls, tc_Int_Oint ) 5.29/5.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.58 ( c_Int_OMin, tc_Int_Oint ) 5.29/5.58 ) 5.29/5.58 (instantiation (forall ((V_k $$unsorted)) (not (= c_Int_OPls (c_Int_OBit1 V_k))) ) 5.29/5.58 ( c_Int_OPls ) 5.29/5.58 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.58 ( c_Int_OMin ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (let ((_let_1 (tc_fun _let_0 _let_0))) (let ((_let_2 (tc_fun tc_Nat_Onat _let_0))) (let ((_let_3 (tc_fun tc_Nat_Onat _let_1))) (forall ((V_z_2 $$unsorted)) (= (hAPP c_Int_Onat V_z_2) (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)))))) ))))) 5.29/5.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_1 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w))) (forall ((V_w $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) _let_1))) (= (c_Divides_Odiv__class_Omod tc_Int_Oint _let_0 _let_1) (hAPP (c_Product__Type_Osnd tc_Int_Oint tc_Int_Oint) (c_Divides_OposDivAlg _let_0 _let_1)))) ))) 5.29/5.58 ( c_Int_OPls ) 5.29/5.58 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.58 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.58 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.58 ( c_Int_OMin ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (c_Finite__Set_Ofold1 T_b (c_Groups_Otimes__class_Otimes T_b)))) (forall ((V_N_2 $$unsorted) (V_h_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 (forall ((B_x $$unsorted) (B_y $$unsorted)) (= (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 (hAPP _let_0 V_N_2)) (hAPP _let_0 (hAPP (c_Set_Oimage T_b T_b V_h_2) V_N_2))))) )) 5.29/5.58 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 5.29/5.58 ) 5.29/5.58 (instantiation (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))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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) (= (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _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)))) )))) 5.29/5.58 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.58 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.58 ( (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)) ) 5.29/5.58 ) 5.29/5.58 (instantiation (forall ((V_n $$unsorted)) (= V_n (hAPP c_Code__Numeral_Onat__of (hAPP c_Code__Numeral_Oof__nat V_n))) ) 5.29/5.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.58 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.29/5.58 ) 5.29/5.58 (instantiation (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_Ofold1 T_b (c_Groups_Otimes__class_Otimes T_b)))) (let ((_let_3 (c_Finite__Set_Ofinite T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Oab__semigroup__idem__mult T_b)) (not (hBOOL (hAPP _let_3 V_A_2))) (= V_A_2 _let_1) (not (hBOOL (hAPP _let_3 V_B_2))) (= V_B_2 _let_1) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_b) (hAPP _let_2 V_A_2)) (hAPP _let_2 V_B_2)) (hAPP _let_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)))) ))))) 5.29/5.58 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.58 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.58 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.58 ) 5.29/5.58 (instantiation (forall ((T_a $$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)))) ) 5.29/5.58 ( tc_Nat_Onat ) 5.29/5.58 ( tc_Int_Oint ) 5.29/5.58 ( tc_Code__Numeral_Ocode__numeral ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (forall ((V_al_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_List_Odistinct T_b) (hAPP (hAPP (c_List_Omap _let_0 T_b) (c_Product__Type_Ofst T_b T_c)) V_al_2)))) (= (c_Map_Oran T_b T_c (c_Map_Omap__of T_b T_c V_al_2)) (hAPP (c_Set_Oimage _let_0 T_c (c_Product__Type_Osnd T_b T_c)) (hAPP (c_List_Oset _let_0) V_al_2)))) )) 5.29/5.58 ( c_Com_Obodies, tc_Com_Ocom, tc_Com_Opname ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (let ((_let_2 (c_Set_Oimage T_c T_b V_f_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP _let_2 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d _let_1) V_A_2) V_B_2)) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d _let_0) V_A_2) (hAPP (hAPP (c_COMBB _let_1 _let_0 T_d) _let_2) V_B_2))) )))) 5.29/5.58 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.29/5.58 ) 5.29/5.58 (instantiation (forall ((V_z_2 $$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))) ) 5.29/5.58 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.29/5.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.58 ( c_Int_OMin, c_Int_OMin ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2))) )) 5.29/5.58 ( c_FunDef_Opair__less, (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.29/5.58 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.58 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_n_H_2 $$unsorted) (V_n_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (forall ((B_n $$unsorted)) (hBOOL (hAPP (hAPP _let_0 (hAPP V_f_2 B_n)) (hAPP V_f_2 (hAPP c_Nat_OSuc B_n)))) )) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_n_2) V_n_H_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP V_f_2 V_n_2)) (hAPP V_f_2 V_n_H_2)))) )) 5.29/5.58 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 5.29/5.58 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint), tc_Int_Oint ) 5.29/5.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 5.29/5.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 5.29/5.58 ( (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)))))), (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 ) 5.29/5.58 ) 5.29/5.58 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Oorder T_1)) (class_Orderings_Oorder (tc_fun T_2 T_1))) ) 5.29/5.58 ( tc_Com_Ocom, tc_HOL_Obool ) 5.29/5.58 ( tc_Nat_Onat, tc_HOL_Obool ) 5.29/5.58 ( tc_HOL_Obool, tc_HOL_Obool ) 5.29/5.58 ( tc_Int_Oint, tc_HOL_Obool ) 5.29/5.58 ( tc_Int_Oint, tc_Int_Oint ) 5.29/5.58 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.29/5.58 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.29/5.58 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.29/5.58 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.29/5.58 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_a_2))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP _let_0 (c_Groups_Ozero__class_Ozero T_b))) (hBOOL (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2))))) )) 5.29/5.58 ( c_Int_OPls, tc_Int_Oint ) 5.29/5.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.58 ( c_Int_OMin, tc_Int_Oint ) 5.29/5.58 ) 5.29/5.58 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (c_List_Olinorder__class_Osorted T_a (c_List_Olist_ONil T_a))) ) 5.29/5.58 ( tc_Nat_Onat ) 5.29/5.58 ( tc_Int_Oint ) 5.29/5.58 ( tc_Code__Numeral_Ocode__numeral ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_1 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_v_2))) (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (= (or (hBOOL (hAPP _let_1 V_v_H_2)) (hBOOL (hAPP _let_1 c_Int_OPls))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP _let_0 V_v_2)) (hAPP _let_0 V_v_H_2)))) ))) 5.29/5.58 ( c_Int_OPls, c_Int_OMin ) 5.29/5.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.58 ( c_Int_OMin, c_Int_OMin ) 5.29/5.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_z_H_2 $$unsorted) (V_z_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_z_2))) (not (hBOOL (hAPP _let_0 V_z_H_2))) (= (= (hAPP c_Int_Onat V_z_2) (hAPP c_Int_Onat V_z_H_2)) (= V_z_H_2 V_z_2))) )) 5.29/5.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.58 ( c_Int_OMin, c_Int_OMin ) 5.29/5.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.29/5.58 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.29/5.58 ) 5.29/5.58 (instantiation (forall ((V_A_2 $$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))) ) 5.29/5.58 ( (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 ) 5.29/5.58 ( 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 ) 5.29/5.58 ) 5.29/5.58 (instantiation (forall ((V_m_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat V_m_2) (hAPP c_Nat_OSuc V_m_2)) (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) V_m_2) (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)))) ) 5.29/5.58 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.29/5.58 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.29/5.58 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (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)))) )) 5.29/5.58 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.29/5.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.29/5.58 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.29/5.58 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.58 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.58 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.58 ) 5.29/5.58 (instantiation (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))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_A_2))) (not (hBOOL (hAPP _let_0 V_B_2))) (not (= (c_Orderings_Obot__class_Obot _let_2) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_2) V_A_2) V_B_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)))) )))) 5.29/5.58 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.58 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.58 ( (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 ) 5.29/5.58 ( (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)) ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (= (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))) )) 5.29/5.58 ( 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) ) 5.29/5.58 ) 5.29/5.58 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (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 (= (hAPP (hAPP _let_0 (hAPP (hAPP _let_0 (c_Groups_Oone__class_Oone T_b)) V_a_2)) V_a_2) (c_Groups_Ozero__class_Ozero T_b)))) )) 5.29/5.58 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.58 ( skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.29/5.58 ) 5.29/5.58 (instantiation (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))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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))) (= (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _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)))) )))) 5.29/5.59 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.59 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ) 5.29/5.59 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Groups_Ozero__class_Ozero T_b)))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2))) (hBOOL (hAPP _let_0 V_a_2)))) )) 5.29/5.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.29/5.59 ) 5.29/5.59 (instantiation (forall ((V_l_2 $$unsorted)) (= (= c_Int_OMin (c_Int_OBit1 V_l_2)) (= c_Int_OMin V_l_2)) ) 5.29/5.59 ( c_Int_OPls ) 5.29/5.59 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.59 ( c_Int_OMin ) 5.29/5.59 ) 5.29/5.59 (instantiation (let ((_let_0 (c_Groups_Oabs__class_Oabs T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) V_b))) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP _let_0 V_a)) (hAPP _let_0 V_b))))) )) 5.29/5.59 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 5.29/5.59 ) 5.29/5.59 (instantiation (forall ((V_y_2 $$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_x_2 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) V_y_2)))) ) 5.29/5.59 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.59 ( (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 ) 5.29/5.59 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.29/5.59 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.29/5.59 ( (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 ) 5.29/5.59 ) 5.29/5.59 (instantiation (let ((_let_0 (c_Relation_Oconverse T_c T_b))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (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))) )) 5.29/5.59 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 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) ) 5.29/5.59 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 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) ) 5.29/5.59 ( (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) ) 5.29/5.59 ) 5.29/5.59 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone tc_Nat_Onat))) (forall ((V_v $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_v) c_Int_OPls))) (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v)) _let_0))) )) 5.29/5.59 ( c_Int_OPls ) 5.29/5.59 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.29/5.59 ( c_Int_OMin ) 5.29/5.59 ) 5.29/5.59 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (forall ((V_v $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_v) c_Int_OPls)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP _let_0 V_v)) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 (c_Int_Osucc V_v)))) )) 5.29/5.59 ( c_Int_OPls ) 5.29/5.59 ( (c_Int_OBit1 c_Int_OPls) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.29/5.59 ( c_Int_OMin ) 5.29/5.59 ) 5.29/5.59 (instantiation (forall ((V_n_2 $$unsorted) (V_Pa_2 $$unsorted)) (or (hBOOL (hAPP V_Pa_2 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (not (hBOOL (hAPP V_Pa_2 V_n_2))) (not (forall ((B_k $$unsorted)) (or (not (forall ((B_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) B_i) B_k))) (not (hBOOL (hAPP V_Pa_2 B_i)))) )) (not (hBOOL (hAPP V_Pa_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) B_k) (c_Groups_Oone__class_Oone tc_Nat_Onat))))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_k) V_n_2)))) ))) ) 5.29/5.59 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 5.29/5.59 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 5.29/5.59 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 5.29/5.59 ( c_Int_OPls, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 5.29/5.59 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 5.29/5.59 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 5.29/5.59 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 5.29/5.59 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 5.29/5.59 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert tc_Nat_Onat) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( 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)) ) 5.29/5.59 ( c_fequal, (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 5.29/5.59 ( c_fequal, (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Nat__Numeral_Oneg ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_Onat ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 5.29/5.59 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat__Numeral_Oneg ) 5.29/5.59 ( (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))))) ) 5.29/5.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 5.29/5.59 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 5.29/5.59 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Nat_OSuc ) 5.29/5.59 ( (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) ) 5.29/5.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 5.29/5.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 5.29/5.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 5.29/5.59 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 5.29/5.59 ( c_Int_Onat, (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat) ) 5.29/5.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 5.29/5.59 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 5.29/5.59 ( (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) ) 5.29/5.59 ( c_fconj, (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) ) 5.29/5.59 ( c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 5.29/5.59 ( c_fTrue, (c_COMBK tc_HOL_Obool tc_Nat_Onat) ) 5.29/5.59 ( (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))) ) 5.29/5.59 ( (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) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Nat_Onat) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( c_Int_OMin, (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 5.29/5.59 ( c_Int_OMin, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 5.29/5.59 ( c_Int_OMin, (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 5.29/5.59 ( c_Int_OMin, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 5.29/5.59 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 5.29/5.59 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 5.29/5.59 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 5.29/5.59 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) ) 5.29/5.59 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc ) 5.29/5.59 ( (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) ) 5.29/5.59 ( c_Com_OWT, (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 5.29/5.59 ( (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) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Oint__of ) 5.29/5.59 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (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))) ) 5.29/5.59 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin), c_Nat__Numeral_Oneg ) 5.29/5.59 ( 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))) ) 5.29/5.59 ( c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)) ) 5.29/5.59 ( c_Com_Ocom_OSKIP, (c_Nat_Osize__class_Osize tc_Com_Ocom) ) 5.29/5.59 ( c_Com_Ocom_OSKIP, c_Com_OWT ) 5.29/5.59 ( 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)) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool), (let ((_let_0 (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)))) (c_COMBB _let_0 _let_0 tc_Int_Oint)) ) 5.29/5.59 ( v_s0, v_ba ) 5.29/5.59 ( (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))) ) 5.29/5.59 ( 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)))) ) 5.29/5.59 ( v_s2, v_b ) 5.29/5.59 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))) ) 5.29/5.59 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)) ) 5.29/5.59 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Orderings_Obot__class_Obot _let_0))) ) 5.29/5.59 ( (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))) ) 5.29/5.59 ( (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))) ) 5.29/5.59 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_0 _let_0))) ) 5.29/5.59 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (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_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))) (hAPP (hAPP (c_Product__Type_OPair (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_0) _let_0))) ) 5.29/5.59 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 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)))) ) 5.29/5.59 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 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)))) ) 5.29/5.59 ( c_FunDef_Omax__weak, (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_0 _let_0) c_FunDef_Omax__strict)) ) 5.29/5.59 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))) ) 5.29/5.59 ( c_FunDef_Omin__weak, (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_0 _let_0) c_FunDef_Omin__strict)) ) 5.29/5.59 ( v_s1, v_b ) 5.29/5.59 ( 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))) ) 5.29/5.59 ( (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))) ) 5.29/5.59 ( c_FunDef_Omax__strict, (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( c_fFalse, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 5.29/5.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), (c_Finite__Set_Ocard tc_HOL_Obool) ) 5.29/5.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Finite__Set_Ocard tc_Product__Type_Ounit) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (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)) ) 5.29/5.59 ( (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 ) 5.29/5.59 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), (c_Finite__Set_Ofinite tc_Com_Opname) ) 5.29/5.59 ( c_Com_Obodies, (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) ) 5.29/5.59 ( (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) ) 5.29/5.59 ( (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) ) 5.29/5.59 ( (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)) ) 5.39/5.59 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Int_Oint) ) 5.39/5.59 ( (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) ) 5.39/5.59 ( (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)) ) 5.39/5.59 ( (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) ) 5.39/5.59 ( (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_fun tc_Int_Oint tc_HOL_Obool)))) (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool))) ) 5.39/5.59 ( (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)) ) 5.39/5.59 ( (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)))))) ) 5.39/5.59 ( (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) ) 5.39/5.59 ( (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT), (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool) ) 5.39/5.59 ( (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (hAPP (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)) skv_9) ) 5.39/5.59 ( (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)) ) 5.39/5.59 ( (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)) ) 5.39/5.59 ( (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)) ) 5.39/5.59 ( (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)) ) 5.39/5.60 ( (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 ) 5.39/5.60 ( skv_2, (c_Fun_Ocomp skv_4 skv_8 skv_6 skv_3) ) 5.39/5.60 ( skv_2, (c_Fun_Ocomp skv_4 skv_7 skv_6 (hAPP (c_Fun_Ocomp skv_8 skv_7 skv_4 skv_5) skv_3)) ) 5.39/5.60 ( skv_3, (c_Fun_Ocomp skv_8 skv_7 skv_4 skv_5) ) 5.39/5.60 ( (hAPP (c_Fun_Ocomp skv_4 skv_8 skv_6 skv_3) skv_2), (c_Fun_Ocomp skv_8 skv_7 skv_6 skv_5) ) 5.39/5.60 ( skv_9, (hAPP (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool) (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT)) ) 5.39/5.60 ( skv_9, (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)) ) 5.39/5.60 ( skv_10, c_Com_OWT ) 5.39/5.60 ( skv_10, (c_Option_Ooption_OSome tc_Com_Ocom) ) 5.39/5.60 ( skv_11, c_Com_Obody ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (not (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) V_A_2))) )) (not (= _let_0 (c_Groups_Oone__class_Oone tc_Nat_Onat)))) (= _let_0 (hAPP (c_Finite__Set_Ocard T_b) V_A_2))) )) 5.39/5.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 5.39/5.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 5.39/5.60 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus (tc_fun T_b tc_HOL_Obool)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) (hAPP _let_0 V_A_2)) (hAPP _let_0 V_B_2)))) )) 5.39/5.60 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.60 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.60 ( (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)) ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) (c_Transitive__Closure_Ortrancl T_b V_r_2)) V_r_2) (c_Transitive__Closure_Otrancl T_b V_r_2)) ) 5.39/5.60 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_Pa_2 $$unsorted) (T_b $$unsorted)) (= (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_OCollect T_b) V_Pa_2)) (forall ((B_x $$unsorted)) (not (hBOOL (hAPP V_Pa_2 B_x))) )) ) 5.39/5.60 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.60 ( (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (c_Relation_ODomain T_b T_c))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP _let_0 V_A_2)) (hAPP _let_0 V_B_2)) (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_c) tc_HOL_Obool)) V_A_2) V_B_2))) )) 5.39/5.60 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.39/5.60 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.39/5.60 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((T_b $$unsorted)) (= (c_Relation_OId__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))) ) 5.39/5.60 ( tc_Nat_Onat ) 5.39/5.60 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.60 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone T_a))) (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) _let_0) _let_0)))) )) 5.39/5.60 ( tc_Nat_Onat ) 5.39/5.60 ( tc_Int_Oint ) 5.39/5.60 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_2 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_3 (hAPP _let_2 V_v_2))) (let ((_let_4 (hAPP _let_2 V_v_H_2))) (let ((_let_5 (hBOOL (hAPP c_Nat__Numeral_Oneg _let_4)))) (let ((_let_6 (hBOOL (hAPP c_Nat__Numeral_Oneg _let_3)))) (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (= (and (or _let_6 (and (or (not _let_5) (= _let_1 _let_3)) (or _let_5 (= V_v_H_2 V_v_2)))) (or (not _let_6) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_4) _let_1)))) (= (hAPP _let_0 V_v_H_2) (hAPP _let_0 V_v_2))) )))))))) 5.39/5.60 ( c_Int_OPls, c_Int_OPls ) 5.39/5.60 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls) ) 5.39/5.60 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.60 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.60 ( c_Int_OMin, c_Int_OMin ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_pn $$unsorted)) (or (= (c_Option_Ooption_ONone tc_Com_Ocom) (hAPP c_Com_Obody V_pn)) (hBOOL (hAPP c_Com_OWT (hAPP c_Com_Ocom_OBODY V_pn)))) ) 5.39/5.60 ( skv_11 ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_B_2) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBS T_b tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_b) c_fdisj) (hAPP (hAPP (c_COMBC T_b T_b tc_HOL_Obool) c_fequal) V_a_2))) (hAPP (hAPP (c_COMBC T_b (tc_fun T_b tc_HOL_Obool) tc_HOL_Obool) (c_member T_b)) V_B_2)))) ) 5.39/5.60 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.60 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.60 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.60 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) V_B_2))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (c_Finite__Set_Ocard (tc_sum T_b T_c)) (c_Sum__Type_OPlus T_b T_c V_A_2 V_B_2)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)) (hAPP (c_Finite__Set_Ocard T_c) V_B_2)))) ) 5.39/5.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit, (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (hAPP (c_COMBC T_b (tc_fun T_b tc_HOL_Obool) tc_HOL_Obool) (c_member T_b)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) 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_0 V_A_2))) (hAPP _let_0 V_B_2)))) )) 5.39/5.60 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.60 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.60 ( (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)) ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (c_Relation_OId T_b))) (forall ((T_b $$unsorted)) (= _let_0 (hAPP (c_Relation_Oconverse T_b T_b) _let_0)) )) 5.39/5.60 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_y $$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))) ) 5.39/5.60 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.39/5.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( (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 ) 5.39/5.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.60 ( (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 ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (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)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_l_2))) )) 5.39/5.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.60 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.60 ( (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) ) 5.39/5.60 ( (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) ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_A_2 $$unsorted)) (or (not (c_Nat__Transfer_Onat__set V_A_2)) (= V_A_2 (hAPP (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) (hAPP (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) V_A_2)))) ) 5.39/5.60 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (= V_a_2 (c_Groups_Ozero__class_Ozero T_b)) (= V_a_2 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)))) ) 5.39/5.60 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x)) (c_Orderings_Obot__class_Obot T_a))) ) 5.39/5.60 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_y $$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))) ) 5.39/5.60 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.39/5.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( (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 ) 5.39/5.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.60 ( (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 ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (c_Product__Type_Omap__pair T_b T_b T_c T_c (c_Fun_Oid T_b) (c_Fun_Oid T_c)) (c_Fun_Oid (tc_prod T_b T_c))) ) 5.39/5.60 ( tc_Com_Ocom, tc_Com_Opname ) 5.39/5.60 ( tc_Nat_Onat, tc_Nat_Onat ) 5.39/5.60 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.60 ( (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) ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((T_b $$unsorted) (V_xs_2 $$unsorted)) (or (= V_xs_2 (c_List_Olist_ONil T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (c_List_Ohd T_b) V_xs_2)) (hAPP (c_List_Oset T_b) V_xs_2)))) ) 5.39/5.60 ( (tc_prod tc_Com_Opname tc_Com_Ocom), c_Com_Obodies ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (c_Lattices_Osemilattice__sup__class_Osup T_b))) (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 $$unsorted)) (= (hAPP V_h_2 (hAPP (hAPP _let_0 B_x) B_y)) (hAPP (hAPP _let_0 (hAPP V_h_2 B_x)) (hAPP V_h_2 B_y))) )) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (= V_N_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (c_Set_Oimage T_b T_b V_h_2) V_N_2)) (hAPP V_h_2 (c_Big__Operators_Olattice__class_OSup__fin T_b V_N_2)))) )) 5.39/5.60 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_w $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (not (class_Int_Oring__char__0 T_a)) (not (c_Int_Oiszero T_a (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit1 V_w))))) ) 5.39/5.60 ( c_Int_OPls, tc_Nat_Onat ) 5.39/5.60 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.60 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.60 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.60 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.60 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_y_2 $$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)))) ) 5.39/5.60 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.39/5.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( (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 ) 5.39/5.60 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.60 ( (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 ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_k $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_k) (hAPP (c_Int_Oring__1__class_Oof__int T_a) V_k))) ) 5.39/5.60 ( c_Int_OPls, tc_Nat_Onat ) 5.39/5.60 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.60 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.60 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.60 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.60 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.39/5.60 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.60 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.60 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.60 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.60 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_a_2 $$unsorted) (V_ba_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_ba_2)) (hAPP _let_1 V_a_2))) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_ba_2)))) ))) 5.39/5.60 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.39/5.60 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.39/5.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_OBit0 (c_Int_Osucc V_k)) (c_Int_Osucc (c_Int_OBit1 V_k))) ) 5.39/5.60 ( c_Int_OPls ) 5.39/5.60 ( (c_Int_OBit1 c_Int_OPls) ) 5.39/5.60 ( c_Int_OMin ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (tc_prod T_c T_b))) (forall ((V_x_2 $$unsorted) (V_xys_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (not (hBOOL (hAPP (hAPP (c_member T_c) V_x_2) (hAPP (c_Set_Oimage _let_0 T_c (c_Product__Type_Ofst T_c T_b)) (hAPP (c_List_Oset _let_0) V_xys_2))))) (= (c_Option_Ooption_ONone T_b) (hAPP (c_Map_Omap__of T_c T_b V_xys_2) V_x_2))) )) 5.39/5.60 ( skv_11, c_Com_Obodies, tc_Com_Ocom, tc_Com_Opname ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (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))))) ))) 5.39/5.60 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.60 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.60 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_a_2 $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool))) (c_SetInterval_Oord_OatLeastAtMost tc_Nat_Onat (c_Rings_Odvd__class_Odvd tc_Nat_Onat) V_a_2 V_a_2)) ) 5.39/5.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (c_Relation_OField T_b))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted)) (= (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))) )) 5.39/5.60 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 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) ) 5.39/5.60 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 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) ) 5.39/5.60 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.60 ) 5.39/5.60 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (= (hAPP _let_1 V_m_2) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP _let_1 V_n_2))) (and (= _let_0 V_m_2) (= _let_0 V_n_2))) ))) 5.39/5.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.60 ( (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))) ) 5.39/5.60 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.60 ( (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))) ) 5.39/5.60 ) 5.39/5.60 (instantiation (forall ((V_n_2 $$unsorted)) (= (= (c_Groups_Ozero__class_Ozero tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n_2)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_n_2)) ) 5.39/5.60 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.60 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.61 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (c_Big__Operators_Olinorder__class_OMin T_b V_A_2))) (forall ((V_x_2 $$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))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= _let_0 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) _let_0))) )) 5.39/5.61 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.39/5.61 ) 5.39/5.61 (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)))) ) 5.39/5.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.61 ) 5.39/5.61 (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))) ) 5.39/5.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.61 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless T_b) V_a_2))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2))) (hBOOL (hAPP _let_0 (c_Groups_Ozero__class_Ozero T_b))))) )) 5.39/5.61 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.61 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (and (= _let_0 V_n_2) (= _let_0 V_m_2)) (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m_2) V_n_2))) )) 5.39/5.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.61 ) 5.39/5.61 (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))))) ) 5.39/5.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.61 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (c_Relation_ORange T_c T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (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)) (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))) )) 5.39/5.61 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 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) ) 5.39/5.61 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 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) ) 5.39/5.61 ( (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) ) 5.39/5.61 ) 5.39/5.61 (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))) ) 5.39/5.61 ( tc_Com_Ocom, tc_HOL_Obool ) 5.39/5.61 ( tc_Nat_Onat, tc_HOL_Obool ) 5.39/5.61 ( tc_HOL_Obool, tc_HOL_Obool ) 5.39/5.61 ( tc_Int_Oint, tc_HOL_Obool ) 5.39/5.61 ( tc_Int_Oint, tc_Int_Oint ) 5.39/5.61 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.39/5.61 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.39/5.61 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.39/5.61 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.39/5.61 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.39/5.61 ) 5.39/5.61 (instantiation (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))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_d $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (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))) ))))) 5.39/5.61 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (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, tc_Nat_Onat ) 5.39/5.61 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (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, tc_Nat_Onat ) 5.39/5.61 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (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, tc_Nat_Onat ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_w))) (forall ((V_w $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Omonoid__mult T_b)) (not (class_Int_Onumber T_b)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_b) _let_0) _let_0) (hAPP (hAPP (c_Power_Opower__class_Opower T_b) _let_0) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))))) )) 5.39/5.61 ( c_Int_OPls, tc_Nat_Onat ) 5.39/5.61 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.61 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.61 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.61 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.61 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.39/5.61 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.61 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.61 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.61 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.61 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP _let_0 V_A_2) V_B_2) (hAPP (hAPP _let_0 V_B_2) V_A_2)) )) 5.39/5.61 ( 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)) ) 5.39/5.61 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.61 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.61 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.61 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.61 ( (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)) ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= V_n_2 V_m_2) (= (hAPP (hAPP _let_0 V_m_2) V_k_2) (hAPP (hAPP _let_0 V_n_2) V_k_2))) )) 5.39/5.61 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (c_List_Olinorder__class_Osorted__list__of__set T_b V_A_2))) (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))) (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))) )) 5.39/5.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.61 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.61 ) 5.39/5.61 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Ozero__neq__one T_a)) (not (= (c_Groups_Oone__class_Oone T_a) (c_Groups_Ozero__class_Ozero T_a)))) ) 5.39/5.61 ( tc_Nat_Onat ) 5.39/5.61 ( tc_Int_Oint ) 5.39/5.61 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_1 (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_w))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit1 V_w)) (hAPP (hAPP _let_0 (hAPP (hAPP _let_0 (c_Groups_Oone__class_Oone T_a)) _let_1)) _let_1))) ))) 5.39/5.61 ( c_Int_OPls, tc_Nat_Onat ) 5.39/5.61 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.61 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.61 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.61 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.61 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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 _let_2) V_A_2) V_B_2)))) )) (not (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)))) (= (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)))) )))) 5.39/5.61 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.61 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.61 ( (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 ) 5.39/5.61 ( (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)) ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2))) (let ((_let_2 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_3 (c_Finite__Set_Ofinite T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_3 V_A_2))) (not (hBOOL (hAPP _let_3 V_B_2))) (= _let_1 (c_Orderings_Obot__class_Obot _let_0)) (= (hAPP (hAPP _let_2 (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2))) (c_Big__Operators_Olinorder__class_OMin T_b _let_1)) (hAPP (hAPP _let_2 (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMin T_b V_B_2)))) ))))) 5.39/5.61 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.61 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.61 ( (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)) ) 5.39/5.61 ) 5.39/5.61 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_y_2) V_x_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2))))) ) 5.39/5.61 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.39/5.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.39/5.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.39/5.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.61 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.39/5.61 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.61 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_member T_b))) (let ((_let_2 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_3 (c_Set_Oinsert T_b))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 _let_0) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (hBOOL (hAPP (hAPP _let_1 (hAPP (hAPP _let_2 B_x) B_y)) (hAPP (hAPP _let_3 B_x) (hAPP (hAPP _let_3 B_y) _let_0)))) )) (hBOOL (hAPP (hAPP _let_1 (c_Big__Operators_Olattice_OInf__fin T_b _let_2 V_A_2)) V_A_2))) ))))) 5.39/5.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.61 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.61 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.61 ) 5.39/5.61 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OlessThan T_b))) (forall ((V_u_2 $$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 _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)))) )) 5.39/5.61 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.39/5.61 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.61 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.61 ( (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 ) 5.39/5.61 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.61 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.61 ( (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 ) 5.39/5.61 ) 5.39/5.61 (instantiation (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_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Divides_OnegDivAlg__rel))) (let ((_let_4 (hAPP V_Pa_2 B_a))) (forall ((V_Pa_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP _let_3 (hAPP (hAPP _let_2 V_a0_2) V_a1_2)))) (not (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (not (hBOOL (hAPP _let_3 (hAPP (hAPP _let_2 B_a) B_b)))) (and (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 (hAPP _let_0 B_b) _let_1))) (not (hBOOL (hAPP _let_4 (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_4 B_b))) )) (hBOOL (hAPP (hAPP V_Pa_2 V_a0_2) V_a1_2))) )))))) 5.39/5.61 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OPls, c_Int_OMin ) 5.39/5.61 ( (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) ) 5.39/5.61 ( (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) ) 5.39/5.61 ( (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) ) 5.39/5.61 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.61 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 5.39/5.61 ( (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) ) 5.39/5.61 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.61 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.61 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.39/5.61 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.61 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.61 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 5.39/5.61 ( (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) ) 5.39/5.61 ( (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) ) 5.39/5.61 ( (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) ) 5.39/5.61 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), (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)) ) 5.39/5.61 ( (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)) ) 5.39/5.61 ( (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)) ) 5.39/5.61 ( (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 ) 5.39/5.61 ( (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) ) 5.39/5.61 ( (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)) ) 5.39/5.61 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 5.39/5.61 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 5.39/5.61 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_0 _let_0))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (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_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_0) _let_0)) ) 5.39/5.62 ( (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)) ) 5.39/5.62 ( (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)) ) 5.39/5.62 ( (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)) ) 5.39/5.62 ( (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)) ) 5.39/5.62 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omax__weak, c_FunDef_Omax__strict ) 5.39/5.62 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omin__weak, c_FunDef_Omin__strict ) 5.39/5.62 ( (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) ) 5.39/5.62 ( (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 ) 5.39/5.62 ( (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 ) 5.39/5.62 ( (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)))) ) 5.39/5.62 ( (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)))) ) 5.39/5.62 ( (let ((_let_0 (tc_fun tc_Int_Oint (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))) (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) ) 5.39/5.62 ( (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) ) 5.39/5.62 ( (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool), skv_9, (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT) ) 5.39/5.62 ( (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)), (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9 ) 5.39/5.62 ( (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 ) 5.39/5.62 ( (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 ) 5.39/5.62 ) 5.39/5.62 (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)) ) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Groups_Otimes__class_Otimes T_b))) (let ((_let_2 (c_Set_Oinsert T_b))) (let ((_let_3 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (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 _let_3) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_x) B_y)) (hAPP (hAPP _let_2 B_x) (hAPP (hAPP _let_2 B_y) _let_3)))) )) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Finite__Set_Ofold1 T_b _let_1) V_A_2)) V_A_2))) ))))) 5.39/5.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.62 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (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)) )) 5.39/5.62 ( c_Int_OPls, c_Int_OMin ) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.39/5.62 ( (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))) ) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.39/5.62 ( (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))) ) 5.39/5.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.62 ( (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) ) 5.39/5.62 ( c_Int_OMin, c_Int_OPls ) 5.39/5.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.62 ( c_Int_OMin, c_Int_OMin ) 5.39/5.62 ( (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) ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (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 _let_2) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) B_x) B_y)) (hAPP (hAPP _let_1 B_x) (hAPP (hAPP _let_1 B_y) _let_2)))) )) (hBOOL (hAPP (hAPP _let_0 (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) V_A_2))) )))) 5.39/5.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.62 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (hAPP _let_0 V_v)) (hAPP _let_0 V_w)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_v) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_w))))) )) 5.39/5.62 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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)))) ))))) 5.39/5.62 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.62 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.62 ( (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)) ) 5.39/5.62 ) 5.39/5.62 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_k_2) V_l_2))) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (c_SetInterval_Oord__class_OgreaterThanAtMost T_b V_k_2 V_l_2)))) ) 5.39/5.62 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.39/5.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.62 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.62 ) 5.39/5.62 (instantiation (forall ((T_a $$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))))) ) 5.39/5.62 ( tc_Nat_Onat ) 5.39/5.62 ( tc_Int_Oint ) 5.39/5.62 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.62 ) 5.39/5.62 (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 tc_Int_Oint) V_x_2) c_Int_OPls)) (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))))) ) 5.39/5.62 ( c_Int_OPls, tc_Nat_Onat ) 5.39/5.62 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.62 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.62 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.62 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.62 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.39/5.62 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.62 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.62 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.62 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.62 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (forall ((V_m $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) V_m))) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n)) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (hAPP _let_0 V_m)) (hAPP _let_0 V_n)))) )) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint tc_HOL_Obool))) (forall ((V_d_2 $$unsorted)) (= (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))))) ))) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.62 ( c_Int_OMin ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v))) (forall ((V_v $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) _let_0))) (= _let_0 (hAPP c_Nat_OSuc (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) _let_0) (c_Groups_Oone__class_Oone tc_Nat_Onat))))) )) 5.39/5.62 ( c_Int_OPls ) 5.39/5.62 ( (c_Int_OBit1 c_Int_OPls) ) 5.39/5.62 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.62 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.62 ) 5.39/5.62 (instantiation (forall ((V_y $$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)))) ) 5.39/5.62 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.62 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.62 ( (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)) ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted)) (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)) )) 5.39/5.62 ( c_Nat_OSuc, tc_Nat_Onat ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_x_2) V_A_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.62 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.62 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.62 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.62 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.39/5.62 ) 5.39/5.62 (instantiation (forall ((V_a_2 $$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))) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Orderings_Oord__class_Omin T_b)) V_a_2) V_A_2) (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)))) ) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.62 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.62 ( (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) ) 5.39/5.62 ( (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) ) 5.39/5.62 ) 5.39/5.62 (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)))) ) 5.39/5.62 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.62 ) 5.39/5.62 (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) (c_Nitpick_Ocard_H T_b V_A_2))) ) 5.39/5.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.62 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (tc_List_Olist T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Nitpick_Ocard_H T_b V_A_2) (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 T_b))) V_A_2))) (c_List_Odistinct T_b)))))) ))) 5.39/5.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.62 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.62 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.62 ) 5.39/5.62 (instantiation (forall ((V_j $$unsorted) (V_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_i) V_j))) (= (hAPP (hAPP (c_List_Olist_OCons tc_Int_Oint) V_i) (c_List_Oupto (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_i) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_j)) (c_List_Oupto V_i V_j))) ) 5.39/5.62 ( c_Int_OPls, c_Int_OMin ) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.62 ( (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) ) 5.39/5.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.62 ( c_Int_OMin, c_Int_OMin ) 5.39/5.62 ( (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) ) 5.39/5.62 ) 5.39/5.62 (instantiation (forall ((V_j $$unsorted) (V_i $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_i) V_j)) (= (c_List_Olist_ONil tc_Int_Oint) (c_List_Oupto V_i V_j))) ) 5.39/5.62 ( c_Int_OPls, c_Int_OMin ) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.62 ( (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) ) 5.39/5.62 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.62 ( c_Int_OMin, c_Int_OMin ) 5.39/5.62 ( (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) ) 5.39/5.62 ) 5.39/5.62 (instantiation (forall ((V_xs_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) (hAPP (c_List_Oset T_b) V_xs_2)))) (not (c_List_Olinorder__class_Osorted T_b V_xs_2)) (= V_xs_2 (hAPP (hAPP (c_List_Olinorder__class_Oinsort__key T_b T_b (c_COMBI T_b)) V_a_2) (c_List_Oremove1 T_b V_a_2 V_xs_2)))) ) 5.39/5.62 ( c_Com_Obodies, skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.39/5.62 ) 5.39/5.62 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Groups_Oabs__class_Oabs T_a) (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OMin)) (c_Groups_Oone__class_Oone T_a))) ) 5.39/5.62 ( tc_Nat_Onat ) 5.39/5.62 ( tc_Int_Oint ) 5.39/5.62 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.62 ) 5.39/5.62 (instantiation (forall ((V_com_H_2 $$unsorted) (V_fun_H_2 $$unsorted)) (not (= c_Com_Ocom_OSKIP (c_Com_Ocom_OWhile V_fun_H_2 V_com_H_2))) ) 5.39/5.62 ( v_c, v_b ) 5.39/5.62 ) 5.39/5.62 (instantiation (forall ((V_z $$unsorted)) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg V_z))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP c_Int_Onat V_z))) ) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.62 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.39/5.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.62 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin) ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (forall ((V_x_2 $$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_member T_b) V_x_2) V_A_2)) (= (hAPP c_Nat_OSuc (hAPP _let_0 V_A_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 5.39/5.62 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.62 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.62 ( (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) ) 5.39/5.62 ( (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) ) 5.39/5.62 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.39/5.62 ) 5.39/5.62 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (let ((_let_1 (tc_Option_Ooption T_c))) (let ((_let_2 (tc_fun T_c _let_1))) (let ((_let_3 (tc_fun T_c tc_HOL_Obool))) (let ((_let_4 (tc_fun _let_1 tc_HOL_Obool))) (forall ((V_xs_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_List_Odistinct T_b) (hAPP (hAPP (c_List_Omap _let_0 T_b) (c_Product__Type_Ofst T_b T_c)) V_xs_2)))) (= (hAPP (c_List_Oset _let_0) V_xs_2) (hAPP (c_Set_OCollect _let_0) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c tc_HOL_Obool) (hAPP (hAPP (c_COMBC T_b _let_2 _let_3) (hAPP (hAPP (c_COMBB _let_4 (tc_fun _let_2 _let_3) T_b) (c_COMBB _let_1 tc_HOL_Obool T_c)) (hAPP (hAPP (c_COMBB _let_1 _let_4 T_b) c_fequal) (c_Map_Omap__of T_b T_c V_xs_2)))) (c_Option_Ooption_OSome T_c)))))) )))))) 5.39/5.63 ( c_Com_Obodies, tc_Com_Ocom, tc_Com_Opname ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (c_Finite__Set_Ofinite T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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))) (= (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_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)))) )))) 5.39/5.63 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.63 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.63 ( (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)) ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (forall ((V_Ga_2 $$unsorted) (V_F_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_F_2))) (not (hBOOL (hAPP _let_0 V_Ga_2))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_F_2) V_Ga_2)))) )) 5.39/5.63 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.63 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.63 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) V_A_2))) ) 5.39/5.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 5.39/5.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 5.39/5.63 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (c_Finite__Set_Ocard T_b) V_A_2) (hAPP (hAPP (hAPP (c_Finite__Set_Ofold__image tc_Nat_Onat T_b (c_Groups_Oplus__class_Oplus tc_Nat_Onat)) (hAPP (c_COMBK tc_Nat_Onat T_b) (c_Groups_Oone__class_Oone tc_Nat_Onat))) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_A_2))) ) 5.39/5.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 5.39/5.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 5.39/5.63 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((V_x $$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)))) ) 5.39/5.63 ( 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)) ) 5.39/5.63 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.63 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) (c_Orderings_Obot__class_Obot _let_0))) )) 5.39/5.63 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.39/5.63 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.63 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP _let_0 (c_Int_Opred V_w)) (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)))) )) 5.39/5.63 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (forall ((V_m $$unsorted) (T_a $$unsorted)) (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)))) )) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.39/5.63 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), tc_Int_Oint ) 5.39/5.63 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), tc_Int_Oint ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Power_Opower T_b)) (= (c_Power_Opower__class_Opower T_b) (c_Power_Opower_Opower T_b (c_Groups_Oone__class_Oone T_b) (c_Groups_Otimes__class_Otimes T_b)))) ) 5.39/5.63 ( tc_Nat_Onat ) 5.39/5.63 ( tc_Int_Oint ) 5.39/5.63 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_b)) (= (= V_y_2 V_x_2) (= (hAPP _let_0 V_x_2) (hAPP _let_0 V_y_2)))) )) 5.39/5.63 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.39/5.63 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.39/5.63 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= V_x (hAPP _let_0 (hAPP _let_0 V_x)))) )) 5.39/5.63 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_n_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (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)) (hAPP (hAPP (c_Set_Oinsert T_b) V_n_2) (c_Orderings_Obot__class_Obot _let_0)))) )) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.63 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.63 ( (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)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.63 ( (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)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.63 ) 5.39/5.63 (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))) (= (hAPP (c_Finite__Set_Ofold1 T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b)) V_A_2) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2))) ) 5.39/5.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.63 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (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)))) )) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_v) V_w)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP _let_0 V_v)) (hAPP _let_0 V_w)))) )) 5.39/5.63 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (c_Fun_Oid (tc_prod T_b T_c)) (c_Product__Type_Omap__pair T_b T_b T_c T_c (c_COMBI T_b) (c_COMBI T_c))) ) 5.39/5.63 ( tc_Com_Ocom, tc_Com_Opname ) 5.39/5.63 ( tc_Nat_Onat, tc_Nat_Onat ) 5.39/5.63 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.63 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_u_2 $$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 (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))) )) 5.39/5.63 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_a_2) V_ba_2))) (not (hBOOL (hAPP (hAPP _let_0 V_ca_2) V_d_2))) (= (and (= V_d_2 V_ba_2) (= V_ca_2 V_a_2)) (= (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_a_2) V_ba_2) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_ca_2) V_d_2)))) )) 5.39/5.63 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( c_Int_OMin, c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( c_Int_OMin, c_Int_OMin, c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (= (hAPP (c_Finite__Set_Ocard T_b) V_A_2) (hAPP (c_Finite__Set_Ocard T_c) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2)) ) 5.39/5.63 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.63 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.63 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OatMost T_b))) (forall ((V_u_2 $$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 _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)))) )) 5.39/5.63 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( (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 ) 5.39/5.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.63 ( (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 ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_b) V_a))) (not (hBOOL (hAPP (hAPP _let_0 V_a) V_b)))) )) 5.39/5.63 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (forall ((T_a $$unsorted)) (or (not (class_Groups_Osgn__if T_a)) (= _let_0 (c_Groups_Osgn__class_Osgn T_a _let_0))) )) 5.39/5.63 ( tc_Nat_Onat ) 5.39/5.63 ( tc_Int_Oint ) 5.39/5.63 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.63 ) 5.39/5.63 (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)))) ) 5.39/5.63 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.39/5.63 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 5.39/5.63 ( (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 ) 5.39/5.63 ) 5.39/5.63 (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) V_r_2) (c_Transitive__Closure_Ortrancl T_b V_r_2))) ) 5.39/5.63 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.39/5.63 ) 5.39/5.63 (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 (hAPP (c_COMBC T_b T_b tc_HOL_Obool) c_fequal) V_a_2))) ) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.63 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.63 ( (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)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.63 ( (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)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((V_w $$unsorted)) (= (hAPP (c_Int_Oring__1__class_Oof__int tc_Int_Oint) V_w) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w)) ) 5.39/5.63 ( c_Int_OPls ) 5.39/5.63 ( (c_Int_OBit1 c_Int_OPls) ) 5.39/5.63 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.63 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.63 ( c_Int_OMin ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((T_b $$unsorted)) (= (c_Option_Oset T_b (c_Option_Ooption_ONone T_b)) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) ) 5.39/5.63 ( tc_Com_Ocom ) 5.39/5.63 ( tc_Nat_Onat ) 5.39/5.63 ( tc_HOL_Obool ) 5.39/5.63 ( tc_Int_Oint ) 5.39/5.63 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.63 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.39/5.63 ( tc_Product__Type_Ounit ) 5.39/5.63 ) 5.39/5.63 (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))) ) 5.39/5.63 ( tc_Com_Ocom, tc_HOL_Obool ) 5.39/5.63 ( tc_Nat_Onat, tc_HOL_Obool ) 5.39/5.63 ( tc_HOL_Obool, tc_HOL_Obool ) 5.39/5.63 ( tc_Int_Oint, tc_HOL_Obool ) 5.39/5.63 ( tc_Int_Oint, tc_Int_Oint ) 5.39/5.63 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.39/5.63 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.39/5.63 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.39/5.63 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.39/5.63 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.39/5.63 ) 5.39/5.63 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (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))) )) 5.39/5.63 ( tc_Com_Ocom, tc_Com_Opname ) 5.39/5.63 ( tc_Nat_Onat, tc_Nat_Onat ) 5.39/5.63 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.63 ( (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) ) 5.39/5.63 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)) (= V_y_2 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) V_y_2)))) ) 5.39/5.63 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.63 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((V_v_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_d $$unsorted)) (= (hAPP V_a_2 (hAPP V_ba_2 V_v_2)) (hAPP (hAPP (c_Fun_Ocomp T_d T_c T_b V_a_2) V_ba_2) V_v_2)) ) 5.39/5.63 ( c_Int_OPls, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 5.39/5.63 ( (c_Int_OBit1 c_Int_OPls), c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 5.39/5.63 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Onat__of, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Code__Numeral_Ocode__numeral, tc_Int_Oint, tc_Nat_Onat ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (not (c_Int_Oiszero T_a (c_Groups_Oone__class_Oone T_a)))) ) 5.39/5.63 ( tc_Nat_Onat ) 5.39/5.63 ( tc_Int_Oint ) 5.39/5.63 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((T_b $$unsorted) (V_as_2 $$unsorted)) (or (= V_as_2 (c_List_Olist_ONil T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (c_List_Olast T_b V_as_2)) (hAPP (c_List_Oset T_b) V_as_2)))) ) 5.39/5.63 ( (tc_prod tc_Com_Opname tc_Com_Ocom), c_Com_Obodies ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((V_ca_2 $$unsorted) (V_ba_2 $$unsorted)) (or (not (hBOOL (hAPP c_Com_OWT (c_Com_Ocom_OWhile V_ba_2 V_ca_2)))) (hBOOL (hAPP c_Com_OWT V_ca_2))) ) 5.39/5.63 ( v_c, v_b ) 5.39/5.63 ) 5.39/5.63 (instantiation (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 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w))) (forall ((V_w $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_2) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (= (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) _let_0) _let_2) (hAPP (c_Product__Type_Ofst tc_Int_Oint tc_Int_Oint) (hAPP c_Divides_OnegateSnd (c_Divides_OnegDivAlg (hAPP _let_1 _let_0) (hAPP _let_1 _let_2)))))) )))) 5.39/5.63 ( c_Int_OPls ) 5.39/5.63 ( (c_Int_OBit1 c_Int_OPls) ) 5.39/5.63 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.63 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.63 ( c_Int_OMin ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (c_Set_Oimage T_c T_b V_f_2) (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) ) 5.39/5.63 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.39/5.63 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 5.39/5.63 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 5.39/5.63 ) 5.39/5.63 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (c_Orderings_Oord_Omin T_b (c_Orderings_Oord__class_Oless__eq T_b)) (c_Orderings_Oord__class_Omin T_b))) ) 5.39/5.64 ( tc_Nat_Onat ) 5.39/5.64 ( tc_HOL_Obool ) 5.39/5.64 ( tc_Int_Oint ) 5.39/5.64 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_b))) (let ((_let_1 (hAPP (c_Orderings_Oord__class_Oless__eq T_b) _let_0))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__comm__monoid__add T_b)) (not (hBOOL (hAPP _let_1 V_x_2))) (not (hBOOL (hAPP _let_1 V_y_2))) (= (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_x_2) V_y_2) _let_0) (and (= V_y_2 _let_0) (= V_x_2 _let_0)))) ))) 5.39/5.64 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.64 ) 5.39/5.64 (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)))) ) 5.39/5.64 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.64 ( (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 ) 5.39/5.64 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_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 ) 5.39/5.64 ) 5.39/5.64 (instantiation (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 (hAPP (c_COMBB _let_1 (tc_fun _let_2 tc_HOL_Obool) T_b) (c_member _let_1)))) (let ((_let_6 (c_Product__Type_OPair T_b T_b))) (let ((_let_7 (c_Transitive__Closure_Ortrancl T_b V_r_2))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (= (c_Transitive__Closure_Otrancl T_b (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP _let_6 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_5 (hAPP (hAPP (c_COMBC T_b T_b _let_1) _let_6) V_y_2))) _let_7)))) (hAPP (hAPP _let_4 (hAPP _let_5 (hAPP _let_6 V_x_2))) _let_7)))))) ))))))))) 5.39/5.64 ( (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 ) 5.39/5.64 ( (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 ) 5.39/5.64 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) 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) ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) (hAPP (c_List_Oset T_b) V_xs_2)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Nat_Osize__class_Osize (tc_List_Olist T_b)) V_xs_2)))) ) 5.39/5.64 ( c_Com_Obodies, skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OPls) (c_Groups_Ozero__class_Ozero T_a))) ) 5.39/5.64 ( tc_Nat_Onat ) 5.39/5.64 ( tc_Int_Oint ) 5.39/5.64 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Oone__class_Oone T_a)) (c_Groups_Ozero__class_Ozero T_a))))) ) 5.39/5.64 ( tc_Nat_Onat ) 5.39/5.64 ( tc_Int_Oint ) 5.39/5.64 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_w_2 $$unsorted) (V_z_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_2))) (= (hBOOL (hAPP (hAPP _let_0 V_w_2) V_z_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP c_Int_Onat V_w_2)) (hAPP c_Int_Onat V_z_2))))) )) 5.39/5.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 5.39/5.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.39/5.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.39/5.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.64 ( c_Int_OMin, c_Int_OMin ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((T_b $$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)))) ) 5.39/5.64 ( tc_Nat_Onat ) 5.39/5.64 ( tc_Int_Oint ) 5.39/5.64 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.64 ( (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.39/5.64 ) 5.39/5.64 (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)))) ) 5.39/5.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.39/5.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.39/5.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.39/5.64 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 5.39/5.64 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.39/5.64 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (= (c_Map_Odom T_b T_c V_f_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= V_f_2 (hAPP (c_COMBK (tc_Option_Ooption T_c) T_b) (c_Option_Ooption_ONone T_c)))) ) 5.39/5.64 ( c_Com_Obody, tc_Com_Ocom, tc_Com_Opname ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((V_n $$unsorted)) (= (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_n))) (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)) ) 5.39/5.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) _let_1)))) (let ((_let_3 (= _let_1 _let_2))) (let ((_let_4 (c_Big__Operators_Olinorder__class_OMax T_b V_A_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (and (or _let_3 (= (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMax T_b _let_2)) _let_4)) (or (not _let_3) (= V_x_2 _let_4)))) )))))) 5.39/5.64 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (c_Nitpick_Onat__gcd V_x_2 V_y_2))) (let ((_let_1 (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_y_2))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Nat_Onat tc_Nat_Onat) c_Nitpick_Onat__gcd__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_x_2) V_y_2)))) (and (or _let_1 (= (c_Nitpick_Onat__gcd V_y_2 (c_Divides_Odiv__class_Omod tc_Nat_Onat V_x_2 V_y_2)) _let_0)) (or (not _let_1) (= V_x_2 _let_0)))) ))) 5.39/5.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) V_n) V_m) (hAPP c_Code__Numeral_Oof__nat (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP c_Code__Numeral_Onat__of V_n)) (hAPP c_Code__Numeral_Onat__of V_m)))) ) 5.39/5.64 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (c_Set_Oinsert T_b))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (or (and (= V_d_2 V_a_2) (= V_ca_2 V_ba_2)) (and (= V_d_2 V_ba_2) (= V_ca_2 V_a_2))) (= (hAPP (hAPP _let_0 V_ca_2) (hAPP (hAPP _let_0 V_d_2) _let_1)) (hAPP (hAPP _let_0 V_a_2) (hAPP (hAPP _let_0 V_ba_2) _let_1)))) ))) 5.39/5.64 ( (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 ) 5.39/5.64 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.64 ( (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)), (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)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.64 ( (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) ) 5.39/5.64 ( (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) ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2))) (forall ((V_ca_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ocancel__semigroup__add T_b)) (= (= V_ca_2 V_ba_2) (= (hAPP _let_0 V_ba_2) (hAPP _let_0 V_ca_2)))) )) 5.39/5.64 ( (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 ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((V_com_2 $$unsorted) (V_fun_2 $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Com_Ocom_Ocom__size V_com_2)) (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Com_Ocom_Ocom__size (c_Com_Ocom_OWhile V_fun_2 V_com_2))) ) 5.39/5.64 ( v_c, v_b ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (hAPP _let_0 V_x))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (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))) ))) 5.39/5.64 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.39/5.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.64 ( c_Int_OMin, c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Set_Oinsert _let_0))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2) (c_Complete__Lattice_OSup__class_OSup _let_0 (hAPP (hAPP _let_1 V_A_2) (hAPP (hAPP _let_1 V_B_2) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))))) ))) 5.39/5.64 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.64 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.64 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP (c_Finite__Set_Ofold1 T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b)) V_A_2)) V_a_2))) ) 5.39/5.64 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.39/5.64 ) 5.39/5.64 (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))) ) 5.39/5.64 ( tc_Com_Ocom, tc_HOL_Obool ) 5.39/5.64 ( tc_Nat_Onat, tc_HOL_Obool ) 5.39/5.64 ( tc_HOL_Obool, tc_HOL_Obool ) 5.39/5.64 ( tc_Int_Oint, tc_HOL_Obool ) 5.39/5.64 ( tc_Int_Oint, tc_Int_Oint ) 5.39/5.64 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.39/5.64 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.39/5.64 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.39/5.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.39/5.64 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) c_Int_OMin))) (forall ((V_l $$unsorted)) (= (c_Int_OBit0 (hAPP _let_0 V_l)) (hAPP _let_0 (c_Int_OBit1 V_l))) )) 5.39/5.64 ( c_Int_OPls ) 5.39/5.64 ( (c_Int_OBit1 c_Int_OPls) ) 5.39/5.64 ( c_Int_OMin ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((T_b $$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)))) ) 5.39/5.64 ( tc_Com_Ocom ) 5.39/5.64 ( tc_Nat_Onat ) 5.39/5.64 ( tc_HOL_Obool ) 5.39/5.64 ( tc_Int_Oint ) 5.39/5.64 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.64 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.64 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.39/5.64 ( tc_Product__Type_Ounit ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((V_n_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_n_2) (hAPP (c_List_Oset tc_Nat_Onat) (c_List_Oupt (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP c_Nat_OSuc V_n_2)))) ) 5.39/5.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.64 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.39/5.64 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((V_ba_2 $$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_ba_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_ba_2))))) ) 5.39/5.64 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.39/5.64 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.64 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.64 ( (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 ) 5.39/5.64 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.64 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.64 ( (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 ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_b)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b))) ) 5.39/5.64 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((V_k_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) (hAPP c_Nat_OSuc V_k_2)) (hAPP (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) V_k_2)) ) 5.39/5.64 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.64 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.39/5.64 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (let ((_let_1 (hAPP _let_0 V_w_2))) (let ((_let_2 (hAPP _let_0 V_v_2))) (forall ((V_w_2 $$unsorted) (V_v_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (class_Int_Onumber T_b)) (= (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) _let_1) _let_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) _let_2) _let_1)))) )))) 5.39/5.64 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.39/5.64 ( c_Int_OPls, (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.64 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Int_Oint ) 5.39/5.64 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 5.39/5.64 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (tc_fun T_c tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (c_Set_Oimage (tc_prod T_b T_c) T_c (c_Product__Type_Osnd T_b T_c)) (hAPP (hAPP (c_Product__Type_OSigma T_b T_c) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hAPP (c_COMBK _let_0 T_b) V_B_2)))) )) 5.39/5.64 ( c_Com_OWT, tc_Com_Ocom, tc_Com_Opname ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_S_2 $$unsorted) (T_b $$unsorted)) (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)))) )) 5.39/5.64 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.64 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.64 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.64 ) 5.39/5.64 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_OBit0 V_k) (c_Int_Opred (c_Int_OBit1 V_k))) ) 5.39/5.64 ( c_Int_OPls ) 5.39/5.64 ( (c_Int_OBit1 c_Int_OPls) ) 5.39/5.64 ( c_Int_OMin ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (forall ((T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool))))) (hBOOL (hAPP (c_Finite__Set_Ofinite _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))))) )) 5.39/5.64 ( tc_Com_Ocom, tc_Com_Opname ) 5.39/5.64 ( tc_Nat_Onat, tc_Nat_Onat ) 5.39/5.64 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.64 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.39/5.64 ) 5.39/5.64 (instantiation (let ((_let_0 (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Wellfounded_Oaccp (tc_prod tc_Nat_Onat tc_Nat_Onat) c_Nitpick_Onat__gcd__rel))) (forall ((V_Pa_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP _let_1 (hAPP (hAPP _let_0 V_a0_2) V_a1_2)))) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (or (not (hBOOL (hAPP _let_1 (hAPP (hAPP _let_0 B_x) B_y)))) (and (not (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) B_y)) (not (hBOOL (hAPP (hAPP V_Pa_2 B_y) (c_Divides_Odiv__class_Omod tc_Nat_Onat B_x B_y))))) (hBOOL (hAPP (hAPP V_Pa_2 B_x) B_y))) )) (hBOOL (hAPP (hAPP V_Pa_2 V_a0_2) V_a1_2))) ))) 5.39/5.64 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OPls, c_Int_OMin ) 5.39/5.64 ( (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) ) 5.39/5.64 ( (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) ) 5.39/5.64 ( (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) ) 5.39/5.64 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.64 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 5.39/5.64 ( (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) ) 5.39/5.64 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.64 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.64 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.39/5.64 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.64 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.64 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 5.39/5.64 ( (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) ) 5.39/5.64 ( (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) ) 5.39/5.64 ( (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) ) 5.39/5.64 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), (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)) ) 5.39/5.65 ( (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)) ) 5.39/5.65 ( (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)) ) 5.39/5.65 ( (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 ) 5.39/5.65 ( (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) ) 5.39/5.65 ( (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)) ) 5.39/5.65 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 5.39/5.65 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 5.39/5.65 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_0 _let_0))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (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_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_0) _let_0)) ) 5.39/5.65 ( (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)) ) 5.39/5.65 ( (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)) ) 5.39/5.65 ( (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)) ) 5.39/5.65 ( (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)) ) 5.39/5.65 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omax__weak, c_FunDef_Omax__strict ) 5.39/5.65 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omin__weak, c_FunDef_Omin__strict ) 5.39/5.65 ( (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) ) 5.39/5.65 ( (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 ) 5.39/5.65 ( (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 ) 5.39/5.65 ( (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)))) ) 5.39/5.65 ( (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)))) ) 5.39/5.65 ( (let ((_let_0 (tc_fun tc_Int_Oint (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))) (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) ) 5.39/5.65 ( (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) ) 5.39/5.65 ( (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool), skv_9, (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT) ) 5.39/5.65 ( (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)), (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9 ) 5.39/5.65 ( (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 ) 5.39/5.65 ( (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 ) 5.39/5.65 ) 5.39/5.65 (instantiation (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (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)))) (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_x_2) V_y_2)) ))) 5.39/5.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.39/5.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.39/5.65 ( (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)), (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) ) 5.39/5.65 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.65 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.65 ) 5.39/5.65 (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))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Complete__Lattice_OInf__class_OInf T_b V_A_2) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2))) ) 5.39/5.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.65 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.65 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.65 ) 5.39/5.65 (instantiation (let ((_let_0 (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_R_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) V_R_2) V_S_2)) V_R_2))) (c_FunDef_Oreduction__pair T_b (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) V_R_2) V_S_2))) )) 5.39/5.65 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.65 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.39/5.65 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.39/5.65 ) 5.39/5.65 (instantiation (forall ((V_z $$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)) ) 5.39/5.65 ( c_Int_OPls ) 5.39/5.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.39/5.65 ( c_Int_OMin ) 5.39/5.65 ) 5.39/5.65 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_z $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_0) V_z)) (= _let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Int_Onat V_z)))) )) 5.39/5.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.39/5.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.65 ( c_Int_OMin ) 5.39/5.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.65 ) 5.39/5.65 (instantiation (forall ((V_z $$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)))) ) 5.39/5.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.39/5.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.65 ( c_Int_OMin ) 5.39/5.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.65 ) 5.39/5.65 (instantiation (let ((_let_0 (c_Set_Oinsert T_b))) (forall ((V_ba_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) V_ba_2) (c_Complete__Lattice_OSup__class_OSup T_b (hAPP (hAPP _let_0 V_a_2) (hAPP (hAPP _let_0 V_ba_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))))) )) 5.39/5.65 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.65 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.65 ( (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)) ) 5.39/5.65 ) 5.39/5.65 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_1 (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_w))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit0 V_w)) (hAPP (hAPP _let_0 (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero T_a)) _let_1)) _let_1))) ))) 5.39/5.65 ( c_Int_OPls, tc_Nat_Onat ) 5.39/5.65 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.65 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.65 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.65 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.65 ) 5.39/5.65 (instantiation (forall ((T_b $$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))))) ) 5.39/5.65 ( tc_Com_Ocom ) 5.39/5.65 ( tc_Nat_Onat ) 5.39/5.65 ( tc_HOL_Obool ) 5.39/5.65 ( tc_Int_Oint ) 5.39/5.65 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.65 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.39/5.65 ( tc_Com_Opname ) 5.39/5.65 ( tc_Product__Type_Ounit ) 5.39/5.65 ) 5.39/5.65 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Groups_Omonoid__add T_b)) (= (c_List_Ofoldl T_b T_b (c_Groups_Oplus__class_Oplus T_b) (c_Groups_Ozero__class_Ozero T_b)) (c_List_Omonoid__add__class_Olistsum T_b))) ) 5.39/5.65 ( tc_Nat_Onat ) 5.39/5.65 ( tc_Int_Oint ) 5.39/5.65 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.65 ) 5.39/5.65 (instantiation (let ((_let_0 (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (let ((_let_2 (hAPP _let_1 V_A_2))) (let ((_let_3 (hAPP _let_1 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or _let_0 (= _let_3 (hAPP c_Nat_OSuc _let_2))) (or (not _let_0) (= _let_2 _let_3)))) ))))) 5.39/5.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.65 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.65 ( (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) ) 5.39/5.65 ( (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) ) 5.39/5.65 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.39/5.65 ) 5.39/5.65 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) V_x_2))) ) 5.39/5.65 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.39/5.65 ) 5.39/5.65 (instantiation (forall ((V_y $$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)))) ) 5.39/5.65 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.65 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.65 ( (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)) ) 5.39/5.65 ) 5.39/5.65 (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)))) ) 5.39/5.65 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.65 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.65 ( 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)) ) 5.39/5.65 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.65 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.65 ) 5.39/5.65 (instantiation (forall ((V_u_2 $$unsorted)) (= (hAPP c_Int_Onat V_u_2) (hAPP (c_Finite__Set_Ocard tc_Int_Oint) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Int_Oint (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_u_2))) ) 5.39/5.65 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.65 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.39/5.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.65 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.65 ) 5.39/5.65 (instantiation (let ((_let_0 (tc_fun T_c tc_HOL_Obool))) (forall ((V_ca_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_Orderings_Otop__class_Otop _let_0) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b _let_0) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hAPP (c_COMBK _let_0 T_b) V_ca_2))) )) 5.39/5.65 ( c_Com_OWT, tc_Com_Ocom, tc_Com_Opname ) 5.39/5.65 ) 5.39/5.65 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_R_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) (hAPP (c_Relation_OImage T_b T_b V_R_2) V_A_2)))) (= V_A_2 (c_Orderings_Obot__class_Obot _let_0))) )) 5.39/5.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.65 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.65 ) 5.39/5.65 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_2 (hAPP _let_1 V_v))) (let ((_let_3 (hAPP _let_1 V_w))) (let ((_let_4 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_3) _let_2)))) (let ((_let_5 (c_Divides_OposDivAlg _let_3 _let_2))) (forall ((V_w $$unsorted) (V_v $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) _let_2))) (and (or _let_4 (= _let_5 (hAPP (c_Divides_Oadjust _let_2) (c_Divides_OposDivAlg _let_3 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP _let_1 (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) _let_2))))) (or (not _let_4) (= _let_5 (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) _let_0) _let_3))))) ))))))) 5.39/5.65 ( c_Int_OPls, c_Int_OPls ) 5.39/5.65 ( c_Int_OPls, (c_Int_OBit1 c_Int_OPls) ) 5.39/5.65 ) 5.39/5.65 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_b))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Nat_Osemiring__char__0 T_b)) (= (= (hAPP _let_0 V_n_2) (hAPP _let_0 V_m_2)) (= V_n_2 V_m_2))) )) 5.39/5.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.39/5.65 ( (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 ) 5.39/5.65 ( (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 ) 5.39/5.65 ( (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_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.39/5.65 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.39/5.65 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 5.39/5.65 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.39/5.65 ( (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_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.39/5.65 ( (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))), tc_Int_Oint ) 5.39/5.65 ) 5.39/5.65 (instantiation (forall ((V_p_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_d $$unsorted) (T_c $$unsorted)) (= (hAPP (hAPP (c_Product__Type_Oprod_Oprod__case T_c T_d T_b) V_f_2) V_p_2) (hAPP (hAPP V_f_2 (hAPP (c_Product__Type_Ofst T_c T_d) V_p_2)) (hAPP (c_Product__Type_Osnd T_c T_d) V_p_2))) ) 5.39/5.65 ( skv_9, (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT), tc_HOL_Obool, tc_Com_Ocom, tc_Com_Opname ) 5.39/5.65 ) 5.39/5.65 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))))) (forall ((V_m $$unsorted)) (= (c_Divides_Odiv__class_Omod tc_Nat_Onat (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_m)) _let_0) (c_Divides_Odiv__class_Omod tc_Nat_Onat V_m _let_0)) )) 5.39/5.65 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.65 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.39/5.65 ) 5.39/5.65 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Olattice (tc_fun T_2 T_1))) ) 5.39/5.65 ( tc_Com_Ocom, tc_HOL_Obool ) 5.39/5.65 ( tc_Nat_Onat, tc_HOL_Obool ) 5.39/5.65 ( tc_HOL_Obool, tc_HOL_Obool ) 5.39/5.65 ( tc_Int_Oint, tc_HOL_Obool ) 5.39/5.65 ( tc_Int_Oint, tc_Int_Oint ) 5.39/5.65 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.39/5.65 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.39/5.65 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.39/5.65 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.39/5.65 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.39/5.65 ) 5.39/5.65 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) V_b) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_b)))) ) 5.39/5.66 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 5.39/5.66 ) 5.39/5.66 (instantiation (forall ((V_n $$unsorted)) (not (= V_n (hAPP c_Nat_OSuc V_n))) ) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.66 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.39/5.66 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.39/5.66 ) 5.39/5.66 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (not (= (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 5.39/5.66 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.66 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.66 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.66 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.66 ) 5.39/5.66 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Groups_Ouminus T_1)) (class_Groups_Ouminus (tc_fun T_2 T_1))) ) 5.39/5.66 ( tc_Com_Ocom, tc_HOL_Obool ) 5.39/5.66 ( tc_Nat_Onat, tc_HOL_Obool ) 5.39/5.66 ( tc_HOL_Obool, tc_HOL_Obool ) 5.39/5.66 ( tc_Int_Oint, tc_HOL_Obool ) 5.39/5.66 ( tc_Int_Oint, tc_Int_Oint ) 5.39/5.66 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.39/5.66 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.39/5.66 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.39/5.66 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.39/5.66 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.39/5.66 ) 5.39/5.66 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Obounded__lattice__top T_a)) (= _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) _let_0))) )) 5.39/5.66 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.66 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.66 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.66 ) 5.39/5.66 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (forall ((V_k_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (= (hAPP c_Nat_OSuc V_k_2) (hAPP _let_0 V_A_2)) (not (forall ((B_b $$unsorted) (B_B $$unsorted)) (or (not (= V_A_2 (hAPP (hAPP (c_Set_Oinsert T_b) B_b) B_B))) (not (= V_k_2 (hAPP _let_0 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))) ))) )) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 5.39/5.66 ( (hAPP c_Nat_OSuc (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 ) 5.39/5.66 ) 5.39/5.66 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OatMost T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (= (hAPP _let_0 V_x_2) (hAPP _let_0 V_y_2)) (= V_y_2 V_x_2))) )) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.66 ) 5.39/5.66 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (= V_m (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) V_m)) V_n)) ) 5.39/5.66 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.66 ) 5.39/5.66 (instantiation (forall ((V_z $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_z) V_z) (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))))) ) 5.39/5.66 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.66 ) 5.39/5.66 (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))) ) 5.39/5.66 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.66 ) 5.39/5.66 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP _let_0 V_v)) (c_Groups_Oone__class_Oone T_a)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_v) (c_Int_OBit1 c_Int_OPls))))) )) 5.39/5.66 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.66 ) 5.39/5.66 (instantiation (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (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)) )) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.66 ) 5.39/5.66 (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))) ) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.66 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.39/5.66 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.39/5.66 ) 5.39/5.66 (instantiation (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))) (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted)) (= (= _let_1 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_i_2) V_k_2)) (or (= _let_1 V_k_2) (and (hBOOL (hAPP (hAPP _let_2 V_k_2) V_i_2)) (hBOOL (hAPP (hAPP _let_0 V_i_2) _let_1))) (and (hBOOL (hAPP (hAPP _let_2 V_i_2) V_k_2)) (hBOOL (hAPP (hAPP _let_0 _let_1) V_i_2))))) )))) 5.39/5.66 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.39/5.66 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.66 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.66 ( c_Int_OMin, c_Int_OMin ) 5.39/5.66 ) 5.39/5.66 (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))))) ) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.39/5.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.39/5.66 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 5.39/5.66 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.39/5.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.39/5.66 ) 5.39/5.66 (instantiation (let ((_let_0 (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) (forall ((V_S_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_R_2)) (not (c_Wellfounded_Owf T_b V_S_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) V_R_2) V_S_2)) V_R_2))) (c_Wellfounded_Owf T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_R_2) V_S_2))) )) 5.39/5.66 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.39/5.66 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.39/5.66 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.66 ) 5.39/5.66 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_x_2 $$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 _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)))) )) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.66 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.66 ( (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) ) 5.39/5.66 ( (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) ) 5.39/5.66 ) 5.39/5.66 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Oone__class_Oone T_a)) (c_Groups_Ozero__class_Ozero T_a))))) ) 5.39/5.66 ( tc_Nat_Onat ) 5.39/5.66 ( tc_Int_Oint ) 5.39/5.66 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.66 ) 5.39/5.66 (instantiation (forall ((V_z $$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))) ) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.66 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.39/5.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.66 ( c_Int_OMin ) 5.39/5.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.66 ) 5.39/5.66 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_b)) (= (and (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) V_ba_2)) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_ba_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_b) V_a_2)) V_ba_2)))) )) 5.39/5.66 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.66 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.39/5.66 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.39/5.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, tc_Int_Oint ) 5.39/5.66 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.39/5.66 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.66 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, tc_Int_Oint ) 5.39/5.66 ) 5.39/5.66 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) V_z) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_z) V_z))) ) 5.39/5.66 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.66 ) 5.39/5.66 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_d $$unsorted) (V_g_2 $$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_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)))) )) 5.39/5.66 ( 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 ) 5.39/5.66 ( (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)) ) 5.39/5.66 ( (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 ) 5.39/5.66 ( (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) ) 5.39/5.66 ( (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) ) 5.39/5.66 ) 5.39/5.66 (instantiation (let ((_let_0 (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Divides_OposDivAlg__rel))) (let ((_let_1 (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint))) (let ((_let_2 (hAPP V_Pa_2 B_a))) (forall ((V_Pa_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 (hAPP (hAPP _let_1 V_a0_2) V_a1_2)))) (not (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (not (hBOOL (hAPP _let_0 (hAPP (hAPP _let_1 B_a) B_b)))) (and (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) B_a) B_b))) (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 _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_Pa_2 V_a0_2) V_a1_2))) )))) 5.39/5.66 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OPls, c_Int_OMin ) 5.39/5.66 ( (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) ) 5.39/5.66 ( (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) ) 5.39/5.66 ( (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) ) 5.39/5.66 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.66 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 5.39/5.66 ( (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) ) 5.39/5.66 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.66 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.66 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.39/5.66 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.66 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.66 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 5.39/5.66 ( (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) ) 5.39/5.66 ( (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) ) 5.39/5.66 ( (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) ) 5.39/5.66 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), (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)) ) 5.39/5.66 ( (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)) ) 5.39/5.66 ( (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)) ) 5.39/5.66 ( (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 ) 5.39/5.66 ( (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) ) 5.39/5.66 ( (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)) ) 5.39/5.66 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 5.39/5.66 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 5.39/5.66 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_0 _let_0))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (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_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_0) _let_0)) ) 5.39/5.66 ( (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)) ) 5.39/5.66 ( (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)) ) 5.39/5.66 ( (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)) ) 5.39/5.66 ( (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)) ) 5.39/5.66 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omax__weak, c_FunDef_Omax__strict ) 5.39/5.66 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omin__weak, c_FunDef_Omin__strict ) 5.39/5.66 ( (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) ) 5.39/5.66 ( (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 ) 5.39/5.66 ( (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 ) 5.39/5.66 ( (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)))) ) 5.39/5.66 ( (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)))) ) 5.39/5.66 ( (let ((_let_0 (tc_fun tc_Int_Oint (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))) (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) ) 5.39/5.66 ( (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) ) 5.39/5.66 ( (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool), skv_9, (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT) ) 5.39/5.66 ( (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)), (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9 ) 5.39/5.66 ( (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 ) 5.39/5.67 ( (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 ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (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)) (= (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)))) )) 5.39/5.67 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_1 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w))) (forall ((V_w $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) _let_1))) (= (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) _let_0) _let_1) (hAPP (c_Product__Type_Ofst tc_Int_Oint tc_Int_Oint) (c_Divides_OposDivAlg _let_0 _let_1)))) ))) 5.39/5.67 ( c_Int_OPls ) 5.39/5.67 ( (c_Int_OBit1 c_Int_OPls) ) 5.39/5.67 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.67 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.67 ( c_Int_OMin ) 5.39/5.67 ) 5.39/5.67 (instantiation (forall ((V_A_2 $$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))))) ) 5.39/5.67 ( (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 ) 5.39/5.67 ( 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 ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_x_2)) (hAPP _let_1 V_y_2))) (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2)))) ))) 5.39/5.67 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.39/5.67 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (c_Finite__Set_Ofinite T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP _let_3 V_A_2))) (not (hBOOL (hAPP _let_3 V_B_2))) (= (hAPP (hAPP _let_0 (hAPP _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_2) V_A_2) V_B_2))) (hAPP _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_2) V_A_2) V_B_2))) (hAPP (hAPP _let_0 (hAPP _let_1 V_A_2)) (hAPP _let_1 V_B_2)))) ))))) 5.39/5.67 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.67 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.67 ( (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)) ) 5.39/5.67 ) 5.39/5.67 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (hAPP (hAPP (c_Product__Type_OSigma T_b T_b) V_A_2) (hAPP (c_COMBK (tc_fun T_b tc_HOL_Obool) T_b) V_A_2))))) ) 5.39/5.67 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v))))) (let ((_let_1 (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v)))) (forall ((V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (and (or _let_0 (= _let_1 (c_Groups_Ozero__class_Ozero T_a))) (or (not _let_0) (= _let_1 (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_v))))) ))) 5.39/5.67 ( c_Int_OPls, tc_Nat_Onat ) 5.39/5.67 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.67 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.67 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.67 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.67 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.39/5.67 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.67 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.67 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.67 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.67 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun T_d _let_0))) (let ((_let_2 (tc_fun T_d tc_HOL_Obool))) (let ((_let_3 (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_d _let_0))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_d $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (hAPP _let_3 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_2) V_A_2) V_B_2)) V_C_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_c _let_1 _let_0) (hAPP (hAPP (c_COMBB _let_2 (tc_fun _let_1 _let_0) T_c) _let_3) V_B_2)) V_C_2))) ))))) 5.39/5.67 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_2 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w))) (let ((_let_3 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_1) _let_2)))) (let ((_let_4 (c_Divides_OposDivAlg _let_1 _let_2))) (forall ((V_w $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) _let_2))) (and (or _let_3 (= (hAPP (c_Divides_Oadjust _let_2) (c_Divides_OposDivAlg _let_1 (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)))) _let_2))) _let_4)) (or (not _let_3) (= (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) _let_0) _let_1) _let_4)))) )))))) 5.39/5.67 ( c_Int_OPls ) 5.39/5.67 ( (c_Int_OBit1 c_Int_OPls) ) 5.39/5.67 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.67 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.67 ( c_Int_OMin ) 5.39/5.67 ) 5.39/5.67 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (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))))) )) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) ) 5.39/5.67 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.67 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.67 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_d tc_HOL_Obool)))) (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (not (c_Fun_Oinj__on T_d T_b V_g_2 _let_0)) (c_Fun_Oinj__on T_d T_c (hAPP (c_Fun_Ocomp T_b T_c T_d V_f_2) V_g_2) _let_0)) )) 5.39/5.67 ( c_Int_Onat, tc_Int_Oint, c_Code__Numeral_Oof__nat, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 5.39/5.67 ( c_Code__Numeral_Onat__of, tc_Code__Numeral_Ocode__numeral, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 5.39/5.67 ( skv_2, skv_6, skv_3, skv_8, skv_4 ) 5.39/5.67 ( skv_2, skv_6, (hAPP (c_Fun_Ocomp skv_8 skv_7 skv_4 skv_5) skv_3), skv_7, skv_4 ) 5.39/5.67 ( skv_3, skv_4, skv_5, skv_7, skv_8 ) 5.39/5.67 ( (hAPP (c_Fun_Ocomp skv_4 skv_8 skv_6 skv_3) skv_2), skv_6, skv_5, skv_7, skv_8 ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (= V_a_2 _let_0) (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2)))) )) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.67 ) 5.39/5.67 (instantiation (forall ((V_n $$unsorted)) (= (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)))) (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_n))) ) 5.39/5.67 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.67 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP _let_0 V_a))) (not (hBOOL (hAPP _let_0 V_b))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)))) )) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Orderings_Oord__class_Omax T_b))) (let ((_let_2 (c_Set_Oinsert T_b))) (let ((_let_3 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 _let_3) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_x) B_y)) (hAPP (hAPP _let_2 B_x) (hAPP (hAPP _let_2 B_y) _let_3)))) )) (hBOOL (hAPP (hAPP _let_0 (c_Big__Operators_Olattice_OSup__fin T_b _let_1 V_A_2)) V_A_2))) ))))) 5.39/5.67 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.67 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.39/5.67 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.39/5.67 ) 5.39/5.67 (instantiation (forall ((V_x $$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)))) ) 5.39/5.67 ( 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)) ) 5.39/5.67 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.67 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.67 ) 5.39/5.67 (instantiation (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (T_e $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_d $$unsorted) (BOUND_VARIABLE_106855 $$unsorted)) (or (not (= (hAPP (c_Fun_Ocomp T_d T_c T_b V_a_2) V_ba_2) (hAPP (c_Fun_Ocomp T_e T_c T_b V_ca_2) V_d_2))) (= (hAPP V_ca_2 (hAPP V_d_2 BOUND_VARIABLE_106855)) (hAPP V_a_2 (hAPP V_ba_2 BOUND_VARIABLE_106855)))) ) 5.39/5.67 ( c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Nat_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.67 ( c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Nat_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.39/5.67 ( c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Nat_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.67 ( c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Nat_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.39/5.67 ) 5.39/5.67 (instantiation (forall ((V_A_2 $$unsorted)) (or (not (c_Nat__Transfer_Onat__set V_A_2)) (= (hAPP (c_Finite__Set_Ocard tc_Int_Oint) 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)))) ) 5.39/5.67 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 5.39/5.67 ) 5.39/5.67 (instantiation (forall ((V_a_2 $$unsorted) (V_ba_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_ba_2) V_a_2))) (= (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_a_2) V_ba_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 5.39/5.67 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.39/5.67 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.67 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.67 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.67 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.67 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.67 ) 5.39/5.67 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (not (class_Int_Onumber__ring T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_x_2)) (c_Groups_Oone__class_Oone T_b))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_x_2) (c_Int_OBit1 c_Int_OPls))))) ) 5.39/5.67 ( c_Int_OPls, tc_Nat_Onat ) 5.39/5.67 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.67 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.67 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.67 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.67 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.39/5.67 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.67 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.67 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.67 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.67 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.67 ) 5.39/5.67 (instantiation (forall ((V_y_2 $$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_y_2) (hAPP V_f_2 V_x_2))) (= V_y_2 V_x_2)) ) 5.39/5.67 ( (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_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 5.39/5.67 ( (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))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_List_Oupto V_i_2 V_j_2))) (let ((_let_1 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_i_2) V_j_2)))) (forall ((V_j_2 $$unsorted) (V_i_2 $$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_i_2) V_j_2)))) (and (or (not _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)) _let_0)) (or _let_1 (= (c_List_Olist_ONil tc_Int_Oint) _let_0)))) ))) 5.39/5.67 ( c_Int_OPls, c_Int_OMin ) 5.39/5.67 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.67 ( (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) ) 5.39/5.67 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.67 ( c_Int_OMin, c_Int_OMin ) 5.39/5.67 ( (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) ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_a_2)) V_ba_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_ba_2)) V_a_2)))) ))) 5.39/5.67 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.39/5.67 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.67 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.39/5.67 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.39/5.67 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.39/5.67 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus T_a))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ocancel__semigroup__add T_a)) (not (= (hAPP (hAPP _let_0 V_b) V_a) (hAPP (hAPP _let_0 V_c) V_a))) (= V_c V_b)) )) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.67 ) 5.39/5.67 (instantiation (forall ((V_u_2 $$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)) ) 5.39/5.67 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.67 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.39/5.67 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (forall ((V_w $$unsorted)) (= (hAPP _let_1 (hAPP _let_0 V_w)) (hAPP _let_0 (hAPP _let_1 V_w))) ))) 5.39/5.67 ( c_Int_OPls ) 5.39/5.67 ( (c_Int_OBit1 c_Int_OPls) ) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.39/5.67 ( c_Int_OMin ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (tc_fun T_b T_c))) (forall ((T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))))) (= (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Finite__Set_Ocard T_c) (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))))) )) 5.39/5.67 ( tc_HOL_Obool, tc_Com_Ocom ) 5.39/5.67 ( tc_HOL_Obool, tc_Nat_Onat ) 5.39/5.67 ( tc_HOL_Obool, tc_HOL_Obool ) 5.39/5.67 ( tc_HOL_Obool, tc_Int_Oint ) 5.39/5.67 ( tc_HOL_Obool, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.67 ( tc_HOL_Obool, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.67 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.39/5.67 ( tc_HOL_Obool, tc_Product__Type_Ounit ) 5.39/5.67 ( tc_Int_Oint, tc_Int_Oint ) 5.39/5.67 ( (tc_fun tc_Int_Oint tc_HOL_Obool), tc_Int_Oint ) 5.39/5.67 ) 5.39/5.67 (instantiation (let ((_let_0 (c_Lattices_Osemilattice__inf__class_Oinf T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2))) (let ((_let_3 (c_Finite__Set_Ofinite T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP _let_3 V_A_2))) (not (hBOOL (hAPP _let_3 V_B_2))) (= _let_2 (c_Orderings_Obot__class_Obot _let_1)) (= (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)) (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_2)))) ))))) 5.39/5.67 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.67 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.67 ( (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)) ) 5.39/5.67 ) 5.39/5.67 (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)))) ) 5.39/5.67 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.39/5.67 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.39/5.67 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 5.39/5.67 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.39/5.67 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.39/5.67 ) 5.39/5.67 (instantiation (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))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (hAPP (hAPP _let_2 V_a_2) (hAPP (hAPP _let_2 V_ba_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_ba_2)) V_r_2))) )))) 5.39/5.68 ( (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 ) 5.39/5.68 ( (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 ) 5.39/5.68 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) 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) ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Olattice T_a)) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)))) ) 5.39/5.68 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.68 ( (let ((_let_0 (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.68 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus _let_0))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (hAPP _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) V_B_2)) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) (hAPP (hAPP (c_COMBB _let_0 _let_0 T_c) _let_1) V_B_2))) ))) 5.39/5.68 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_r_2 $$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 (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)))) )) 5.39/5.68 ( 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) ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP _let_0 V_A_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2))))) )) 5.39/5.68 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.68 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.68 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.68 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (hAPP (hAPP _let_0 V_m) (hAPP c_Nat_OSuc V_n)) (hAPP (hAPP _let_0 (hAPP c_Nat_OSuc V_m)) V_n)) )) 5.39/5.68 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.39/5.68 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (let ((_let_2 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w))) (forall ((V_w $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_2) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (= (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_2)))) (c_Divides_Odiv__class_Omod tc_Int_Oint _let_0 _let_2))) )))) 5.39/5.68 ( c_Int_OPls ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls) ) 5.39/5.68 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.68 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.68 ( c_Int_OMin ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_c))) (let ((_let_1 (c_Set_OCollect T_c))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (forall ((V_Q_2 $$unsorted) (T_c $$unsorted) (V_Pa_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (hAPP (c_Set_OCollect T_b) V_Pa_2)))) (= (hBOOL (hAPP _let_0 (hAPP _let_1 (hAPP (hAPP (c_COMBB _let_2 tc_HOL_Obool T_c) (c_HOL_OEx T_b)) (hAPP (hAPP (c_COMBB _let_2 _let_2 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_Pa_2))) V_Q_2))))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP V_Pa_2 B_y))) (hBOOL (hAPP _let_0 (hAPP _let_1 (hAPP (hAPP (c_COMBC T_c T_b tc_HOL_Obool) V_Q_2) B_y))))) ))) )))) 5.39/5.68 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), tc_Int_Oint, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_3 (c_Finite__Set_Ofinite T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP _let_3 V_A_2))) (= V_A_2 _let_1) (not (hBOOL (hAPP _let_3 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))) (= (c_Big__Operators_Olattice_OInf__fin T_b _let_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)) (hAPP (hAPP _let_2 (c_Big__Operators_Olattice_OInf__fin T_b _let_2 V_A_2)) (c_Big__Operators_Olattice_OInf__fin T_b _let_2 V_B_2)))) ))))) 5.39/5.68 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.68 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.68 ( (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)) ) 5.39/5.68 ) 5.39/5.68 (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)))) ) 5.39/5.68 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((T_d $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_Product__Type_Oprod_Oprod__case T_b T_c T_d) (c_Product__Type_Ointernal__split T_b T_c T_d)) ) 5.39/5.68 ( tc_HOL_Obool, tc_Com_Ocom, tc_Com_Opname ) 5.39/5.68 ( tc_HOL_Obool, tc_Nat_Onat, tc_Nat_Onat ) 5.39/5.68 ( tc_HOL_Obool, tc_Int_Oint, tc_Int_Oint ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((V_n_2 $$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)) ) 5.39/5.68 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((V_v $$unsorted)) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v)))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v))) ) 5.39/5.68 ( c_Int_OPls ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls) ) 5.39/5.68 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.68 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.39/5.68 ( c_Int_OMin ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_OBit1 V_k) (c_Int_Osucc (c_Int_OBit0 V_k))) ) 5.39/5.68 ( c_Int_OPls ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls) ) 5.39/5.68 ( c_Int_OMin ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (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)))) )) 5.39/5.68 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.68 ( skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 V_m))) (let ((_let_2 (hAPP _let_0 V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (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))) )))) 5.39/5.68 ( c_Int_OPls, c_Int_OPls ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls ) 5.39/5.68 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls ) 5.39/5.68 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 V_m))) (let ((_let_2 (hAPP _let_0 V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (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)))) )))) 5.39/5.68 ( c_Int_OPls, c_Int_OPls ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls ) 5.39/5.68 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls ) 5.39/5.68 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (c_Finite__Set_Ofun__left__comm T_b (tc_List_Olist T_b) (c_List_Olinorder__class_Oinsort__key T_b T_b (c_COMBI T_b)))) ) 5.39/5.68 ( tc_Nat_Onat ) 5.39/5.68 ( tc_Int_Oint ) 5.39/5.68 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (= V_y V_x)) ) 5.39/5.68 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.68 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.39/5.68 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.68 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.39/5.68 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.68 ( (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 ) 5.39/5.68 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.68 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.68 ( (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 ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((V_ca_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool)) (hAPP (c_Set_Oimage T_b T_c (hAPP (c_COMBK T_c T_b) V_ca_2)) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 5.39/5.68 ( c_fTrue, tc_HOL_Obool, tc_Nat_Onat ) 5.39/5.68 ( c_Com_OWT, (tc_fun tc_Com_Ocom tc_HOL_Obool), tc_Com_Opname ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$unsorted)) (= (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)))) )) 5.39/5.68 ( tc_Nat_Onat ) 5.39/5.68 ( tc_HOL_Obool ) 5.39/5.68 ( tc_Int_Oint ) 5.39/5.68 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.68 ( tc_Product__Type_Ounit ) 5.39/5.68 ) 5.39/5.68 (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 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)))) ) 5.39/5.68 ( c_Int_OPls, tc_Nat_Onat ) 5.39/5.68 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.68 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.39/5.68 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.68 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.68 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.68 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.68 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (let ((_let_1 (hAPP (c_Orderings_Oord__class_Oless T_a) _let_0))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP _let_1 V_a))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) _let_0) V_b))) (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)))) ))) 5.39/5.68 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w) V_z))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_w) (c_Groups_Oone__class_Oone tc_Int_Oint))) V_z))) ) 5.39/5.68 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.68 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.39/5.68 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.68 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.39/5.68 ( c_Int_OMin, c_Int_OMin ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((V_ba_2 $$unsorted) (V_ca_2 $$unsorted)) (or (not (hBOOL (hAPP c_Com_OWT V_ca_2))) (hBOOL (hAPP c_Com_OWT (c_Com_Ocom_OWhile V_ba_2 V_ca_2)))) ) 5.39/5.68 ( v_b, v_c ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (and (= _let_0 V_n_2) (= _let_0 V_m_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP _let_1 V_n_2)) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP _let_1 V_m_2))))) ))) 5.39/5.68 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.68 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((V_a $$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))) ) 5.39/5.68 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$unsorted)) (not (= (c_Orderings_Otop__class_Otop _let_0) (c_Orderings_Obot__class_Obot _let_0))) )) 5.39/5.68 ( tc_Com_Ocom ) 5.39/5.68 ( tc_Nat_Onat ) 5.39/5.68 ( tc_HOL_Obool ) 5.39/5.68 ( tc_Int_Oint ) 5.39/5.68 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.68 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.68 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.39/5.68 ( tc_Product__Type_Ounit ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((T_b $$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)))) ) 5.39/5.68 ( tc_Nat_Onat ) 5.39/5.68 ( tc_Int_Oint ) 5.39/5.68 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.68 ( (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.39/5.68 ) 5.39/5.68 (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))))) ) 5.39/5.68 ( c_Int_OPls, tc_Nat_Onat ) 5.39/5.68 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.68 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.39/5.68 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.68 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.68 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.68 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.68 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_x_2))) (let ((_let_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP _let_1 (c_Orderings_Obot__class_Obot _let_0))))) (let ((_let_3 (= (c_Orderings_Obot__class_Obot _let_0) _let_2))) (let ((_let_4 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_5 (c_Big__Operators_Olattice_OInf__fin T_b _let_4 (hAPP _let_1 V_A_2)))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or (not _let_3) (= V_x_2 _let_5)) (or _let_3 (= _let_5 (hAPP (hAPP _let_4 V_x_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_4 _let_2)))))) ))))))) 5.39/5.68 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.39/5.68 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.39/5.68 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.68 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_x))) (let ((_let_1 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) _let_0) (c_Groups_Ozero__class_Ozero T_a))))) (let ((_let_2 (hAPP (c_Groups_Oabs__class_Oabs T_a) _let_0))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (not (class_Rings_Olinordered__idom T_a)) (and (or (not _let_1) (= _let_2 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) _let_0))) (or _let_1 (= _let_0 _let_2)))) )))) 5.39/5.68 ( c_Int_OPls, tc_Nat_Onat ) 5.39/5.68 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.68 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.68 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.39/5.68 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.68 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.68 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.68 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.68 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.68 ) 5.39/5.68 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 _let_1) V_a_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) _let_1)))) ))) 5.39/5.68 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.68 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.39/5.68 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.68 ) 5.39/5.68 (instantiation (forall ((T_b $$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))) ) 5.39/5.68 ( tc_Nat_Onat ) 5.39/5.68 ( tc_Int_Oint ) 5.39/5.68 ( tc_Code__Numeral_Ocode__numeral ) 5.39/5.68 ) 5.39/5.68 (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))) ) 5.39/5.68 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.39/5.68 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.68 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.68 ( (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 ) 5.39/5.68 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.39/5.68 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.39/5.68 ( (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 ) 5.39/5.68 ( 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)) ) 5.39/5.68 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.69 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.39/5.69 ) 5.39/5.69 (instantiation (forall ((V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Int_Oring__1__class_Oof__int T_a) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v)) (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_v))) ) 5.39/5.69 ( c_Int_OPls, tc_Nat_Onat ) 5.39/5.69 ( c_Int_OPls, tc_Int_Oint ) 5.39/5.69 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.39/5.69 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.39/5.69 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.39/5.69 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.39/5.69 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.69 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.69 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.39/5.69 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.39/5.69 ( c_Int_OMin, tc_Int_Oint ) 5.39/5.69 ) 5.39/5.69 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (let ((_let_2 (c_Relation_OImage T_c T_b V_r_2))) (forall ((V_B_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP _let_2 V_B_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_B_2) (hAPP (hAPP (c_COMBB _let_1 _let_0 T_c) _let_2) (hAPP (hAPP (c_COMBC T_c _let_1 _let_1) (c_Set_Oinsert T_c)) (c_Orderings_Obot__class_Obot _let_1))))) )))) 5.48/5.69 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.48/5.69 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.48/5.69 ) 5.48/5.69 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_x) V_x)))) ) 5.48/5.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( c_Int_OMin, tc_Int_Oint ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) V_B_2) (c_Complete__Lattice_OInf__class_OInf _let_0 (hAPP (c_Set_Oimage T_c _let_0 V_B_2) V_A_2))) )) 5.48/5.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (hAPP c_Nat_OSuc (hAPP (hAPP _let_0 V_m) V_n)) (hAPP (hAPP _let_0 (hAPP c_Nat_OSuc V_m)) V_n)) )) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.48/5.69 ) 5.48/5.69 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (c_Int_OBit1 V_k_2) (c_Int_OBit1 V_l_2)) (= V_l_2 V_k_2)) ) 5.48/5.69 ( c_Int_OPls, c_Int_OPls ) 5.48/5.69 ( c_Int_OPls, (c_Int_OBit1 c_Int_OPls) ) 5.48/5.69 ( c_Int_OPls, c_Int_OMin ) 5.48/5.69 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls ) 5.48/5.69 ( c_Int_OMin, (c_Int_OBit1 c_Int_OPls) ) 5.48/5.69 ) 5.48/5.69 (instantiation (forall ((V_y_2 $$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))) ) 5.48/5.69 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.48/5.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( (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 ) 5.48/5.69 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.48/5.69 ( (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 ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (let ((_let_1 (c_Orderings_Oord__class_Oless T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_a) _let_0))) (not (hBOOL (hAPP (hAPP _let_1 V_b) _let_0))) (hBOOL (hAPP (hAPP _let_1 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_0))) ))) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus T_b))) (forall ((V_ca_2 $$unsorted) (V_a_2 $$unsorted) (V_ba_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ocancel__semigroup__add T_b)) (= (= V_ca_2 V_ba_2) (= (hAPP (hAPP _let_0 V_ca_2) V_a_2) (hAPP (hAPP _let_0 V_ba_2) V_a_2)))) )) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless T_b) (c_Groups_Ozero__class_Ozero T_b)))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP _let_0 V_a_2)) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2))))) )) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (forall ((B_n $$unsorted)) (hBOOL (hAPP (hAPP _let_0 (hAPP V_f_2 B_n)) (hAPP V_f_2 (hAPP c_Nat_OSuc B_n)))) )) (= (hBOOL (hAPP (hAPP _let_0 (hAPP V_f_2 V_n_2)) (hAPP V_f_2 V_m_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_n_2) V_m_2)))) )) 5.48/5.69 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( (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)))))), (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 ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_C_2))) (let ((_let_2 (hAPP (c_Set_Oinsert T_b) V_a_2))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_C_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP _let_2 (hAPP _let_1 V_B_2)) (hAPP _let_1 (hAPP (hAPP (c_COMBB _let_0 _let_0 T_c) _let_2) V_B_2))) )))) 5.48/5.69 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 5.48/5.69 ) 5.48/5.69 (instantiation (forall ((V_k_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_k_2) (hAPP (c_Groups_Ouminus__class_Ouminus (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_k_2)))) ) 5.48/5.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) _let_1)))) (let ((_let_3 (c_Big__Operators_Olinorder__class_OMin T_b V_A_2))) (let ((_let_4 (= _let_1 _let_2))) (forall ((V_x_2 $$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))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (and (or _let_4 (= (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMin T_b _let_2)) _let_3)) (or (not _let_4) (= V_x_2 _let_3)))) )))))) 5.48/5.69 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_member T_b))) (let ((_let_2 (c_Set_Oinsert T_b))) (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 _let_0) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (hBOOL (hAPP (hAPP _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) B_x) B_y)) (hAPP (hAPP _let_2 B_x) (hAPP (hAPP _let_2 B_y) _let_0)))) )) (hBOOL (hAPP (hAPP _let_1 (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)) V_A_2))) )))) 5.48/5.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.48/5.69 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.48/5.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (c_Set_OPow T_b) V_A_2))) (let ((_let_2 (hAPP (c_Set_Oinsert T_b) V_a_2))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (c_Set_OPow T_b) (hAPP _let_2 V_A_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun _let_0 tc_HOL_Obool)) _let_1) (hAPP (c_Set_Oimage _let_0 _let_0 _let_2) _let_1))) )))) 5.48/5.69 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.48/5.69 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.48/5.69 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.48/5.69 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.48/5.69 ) 5.48/5.69 (instantiation (forall ((V_x $$unsorted)) (= V_x (c_Int_Osucc (c_Int_Opred V_x))) ) 5.48/5.69 ( c_Int_OPls ) 5.48/5.69 ( c_Int_OMin ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_x) V_y))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_y)) (hAPP _let_1 V_x)))) ))) 5.48/5.69 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.48/5.69 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (hAPP _let_0 V_v)) (hAPP _let_0 V_w)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_v) V_w)))) )) 5.48/5.69 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (tc_Option_Ooption T_b))) (forall ((T_b $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert _let_0) (c_Option_Ooption_ONone T_b)) (hAPP (c_Set_Oimage T_b _let_0 (c_Option_Ooption_OSome T_b)) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))) )) 5.48/5.69 ( tc_Com_Ocom ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_1 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_i)))) (let ((_let_2 (c_Groups_Osgn__class_Osgn tc_Int_Oint V_i))) (forall ((V_i $$unsorted)) (or (= (c_Groups_Ozero__class_Ozero tc_Int_Oint) V_i) (and (or _let_1 (= (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) _let_0) _let_2)) (or (not _let_1) (= _let_0 _let_2)))) )))) 5.48/5.69 ( c_Int_OPls ) 5.48/5.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.48/5.69 ( c_Int_OMin ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted)) (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))) )) 5.48/5.69 ( c_Nat_OSuc, tc_Nat_Onat ) 5.48/5.69 ) 5.48/5.69 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (c_Int_OBit0 V_k_2) (c_Int_OBit0 V_l_2)) (= V_l_2 V_k_2)) ) 5.48/5.69 ( c_Int_OPls, c_Int_OMin ) 5.48/5.69 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls ) 5.48/5.69 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls) ) 5.48/5.69 ( (c_Int_OBit1 c_Int_OPls), c_Int_OMin ) 5.48/5.69 ( c_Int_OMin, (c_Int_OBit1 c_Int_OPls) ) 5.48/5.69 ) 5.48/5.69 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_a_2) (c_Complete__Lattice_OInf__class_OInf T_b V_A_2)) (c_Complete__Lattice_OInf__class_OInf T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)))) ) 5.48/5.69 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.48/5.69 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.48/5.69 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.48/5.69 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.48/5.69 ) 5.48/5.69 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)))) ) 5.48/5.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.48/5.69 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.48/5.69 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (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))) )) 5.48/5.69 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.48/5.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( (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 ) 5.48/5.69 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.48/5.69 ( (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 ) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( (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 ) 5.48/5.69 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.48/5.69 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.48/5.69 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.48/5.69 ( (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 ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (hAPP c_Nat_OSuc (hAPP _let_0 V_n)) (hAPP _let_0 (hAPP c_Nat_OSuc V_n))) )) 5.48/5.69 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.48/5.69 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.48/5.69 ) 5.48/5.69 (instantiation (let ((_let_0 (c_Lattices_Osemilattice__sup__class_Osup T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Olattice T_a)) (= (hAPP (hAPP _let_0 V_x) V_y) (hAPP (hAPP _let_0 V_y) V_x))) )) 5.48/5.69 ( 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_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.48/5.69 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.48/5.69 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.48/5.69 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.48/5.69 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.48/5.69 ( (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_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.48/5.69 ) 5.48/5.69 (instantiation (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))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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)) (= (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)) (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)))) )))) 5.48/5.69 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.48/5.69 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.48/5.70 ( (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)) ) 5.48/5.70 ) 5.48/5.70 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_b))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP _let_0 V_m_2)) (hAPP _let_0 V_n_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_n_2)))) )) 5.48/5.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.48/5.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.48/5.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.48/5.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.48/5.70 ) 5.48/5.70 (instantiation (forall ((V_i $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_i) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (= V_i (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) V_i))) ) 5.48/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.48/5.70 ( c_Int_OMin ) 5.48/5.70 ) 5.48/5.70 (instantiation (forall ((V_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_i) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (= (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) V_i) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_i))) ) 5.48/5.70 ( c_Int_OPls ) 5.48/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.48/5.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.48/5.70 ( c_Int_OMin ) 5.48/5.70 ) 5.48/5.70 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_S_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_S_2))) (= V_S_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP _let_0 (c_Big__Operators_Olinorder__class_OMax T_b V_S_2)) (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (c_Set_Oimage T_b T_b _let_0) V_S_2)))) )) 5.48/5.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.48/5.70 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.48/5.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.48/5.70 ) 5.48/5.70 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Ocomm__ring__1 T_a)) (= (hAPP _let_0 V_x) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (hAPP _let_0 (c_Groups_Oone__class_Oone T_a))) V_x))) )) 5.48/5.70 ( c_Int_OPls, tc_Int_Oint ) 5.48/5.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.48/5.70 ( c_Int_OMin, tc_Int_Oint ) 5.48/5.70 ) 5.48/5.70 (instantiation (forall ((V_Pa_2 $$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_Pa_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_Pa_2))) ) 5.48/5.70 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.48/5.70 ( (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 ) 5.48/5.70 ( (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_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 ) 5.48/5.70 ( (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT), tc_Com_Ocom, tc_Com_Opname ) 5.48/5.70 ) 5.48/5.70 (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)))) ) 5.48/5.70 ( c_Int_OPls, tc_Nat_Onat ) 5.48/5.70 ( c_Int_OPls, tc_Int_Oint ) 5.48/5.70 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.48/5.70 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.48/5.70 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.48/5.70 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.48/5.70 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.48/5.70 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.48/5.70 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.48/5.70 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.48/5.70 ( c_Int_OMin, tc_Int_Oint ) 5.48/5.70 ) 5.48/5.70 (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)))))) ) 5.48/5.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.48/5.70 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.48/5.70 ( (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) ) 5.48/5.70 ( (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) ) 5.48/5.70 ) 5.48/5.70 (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)))) ) 5.48/5.70 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.48/5.70 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.48/5.70 ( (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 ) 5.48/5.70 ) 5.48/5.70 (instantiation (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ogroup__add T_b)) (= (= (c_Groups_Ozero__class_Ozero T_b) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_ba_2)) (= V_a_2 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_ba_2)))) ) 5.48/5.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.48/5.70 ) 5.48/5.70 (instantiation (forall ((V_n $$unsorted) (V_i $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP c_Int_Onat V_i)) V_n) (c_Int_Onat__aux V_i V_n)) ) 5.48/5.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.48/5.70 ) 5.48/5.70 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) (= (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a))) ) 5.48/5.70 ( c_Int_OPls, tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( c_Int_OMin, tc_Int_Oint ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Equiv__Relations_Oquotient T_b))) (let ((_let_2 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_3 (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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_3 _let_2) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_3 _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 _let_0) (hAPP (hAPP _let_1 V_A_2) V_r_2)) (hAPP (c_Finite__Set_Ocard T_b) V_A_2))) ))))) 5.49/5.70 ( 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) ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OgreaterThan T_b))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (c_SetInterval_Oord__class_OgreaterThanAtMost T_b V_l_2 V_u_2)) (hAPP _let_0 V_u_2)) (hAPP _let_0 V_l_2))) )) 5.49/5.70 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.49/5.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless T_a) V_a))) (let ((_let_1 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (c_Groups_Oone__class_Oone T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Fields_Olinordered__field T_a)) (not (hBOOL (hAPP _let_0 V_b))) (hBOOL (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))))) )))) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_w)) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (hAPP _let_0 V_w)))) )) 5.49/5.70 ( c_Int_OPls, tc_Nat_Onat ) 5.49/5.70 ( c_Int_OPls, tc_Int_Oint ) 5.49/5.70 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.49/5.70 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( c_Int_OMin, tc_Nat_Onat ) 5.49/5.70 ( c_Int_OMin, tc_Int_Oint ) 5.49/5.70 ( c_Int_OMin, tc_Code__Numeral_Ocode__numeral ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_x))) (not (hBOOL (hAPP (hAPP _let_0 V_x) V_y))) (= V_x V_y)) )) 5.49/5.70 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.49/5.70 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.49/5.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ) 5.49/5.70 (instantiation (forall ((V_n $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Ozero__class_Ozero T_a)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) V_n)))) ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.49/5.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.49/5.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.49/5.70 ) 5.49/5.70 (instantiation (forall ((V_R_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_R_2)) (c_Wellfounded_OwfP T_b (c_FunDef_Oin__rel T_b T_b V_R_2))) ) 5.49/5.70 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.49/5.70 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.49/5.70 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 5.49/5.70 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (tc_Option_Ooption T_c))) (forall ((V_m_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_Map_Odom T_b T_c V_m_2) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBB tc_HOL_Obool tc_HOL_Obool T_b) c_fNot) (hAPP (hAPP (c_COMBC T_b _let_0 tc_HOL_Obool) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_0 tc_HOL_Obool) T_b) c_fequal) V_m_2)) (c_Option_Ooption_ONone T_c))))) )) 5.49/5.70 ( c_Com_Obody, tc_Com_Ocom, tc_Com_Opname ) 5.49/5.70 ) 5.49/5.70 (instantiation (forall ((T_b $$unsorted)) (= (hAPP (c_Set_OCollect T_b) (hAPP (c_COMBK tc_HOL_Obool T_b) c_fTrue)) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))) ) 5.49/5.70 ( tc_Com_Ocom ) 5.49/5.70 ( tc_Nat_Onat ) 5.49/5.70 ( tc_HOL_Obool ) 5.49/5.70 ( tc_Int_Oint ) 5.49/5.70 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.49/5.70 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.49/5.70 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.49/5.70 ( tc_Product__Type_Ounit ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) _let_0))) (not (= (hAPP _let_1 V_A_2) (hAPP _let_1 _let_0))) (= V_A_2 _let_0)) ))) 5.49/5.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 5.49/5.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (forall ((V_k $$unsorted)) (= (hAPP _let_0 (c_Int_OBit0 V_k)) (c_Int_OBit0 (hAPP _let_0 V_k))) )) 5.49/5.70 ( c_Int_OPls ) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.49/5.70 ( c_Int_OMin ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_n)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (hAPP _let_0 V_m)) (hAPP _let_0 V_n))) )) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_x_2))) (not (hBOOL (hAPP _let_0 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))))) )) 5.49/5.70 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.49/5.70 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.49/5.70 ( c_Int_OMin, c_Int_OMin ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (forall ((V_w_2 $$unsorted)) (= (hAPP (hAPP (c_HOL_OLet tc_Nat_Onat tc_Nat_Onat) (hAPP _let_0 V_w_2)) (hAPP (hAPP (c_COMBS tc_Nat_Onat tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oplus__class_Oplus tc_Nat_Onat)) (c_COMBI tc_Nat_Onat))) (hAPP _let_0 (c_Int_OBit0 V_w_2))) )) 5.49/5.70 ( c_Int_OPls ) 5.49/5.70 ( (c_Int_OBit1 c_Int_OPls) ) 5.49/5.70 ( c_Int_OMin ) 5.49/5.70 ) 5.49/5.70 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_y (hAPP (c_Product__Type_Osnd T_b T_a) (hAPP (hAPP (c_Product__Type_OPair T_b T_a) V_x) V_y))) ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.49/5.70 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.49/5.70 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.49/5.70 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (hAPP (c_Set_Oinsert T_b) V_x_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP _let_0 (hAPP _let_2 V_A_2)) (hAPP c_Nat_OSuc (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP _let_2 (c_Orderings_Obot__class_Obot _let_1))))))) )))) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.49/5.70 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.49/5.70 ( (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) ) 5.49/5.70 ( (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) ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (c_Relation_ORange T_b T_b))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (hAPP _let_0 (c_Transitive__Closure_Otrancl T_b V_r_2)) (hAPP _let_0 V_r_2)) )) 5.49/5.70 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (let ((_let_1 (c_Big__Operators_Olattice_OSup__fin T_b _let_0 V_A_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= _let_1 (hAPP (hAPP _let_0 V_x_2) _let_1))) ))) 5.49/5.70 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (hAPP _let_0 V_x))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP _let_1 V_y))) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_z))) (hBOOL (hAPP _let_1 V_z))) ))) 5.49/5.70 ( c_Int_OPls, c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( c_Int_OMin, c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.49/5.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (forall ((V_k $$unsorted)) (= (c_Int_OBit1 (c_Int_Opred (hAPP _let_0 V_k))) (hAPP _let_0 (c_Int_OBit1 V_k))) )) 5.49/5.70 ( c_Int_OPls ) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.49/5.70 ( c_Int_OMin ) 5.49/5.70 ) 5.49/5.70 (instantiation (forall ((V_v_H $$unsorted)) (= (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Nat_Onat) (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v_H)) (hAPP c_Int_Onat (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v_H)))) ) 5.49/5.70 ( c_Int_OPls ) 5.49/5.70 ( (c_Int_OBit1 c_Int_OPls) ) 5.49/5.70 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.49/5.70 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.49/5.70 ( c_Int_OMin ) 5.49/5.70 ) 5.49/5.70 (instantiation (forall ((V_i_2 $$unsorted) (V_j_2 $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_j_2) V_i_2)) (= (c_SetInterval_Oord__class_OatLeastAtMost tc_Int_Oint V_i_2 V_j_2) (hAPP (hAPP (c_Set_Oinsert tc_Int_Oint) V_i_2) (c_SetInterval_Oord__class_OatLeastAtMost tc_Int_Oint (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_i_2) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_j_2)))) ) 5.49/5.70 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.49/5.70 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.49/5.70 ( c_Int_OMin, c_Int_OMin ) 5.49/5.70 ) 5.49/5.70 (instantiation (forall ((V_i_2 $$unsorted) (V_j_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_j_2) V_i_2))) (= (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) (c_SetInterval_Oord__class_OatLeastAtMost tc_Int_Oint V_i_2 V_j_2))) ) 5.49/5.70 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.49/5.70 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.49/5.70 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.49/5.70 ( c_Int_OMin, c_Int_OMin ) 5.49/5.70 ) 5.49/5.70 (instantiation (forall ((V_v_2 $$unsorted) (V_ca_2 $$unsorted) (V_ba_2 $$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_ba_2) (hAPP (c_Fun_Ocomp T_c T_c T_b (c_Fun_Oid T_c)) V_ca_2))) (= (hAPP V_ca_2 V_v_2) (hAPP V_a_2 (hAPP V_ba_2 V_v_2)))) ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (hAPP (c_Fun_Ocomp skv_4 skv_8 skv_6 skv_3) skv_2), skv_5, skv_6, skv_7, skv_8 ) 5.49/5.70 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat, c_Int_Onat, c_Code__Numeral_Oof__nat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 5.49/5.70 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), skv_2, (hAPP (c_Fun_Ocomp skv_8 skv_7 skv_4 skv_5) skv_3), skv_6, skv_7, skv_4 ) 5.49/5.70 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), 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 ) 5.49/5.70 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat, skv_3, skv_5, skv_4, skv_7, skv_8 ) 5.49/5.70 ( c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool), skv_2, skv_3, skv_6, skv_8, skv_4 ) 5.49/5.70 ) 5.49/5.70 (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))) ) 5.49/5.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.49/5.70 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.49/5.70 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.49/5.70 ) 5.49/5.70 (instantiation (let ((_let_0 (hBOOL (hAPP V_ba_2 V_s_2)))) (let ((_let_1 (c_Com_Ocom_OWhile V_ba_2 V_ca_2))) (forall ((V_t_2 $$unsorted) (V_n_2 $$unsorted) (V_s_2 $$unsorted) (V_ca_2 $$unsorted) (V_ba_2 $$unsorted)) (or (not (c_Natural_Oevaln _let_1 V_s_2 V_n_2 V_t_2)) (and (= V_t_2 V_s_2) (not _let_0)) (and _let_0 (not (forall ((B_s1 $$unsorted)) (or (not (c_Natural_Oevaln V_ca_2 V_s_2 V_n_2 B_s1)) (not (c_Natural_Oevaln _let_1 B_s1 V_n_2 V_t_2))) )))) ))) 5.49/5.71 ( v_s2, v_na, v_s1, v_c, v_b ) 5.49/5.71 ) 5.49/5.71 (instantiation (forall ((V_n $$unsorted) (V_z $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Rings_Odvd__class_Odvd tc_Int_Oint) V_z) V_n))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_n))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_z) V_n))) ) 5.49/5.71 ( c_Int_OPls, c_Int_OMin ) 5.49/5.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.49/5.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.49/5.71 ( (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) ) 5.49/5.71 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.49/5.71 ( c_Int_OMin, c_Int_OMin ) 5.49/5.71 ( (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) ) 5.49/5.71 ) 5.49/5.71 (instantiation (forall ((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_a_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 5.49/5.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.49/5.71 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.71 ( (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)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ( (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)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v))))) (let ((_let_1 (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v)))) (forall ((V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (and (or (not _let_0) (= _let_1 (c_Groups_Ozero__class_Ozero T_a))) (or _let_0 (= _let_1 (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_v))))) ))) 5.50/5.71 ( c_Int_OPls, tc_Nat_Onat ) 5.50/5.71 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.71 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.50/5.71 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.50/5.71 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.50/5.71 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.50/5.71 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.50/5.71 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.50/5.71 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.50/5.71 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.50/5.71 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.71 ) 5.50/5.71 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)))) ) 5.50/5.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.71 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.71 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_0)))) (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (c_Relation_OImage T_b T_b V_r_2) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))) (hAPP (hAPP (c_Equiv__Relations_Oquotient T_b) _let_1) V_r_2)) ))) 5.50/5.71 ( 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) ) 5.50/5.71 ( 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) ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_x_2))) (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) (hAPP _let_1 V_A_2)) (hAPP _let_1 (c_Orderings_Obot__class_Obot _let_0))))) ))) 5.50/5.71 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.71 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.71 ( (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (tc_List_Olist T_b))) (forall ((T_b $$unsorted)) (= (c_List_Olists T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (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)))) )) 5.50/5.71 ( tc_Nat_Onat ) 5.50/5.71 ( tc_Int_Oint ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_x_2))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_3 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP _let_1 _let_2)))) (let ((_let_4 (= _let_2 _let_3))) (let ((_let_5 (c_Big__Operators_Olinorder__class_OMin T_b (hAPP _let_1 V_A_2)))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or _let_4 (= _let_5 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMin T_b _let_3)))) (or (not _let_4) (= V_x_2 _let_5)))) ))))))) 5.50/5.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.71 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.71 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ogroup__add T_b)) (= (= V_a_2 (hAPP _let_0 V_ba_2)) (= V_ba_2 (hAPP _let_0 V_a_2)))) )) 5.50/5.71 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.50/5.71 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.71 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.71 ) 5.50/5.71 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_Opred V_k) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) c_Int_OMin) V_k)) ) 5.50/5.71 ( c_Int_OPls ) 5.50/5.71 ( c_Int_OMin ) 5.50/5.71 ) 5.50/5.71 (instantiation (forall ((V_xs_2 $$unsorted) (T_b $$unsorted)) (= (= V_xs_2 (c_List_Olist_ONil T_b)) (= (hAPP (c_List_Oset T_b) V_xs_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 5.50/5.71 ( c_Com_Obodies, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (c_Groups_Oabs__class_Oabs T_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (= (hAPP _let_0 V_a) (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)))) )) 5.50/5.71 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.71 ) 5.50/5.71 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Transitive__Closure_Ortrancl T_b V_r_2) (c_Transitive__Closure_Otrancl T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (c_Relation_OId T_b)))) ) 5.50/5.71 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.71 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (c_member T_b))) (forall ((V_A_2 $$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_110707 $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 B_x) V_A_2))) (not (hBOOL (hAPP (hAPP _let_0 BOUND_VARIABLE_110707) V_A_2))) (not (= (hAPP V_f_2 B_x) (hAPP V_f_2 BOUND_VARIABLE_110707))) (= B_x BOUND_VARIABLE_110707)) )) )) 5.50/5.71 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Nat_Osemiring__1__class_Oof__nat T_b))) (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted) (T_b $$unsorted)) (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)))) ))) 5.50/5.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.50/5.71 ) 5.50/5.71 (instantiation (forall ((V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) V_n) (hAPP c_Nat_OSuc V_n)) ) 5.50/5.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.71 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.50/5.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.50/5.71 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2))) (let ((_let_3 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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_2) (= (hAPP (hAPP _let_3 (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_2)) (hAPP (hAPP _let_3 (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMax T_b V_B_2)))) ))))) 5.50/5.71 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.71 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.71 ( (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)) ) 5.50/5.71 ) 5.50/5.71 (instantiation (forall ((T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Relation_OField T_b) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)))) ) 5.50/5.71 ( tc_Nat_Onat ) 5.50/5.71 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= V_n_2 V_m_2) (= (hAPP _let_0 V_m_2) (hAPP _let_0 V_n_2))) )) 5.50/5.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.50/5.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.50/5.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.50/5.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.50/5.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.50/5.71 ) 5.50/5.71 (instantiation (forall ((V_k_2 $$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)))) ) 5.50/5.71 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( (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 ) 5.50/5.71 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.71 ( (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 ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2))) (= (= V_x_2 V_y_2) (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2)))) )) 5.50/5.71 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.50/5.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.50/5.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.50/5.71 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.71 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ) 5.50/5.71 (instantiation (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_a_2) V_ba_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_a_2) V_ba_2))))) ) 5.50/5.71 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.71 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.71 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.71 ) 5.50/5.71 (instantiation (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_B_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBC T_b T_b tc_HOL_Obool) c_fequal) V_a_2))) V_B_2)) ) 5.50/5.71 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.71 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.71 ) 5.50/5.71 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) (hAPP (c_Set_Oimage T_c T_b V_f_2) V_A_2))) (hAPP (c_Finite__Set_Ocard T_c) V_A_2)))) (not (c_Fun_Oinj__on T_c T_b V_f_2 V_A_2))) ) 5.50/5.71 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.71 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 5.50/5.71 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 5.50/5.71 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 5.50/5.71 ) 5.50/5.71 (instantiation (forall ((T_a $$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)))) ) 5.50/5.71 ( tc_Nat_Onat ) 5.50/5.71 ( tc_Int_Oint ) 5.50/5.71 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (hAPP c_Nat_OSuc _let_0))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= _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)))) ))) 5.50/5.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.50/5.71 ) 5.50/5.71 (instantiation (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)))) (forall ((V_a_2 $$unsorted) (V_ba_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) _let_2))) (hAPP _let_0 (hAPP (hAPP _let_1 V_a_2) _let_2))))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_ba_2) V_A_2))) (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_ba_2)) V_r_2))) )))) 5.50/5.71 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_2 (hAPP _let_1 V_w))) (let ((_let_3 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) _let_0) _let_2))) (let ((_let_4 (c_Divides_OnegDivAlg _let_0 _let_2))) (let ((_let_5 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) _let_3)))) (forall ((V_w $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) _let_2))) (and (or (not _let_5) (= (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) (hAPP _let_1 c_Int_OMin)) _let_3) _let_4)) (or _let_5 (= _let_4 (hAPP (c_Divides_Oadjust _let_2) (c_Divides_OnegDivAlg _let_0 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP _let_1 (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) _let_2))))))) ))))))) 5.50/5.71 ( c_Int_OPls ) 5.50/5.71 ( (c_Int_OBit1 c_Int_OPls) ) 5.50/5.71 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.50/5.71 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.50/5.71 ( c_Int_OMin ) 5.50/5.71 ) 5.50/5.71 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_x_2))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) V_A_2) (hAPP _let_1 (c_Orderings_Obot__class_Obot _let_2))))) (hAPP _let_0 (hAPP _let_1 V_A_2)))) )))) 5.50/5.71 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.71 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.72 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.72 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.72 ) 5.50/5.72 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) V_n) V_m) (hAPP (hAPP c_Code__Numeral_Osubtract__code__numeral V_n) V_m)) ) 5.50/5.72 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 5.50/5.72 ) 5.50/5.72 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (= (hAPP c_Nat_OSuc V_x) (hAPP c_Nat_OSuc V_y))) (= V_y V_x)) ) 5.50/5.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.50/5.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.50/5.72 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.72 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.50/5.72 ) 5.50/5.72 (instantiation (forall ((V_y_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (not (class_Int_Onumber__ring T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Int_OBit1 c_Int_OPls)) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Groups_Oone__class_Oone T_b)) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_y_2))))) ) 5.50/5.72 ( c_Int_OPls, tc_Nat_Onat ) 5.50/5.72 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.72 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.50/5.72 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.50/5.72 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.50/5.72 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.50/5.72 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.50/5.72 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.50/5.72 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.50/5.72 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.50/5.72 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.72 ) 5.50/5.72 (instantiation (forall ((V_v $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_v) 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) V_v)) (c_Groups_Oone__class_Oone tc_Nat_Onat)))) ) 5.50/5.72 ( c_Int_OPls ) 5.50/5.72 ( (c_Int_OBit1 c_Int_OPls) ) 5.50/5.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.72 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.50/5.72 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.50/5.72 ( c_Int_OMin ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (forall ((V_v $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_v) c_Int_OPls)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP _let_0 V_v)) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 (c_Int_Opred V_v)))) )) 5.50/5.72 ( c_Int_OPls ) 5.50/5.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.72 ( c_Int_OMin ) 5.50/5.72 ) 5.50/5.72 (instantiation (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Groups_Ocomm__monoid__mult T_c)) (not (c_Fun_Oinj__on T_b T_c V_f_2 V_B_2)) (= (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__mult__class_Osetprod T_b T_c) V_f_2) V_B_2) (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__mult__class_Osetprod T_c T_c) (c_Fun_Oid T_c)) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_B_2)))) ) 5.50/5.72 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.72 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 5.50/5.72 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 5.50/5.72 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 5.50/5.72 ) 5.50/5.72 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Complete__Lattice_OSup__class_OSup T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_a_2) (c_Complete__Lattice_OSup__class_OSup T_b V_A_2)))) ) 5.50/5.72 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.72 ( (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) ) 5.50/5.72 ( (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 (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.72 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (c_Nat_Osize__class_Osize (tc_List_Olist T_b)))) (forall ((V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) (hAPP (c_List_Oset T_b) V_xs_2)))) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP _let_0 V_xs_2)) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 (c_List_Oremove1 T_b V_x_2 V_xs_2)))) )) 5.50/5.72 ( c_Com_Obodies, skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (c_Nat_Osize__class_Osize (tc_List_Olist T_b)))) (forall ((V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) (hAPP (c_List_Oset T_b) V_xs_2))) (= (hAPP _let_0 V_xs_2) (hAPP _let_0 (c_List_Oremove1 T_b V_x_2 V_xs_2)))) )) 5.50/5.72 ( c_Com_Obodies, skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (forall ((V_w_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Oring__char__0 T_b)) (not (class_Int_Onumber__ring 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)))) )) 5.50/5.72 ( c_Int_OPls, tc_Nat_Onat ) 5.50/5.72 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.72 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.50/5.72 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.50/5.72 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Nat_Onat))) (let ((_let_1 (hBOOL (hAPP (hAPP V_Pa_2 V_n_2) V_m_2)))) (let ((_let_2 (not _let_1))) (forall ((V_Pa_2 $$unsorted) (V_n_2 $$unsorted) (V_m_2 $$unsorted)) (or (and (hBOOL (hAPP (hAPP _let_0 V_m_2) V_n_2)) _let_2) (and (= V_n_2 V_m_2) _let_2) (and (hBOOL (hAPP (hAPP _let_0 V_n_2) V_m_2)) _let_2) _let_1) )))) 5.50/5.72 ( (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) ) 5.50/5.72 ( (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) ) 5.50/5.72 ( (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))) ) 5.50/5.72 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.50/5.72 ( (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))) ) 5.50/5.72 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OPls ) 5.50/5.72 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 5.50/5.72 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.50/5.72 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 5.50/5.72 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.50/5.72 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.50/5.72 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.72 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 5.50/5.72 ( (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) ) 5.50/5.72 ( (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) ) 5.50/5.72 ( (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) ) 5.50/5.72 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), (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)) ) 5.50/5.72 ( (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)) ) 5.50/5.72 ( (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)) ) 5.50/5.72 ( (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)) ) 5.50/5.72 ( (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)) ) 5.50/5.72 ( (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) ) 5.50/5.72 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) 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_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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))) ) 5.50/5.72 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) 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_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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))) ) 5.50/5.72 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_0 _let_0))), (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))) ) 5.50/5.72 ( (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) ) 5.50/5.72 ( (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) ) 5.50/5.72 ( (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) ) 5.50/5.72 ( (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 ) 5.50/5.72 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omin__strict, c_FunDef_Omin__weak ) 5.50/5.72 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omax__strict, c_FunDef_Omax__weak ) 5.50/5.72 ( (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 ) 5.50/5.72 ( (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 ) 5.50/5.72 ( (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) ) 5.50/5.72 ( (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)))) ) 5.50/5.72 ( (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) ) 5.50/5.72 ( (let ((_let_0 (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)))) (c_COMBB _let_0 _let_0 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)) ) 5.50/5.72 ( (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 ) 5.50/5.72 ( (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool), (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT), skv_9 ) 5.50/5.72 ( (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)), skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies) ) 5.50/5.72 ( (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)) ) 5.50/5.72 ( (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) ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (c_Finite__Set_Ofold1 T_b _let_0) V_A_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 V_A_2))) )) 5.50/5.72 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.72 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.50/5.72 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ogroup__add T_b)) (= (= V_ba_2 V_a_2) (= (hAPP _let_0 V_a_2) (hAPP _let_0 V_ba_2)))) )) 5.50/5.72 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.50/5.72 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.72 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.72 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.72 ) 5.50/5.72 (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)))))) ) 5.50/5.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.72 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.72 ( (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)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.72 ( (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)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.72 ) 5.50/5.72 (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 $$unsorted)) (or (not (= (hAPP V_f_2 (hAPP V_g_2 V_x_2)) (hAPP V_f_H_2 (hAPP V_g_H_2 V_x_H_2)))) (= (hAPP (hAPP (c_Fun_Ocomp T_c T_b T_d V_f_2) V_g_2) V_x_2) (hAPP (hAPP (c_Fun_Ocomp T_e T_b T_f V_f_H_2) V_g_H_2) V_x_H_2))) ) 5.50/5.72 ( tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc, c_Code__Numeral_Oof__nat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc, c_Code__Numeral_Oof__nat ) 5.50/5.72 ( tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Finite__Set_Ocard tc_Product__Type_Ounit), c_Code__Numeral_Oof__nat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc, c_Code__Numeral_Oof__nat ) 5.50/5.72 ( tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral, tc_Int_Oint, tc_Nat_Onat, (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 5.50/5.72 ( tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral, tc_Int_Oint, tc_Nat_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 5.50/5.72 ) 5.50/5.72 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Obounded__lattice__bot T_a)) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) (c_Orderings_Obot__class_Obot T_a)))) ) 5.50/5.72 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.72 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.72 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Int_Oring__1__class_OInts T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Oring__1 T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) _let_1))) ))) 5.50/5.72 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.72 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.72 ) 5.50/5.72 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= V_x_2 (c_Big__Operators_Olattice_OInf__fin T_b (c_Orderings_Oord__class_Omin T_b) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 5.50/5.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.72 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.72 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.72 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (c_member T_b))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (forall ((B_Q $$unsorted) (BOUND_VARIABLE_111703 $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 BOUND_VARIABLE_111703) B_Q))) (not (forall ((B_x $$unsorted)) (or (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) B_y) B_x)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 B_y) B_Q)))) )) (not (hBOOL (hAPP (hAPP _let_0 B_x) B_Q)))) ))) ) (c_Wellfounded_Owf T_b V_r_2)) )) 5.50/5.72 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.72 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.50/5.72 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 5.50/5.72 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_a) (c_Groups_Ozero__class_Ozero T_a))))) (let ((_let_1 (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oabs__if T_a)) (and (or (not _let_0) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a) _let_1)) (or _let_0 (= V_a _let_1)))) ))) 5.50/5.72 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.72 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_c) B_x) V_A_2))) (= _let_1 (hAPP V_B_2 B_x))) ) (= _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) V_B_2))) ))) 5.50/5.72 ( (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 ) 5.50/5.72 ( (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 ) 5.50/5.72 ( (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 ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Nat_Osemiring__1__class_ONats T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Osemiring__1 T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 V_ba_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_ba_2)) _let_1))) ))) 5.50/5.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (c_Nat_Osize__class_Osize (tc_List_Olist T_b)))) (forall ((V_Pa_2 $$unsorted) (V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) (hAPP (c_List_Oset T_b) V_xs_2)))) (hBOOL (hAPP V_Pa_2 V_x_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP _let_0 (hAPP (c_List_Ofilter T_b V_Pa_2) V_xs_2))) (hAPP _let_0 V_xs_2)))) )) 5.50/5.72 ( c_Int_Onat, c_Com_Obodies, (c_Groups_Ozero__class_Ozero tc_Int_Oint), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.72 ) 5.50/5.72 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OlessThan T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (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)))) )) 5.50/5.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.72 ) 5.50/5.72 (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)))) ) 5.50/5.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.72 ) 5.50/5.73 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (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 $$unsorted)) (= (hAPP (hAPP _let_0 (hAPP V_h_2 B_x)) (hAPP V_h_2 B_y)) (hAPP V_h_2 (hAPP (hAPP _let_0 B_x) B_y))) )) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (= V_N_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (c_Set_Oimage T_b T_b V_h_2) V_N_2)) (hAPP V_h_2 (c_Big__Operators_Olinorder__class_OMin T_b V_N_2)))) )) 5.50/5.73 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 5.50/5.73 ) 5.50/5.73 (instantiation (forall ((V_x_2 $$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))) ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.73 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.73 ( (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) ) 5.50/5.73 ( (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) ) 5.50/5.73 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (c_Lattices_Osemilattice__sup__class_Osup T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__sup T_a)) (= (hAPP (hAPP _let_0 V_y) V_x) (hAPP (hAPP _let_0 V_x) V_y))) )) 5.50/5.73 ( 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)) ) 5.50/5.73 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.73 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.73 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.73 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.73 ( (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)) ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_m))) (not (hBOOL (hAPP (hAPP _let_0 V_m) V_n))) (not (hBOOL (hAPP (hAPP (c_Rings_Odvd__class_Odvd tc_Int_Oint) V_n) V_m)))) )) 5.50/5.73 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.50/5.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.73 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.73 ( c_Int_OMin, c_Int_OMin ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (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)) ))) 5.50/5.73 ( 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) ) 5.50/5.73 ) 5.50/5.73 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (c_Int_Oiszero T_a (c_Groups_Ozero__class_Ozero T_a))) ) 5.50/5.73 ( tc_Nat_Onat ) 5.50/5.73 ( tc_Int_Oint ) 5.50/5.73 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.73 ) 5.50/5.73 (instantiation (forall ((V_a_2 $$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))) ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.73 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.73 ( (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) ) 5.50/5.73 ( (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) ) 5.50/5.73 ) 5.50/5.73 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (= (c_Groups_Ozero__class_Ozero T_a) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) ) 5.50/5.73 ( tc_Nat_Onat ) 5.50/5.73 ( tc_Int_Oint ) 5.50/5.73 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (hAPP (c_Set_Oinsert T_b) V_x_2))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (forall ((V_x_2 $$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))) (= (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_1) V_A_2) (hAPP _let_0 (c_Orderings_Obot__class_Obot _let_1))))) (c_List_Olinorder__class_Osorted__list__of__set T_b (hAPP _let_0 V_A_2)))) ))) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.73 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.73 ( (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) ) 5.50/5.73 ( (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) ) 5.50/5.73 ) 5.50/5.73 (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))) ) 5.50/5.73 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.73 ( c_Int_OPls, c_Int_OMin ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.50/5.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.73 ( (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) ) 5.50/5.73 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.73 ( c_Int_OMin, c_Int_OMin ) 5.50/5.73 ( (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) ) 5.50/5.73 ) 5.50/5.73 (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)))) ) 5.50/5.73 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.73 ( (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) ) 5.50/5.73 ( (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) ) 5.50/5.73 ) 5.50/5.73 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_y) V_x)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) ) 5.50/5.73 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) (hAPP _let_0 V_x)) (hAPP _let_0 V_y)))) )) 5.50/5.73 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.73 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.73 ( (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)) ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (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))) (= (hAPP (c_Finite__Set_Ofold1 T_b _let_0) V_A_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 V_A_2))) )) 5.50/5.73 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.73 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.50/5.73 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2)) (= (= V_x_2 V_y_2) (not (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2))))) )) 5.50/5.73 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (tc_fun T_c tc_HOL_Obool))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (tc_fun T_c _let_1))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_1) V_A_2) V_B_2) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBB _let_0 tc_HOL_Obool T_b) (c_HOL_OAll T_c)) (hAPP (hAPP (c_COMBB _let_0 _let_0 T_b) (hAPP (c_COMBS T_c tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_c) c_fimplies) (hAPP (hAPP (c_COMBC T_c _let_0 tc_HOL_Obool) (c_member T_c)) V_A_2)))) (hAPP (hAPP (c_COMBC T_b _let_2 _let_0) (hAPP (hAPP (c_COMBB (tc_fun _let_1 tc_HOL_Obool) (tc_fun _let_2 _let_0) T_b) (c_COMBB _let_1 tc_HOL_Obool T_c)) (c_member T_b))) V_B_2))))) )))) 5.50/5.73 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.73 ) 5.50/5.73 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) (c_Transitive__Closure_Otrancl T_b V_r_2)) (c_Relation_OId T_b)) (c_Transitive__Closure_Ortrancl T_b V_r_2)) ) 5.50/5.73 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((T_b $$unsorted)) (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)))) )) 5.50/5.73 ( tc_Com_Ocom ) 5.50/5.73 ( tc_Nat_Onat ) 5.50/5.73 ( tc_HOL_Obool ) 5.50/5.73 ( tc_Int_Oint ) 5.50/5.73 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.73 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.73 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.50/5.73 ( tc_Com_Opname ) 5.50/5.73 ( tc_Product__Type_Ounit ) 5.50/5.73 ) 5.50/5.73 (instantiation (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Product__Type_Ocurry T_b T_c tc_HOL_Obool V_f_2) V_a_2) V_ba_2))) (hBOOL (hAPP V_f_2 (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_a_2) V_ba_2)))) ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.73 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_0 _let_0))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (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))) )) 5.50/5.73 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, tc_Int_Oint ) 5.50/5.73 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.50/5.73 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, tc_Int_Oint ) 5.50/5.73 ) 5.50/5.73 (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))) ) 5.50/5.73 ( c_Int_OPls, c_Int_OMin ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.73 ( (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) ) 5.50/5.73 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.73 ( c_Int_OMin, c_Int_OMin ) 5.50/5.73 ( (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) ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat))) (let ((_let_2 (c_Set_Oinsert _let_0))) (let ((_let_3 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (let ((_let_4 (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (hAPP c_Int_OAbs__Integ (hAPP _let_4 (hAPP (hAPP _let_2 (hAPP (hAPP _let_1 V_y_2) V_x_2)) _let_3))) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP c_Int_OAbs__Integ (hAPP _let_4 (hAPP (hAPP _let_2 (hAPP (hAPP _let_1 V_x_2) V_y_2)) _let_3))))) )))))) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.50/5.73 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (hAPP c_Nat_OSuc _let_0))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= _let_1 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m_2) V_n_2)) (or (and (= _let_1 V_n_2) (= _let_0 V_m_2)) (and (= _let_1 V_m_2) (= _let_0 V_n_2)))) ))) 5.50/5.73 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.50/5.73 ) 5.50/5.73 (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)))) ) 5.50/5.73 ( tc_Com_Ocom, tc_Com_Opname ) 5.50/5.73 ( tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.73 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.73 ( (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) ) 5.50/5.73 ) 5.50/5.73 (instantiation (forall ((V_xs_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_List_Odistinct T_b) V_xs_2))) (= (hAPP (c_Nat_Osize__class_Osize (tc_List_Olist T_b)) V_xs_2) (hAPP (c_Finite__Set_Ocard T_b) (hAPP (c_List_Oset T_b) V_xs_2)))) ) 5.50/5.73 ( c_Com_Obodies, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.73 ) 5.50/5.73 (instantiation (forall ((V_nat $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Nat_Onat_Onat__size V_nat)) (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Nat_Onat_Onat__size (hAPP c_Nat_OSuc V_nat))) ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.73 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.50/5.73 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.50/5.73 ) 5.50/5.73 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (= (= (c_Groups_Osgn__class_Osgn T_b V_a_2) (c_Groups_Oone__class_Oone T_b)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (c_Groups_Ozero__class_Ozero T_b)) V_a_2)))) ) 5.50/5.73 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.73 ) 5.50/5.73 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Opreorder T_b)) (= (and (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2)) (not (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2)))) )) 5.50/5.73 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( (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 ) 5.50/5.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.73 ( (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 ) 5.50/5.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( (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 ) 5.50/5.73 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.50/5.73 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.73 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.73 ( (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 ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 V_A_2)) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.74 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.74 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.74 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.74 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) V_ba_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_ba_2)) (c_Groups_Ozero__class_Ozero T_b))))) )) 5.50/5.74 ( (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 ) 5.50/5.74 ) 5.50/5.74 (instantiation (forall ((V_k $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (= (hAPP (c_Groups_Oabs__class_Oabs T_a) V_k) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) V_k) (c_Groups_Osgn__class_Osgn T_a V_k)))) ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ) 5.50/5.74 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (and (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)) (not (= V_y_2 V_x_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2)))) ) 5.50/5.74 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.74 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ) 5.50/5.74 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_a) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_b) V_a))) (= V_a (c_Divides_Odiv__class_Omod tc_Int_Oint V_a V_b))) ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.50/5.74 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.74 ( c_Int_OMin, c_Int_OMin ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (hBOOL (hAPP (hAPP _let_0 V_x) V_y)) (= V_y V_x) (hBOOL (hAPP (hAPP _let_0 V_y) V_x))) )) 5.50/5.74 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.50/5.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.74 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.74 ( c_Int_OMin, c_Int_OMin ) 5.50/5.74 ) 5.50/5.74 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Power_Opower__class_Opower tc_Nat_Onat) (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)) (hAPP (c_Finite__Set_Ocard (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_OPow T_b) V_A_2)))) ) 5.50/5.74 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.74 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.50/5.74 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) (hAPP _let_1 V_ba_2))) (hBOOL (hAPP (hAPP _let_0 V_ba_2) (hAPP _let_1 V_a_2))))) ))) 5.50/5.74 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.74 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.50/5.74 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) V_n))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (= _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) _let_0))) )) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.50/5.74 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.50/5.74 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.50/5.74 ) 5.50/5.74 (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 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_x) V_N_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_x) B_m))) )) ))) ) 5.50/5.74 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) (hAPP (c_Groups_Ouminus__class_Ouminus _let_0) V_A_2)) (c_Orderings_Otop__class_Otop _let_0)) )) 5.50/5.74 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.50/5.74 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.74 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.74 ) 5.50/5.74 (instantiation (forall ((V_k_2 $$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)))) ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.74 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.74 ) 5.50/5.74 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_OBit0 V_k) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_k) V_k)) ) 5.50/5.74 ( c_Int_OPls ) 5.50/5.74 ( (c_Int_OBit1 c_Int_OPls) ) 5.50/5.74 ( c_Int_OMin ) 5.50/5.74 ) 5.50/5.74 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_x))) ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_u_2 $$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 _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))) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_l_2 V_u_2))) )) 5.50/5.74 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( (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 ) 5.50/5.74 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.74 ( (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 ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone T_a))) (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (= _let_0 (hAPP (hAPP (c_Power_Opower__class_Opower T_a) _let_0) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))))) )) 5.50/5.74 ( tc_Nat_Onat ) 5.50/5.74 ( tc_Int_Oint ) 5.50/5.74 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.74 ) 5.50/5.74 (instantiation (forall ((V_Pa_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (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_Pa_2))) (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_Pa_2)))) ) 5.50/5.74 ( c_fequal, tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.74 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.74 ( (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), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.74 ( (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 ) 5.50/5.74 ( (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT), tc_Com_Ocom, tc_Com_Opname ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (c_Big__Operators_Olinorder__class_OMax T_b V_A_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= _let_0 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) _let_0))) )) 5.50/5.74 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2))) (let ((_let_3 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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_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)) (hAPP (hAPP _let_3 (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))) (c_Big__Operators_Olattice_OInf__fin T_b _let_3 _let_2)))) ))))) 5.50/5.74 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.74 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.74 ( (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)) ) 5.50/5.74 ) 5.50/5.74 (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))) ) 5.50/5.74 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_HOL_Obool, tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.74 ( (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), tc_HOL_Obool, tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.74 ( (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 ) 5.50/5.74 ( (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT), tc_HOL_Obool, tc_Com_Ocom, tc_Com_Opname ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$unsorted)) (= (hAPP (c_Groups_Ouminus__class_Ouminus _let_0) (c_Orderings_Obot__class_Obot _let_0)) (c_Orderings_Otop__class_Otop _let_0)) )) 5.50/5.74 ( tc_Com_Ocom ) 5.50/5.74 ( tc_Nat_Onat ) 5.50/5.74 ( tc_HOL_Obool ) 5.50/5.74 ( tc_Int_Oint ) 5.50/5.74 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.74 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.50/5.74 ( tc_Product__Type_Ounit ) 5.50/5.74 ) 5.50/5.74 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Osemilattice__sup T_b)) (= (= V_y_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup 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)))) ) 5.50/5.74 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( (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 ) 5.50/5.74 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.74 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.74 ( (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 ) 5.50/5.74 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.74 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.74 ( (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_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.74 ) 5.50/5.74 (instantiation (forall ((V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP c_Nat_OSuc V_n)) ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.74 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.50/5.74 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.50/5.74 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (let ((_let_1 (tc_fun T_c T_d))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_e $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c T_d) (hAPP (hAPP (c_COMBB T_e _let_1 T_b) V_f_2) V_g_2)) (hAPP (hAPP (c_COMBS _let_0 T_c T_d) (hAPP (hAPP (c_COMBB T_e _let_1 _let_0) V_f_2) (hAPP (hAPP (c_COMBB T_b T_e _let_0) V_g_2) (c_Product__Type_Ofst T_b T_c)))) (c_Product__Type_Osnd T_b T_c))) ))) 5.50/5.74 ( c_Nat_OSuc, (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal), tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.74 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint)))), (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (tc_fun tc_Int_Oint tc_HOL_Obool), tc_HOL_Obool, tc_Int_Oint, tc_Int_Oint ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (c_Set_Oinsert T_b))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (= (hAPP (hAPP _let_0 V_a_2) _let_1) (hAPP (hAPP _let_0 V_ba_2) _let_1))) (= V_ba_2 V_a_2)) ))) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.74 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.74 ( (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)), (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) ) 5.50/5.74 ( (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)), (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) ) 5.50/5.74 ( (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)), (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) ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (c_Finite__Set_Ofold1 T_b (c_Groups_Otimes__class_Otimes T_b)))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oab__semigroup__mult T_b)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_b) V_x_2) (hAPP _let_0 V_A_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.74 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.74 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.74 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.74 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.74 ) 5.50/5.74 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_w_2))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP c_Int_Onat V_w_2)) (hAPP c_Int_Onat V_z_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w_2) V_z_2)))) ) 5.50/5.74 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.50/5.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.74 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.74 ( c_Int_OMin, c_Int_OMin ) 5.50/5.74 ) 5.50/5.74 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) (hAPP _let_1 V_ba_2))) (hBOOL (hAPP (hAPP _let_0 V_ba_2) (hAPP _let_1 V_a_2))))) ))) 5.50/5.75 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.75 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) V_b))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) V_b))) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a)) V_b))) )) 5.50/5.75 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((T_a $$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))) ) 5.50/5.75 ( tc_Nat_Onat ) 5.50/5.75 ( tc_HOL_Obool ) 5.50/5.75 ( tc_Int_Oint ) 5.50/5.75 ( (tc_fun tc_HOL_Obool tc_HOL_Obool) ) 5.50/5.75 ( (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 5.50/5.75 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.75 ( (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.50/5.75 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.75 ( (tc_fun tc_Product__Type_Ounit tc_HOL_Obool) ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_Groups_Ominus__class_Ominus T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oab__group__add T_a)) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (hAPP (hAPP _let_0 V_a) V_b)) (hAPP (hAPP _let_0 V_b) V_a))) )) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_y) V_x)) (= (c_Groups_Ozero__class_Ozero tc_Int_Oint) (c_Nat__Transfer_Otsub V_x V_y))) ) 5.50/5.75 ( c_Int_OPls, c_Int_OMin ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.75 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.75 ( c_Int_OMin, c_Int_OMin ) 5.50/5.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_u_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_u_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_u_2) (c_Orderings_Obot__class_Obot _let_0))) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_u_2))) )) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.75 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.75 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.75 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (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))) )) 5.50/5.75 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (= _let_0 (hAPP (hAPP (c_Power_Opower__class_Opower T_a) _let_0) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))))) )) 5.50/5.75 ( tc_Nat_Onat ) 5.50/5.75 ( tc_Int_Oint ) 5.50/5.75 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_S_2 $$unsorted)) (= (c_Nat__Transfer_Onat__set V_S_2) (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Int_Oint) B_x) V_S_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) B_x))) )) ) 5.50/5.75 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_y $$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))) ) 5.50/5.75 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( (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 ) 5.50/5.75 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.75 ( (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 ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_i_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_i_2) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP c_Int_Onat V_i_2))) ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.50/5.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.50/5.75 ( c_Int_OMin ) 5.50/5.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_a_H $$unsorted) (T_a $$unsorted)) (not (= (hAPP (c_Option_Ooption_OSome T_a) V_a_H) (c_Option_Ooption_ONone T_a))) ) 5.50/5.75 ( skv_10, tc_Com_Ocom ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_x_2 $$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_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)))) )) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.75 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.75 ( (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) ) 5.50/5.75 ( (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) ) 5.50/5.75 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) (hAPP (c_List_Oset T_b) V_xs_2))) (not (forall ((B_i $$unsorted)) (or (not (= V_x_2 (hAPP (hAPP (c_List_Onth T_b) V_xs_2) B_i))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_i) (hAPP (c_Nat_Osize__class_Osize (tc_List_Olist T_b)) V_xs_2))))) ))) ) 5.50/5.75 ( c_Com_Obodies, skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v_2))) (forall ((V_v_2 $$unsorted) (V_m_2 $$unsorted)) (= (= _let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2)) (and (= V_m_2 (hAPP c_Int_Onat _let_0)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) _let_0)))) )) 5.50/5.75 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.75 ( (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))) ) 5.50/5.75 ( (c_Int_OBit1 (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))) ) 5.50/5.75 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_z $$unsorted)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) V_z) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_z) V_z)) ) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_X_2 $$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))) ) 5.50/5.75 ( (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) ) 5.50/5.75 ( (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) ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Finite__Set_Ofun__left__comm__idem T_b T_c V_f_2)) (c_Finite__Set_Ofun__left__comm__idem T_d T_c (hAPP (hAPP (c_COMBB T_b (tc_fun T_c T_c) T_d) V_f_2) V_g_2))) ) 5.50/5.75 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint, c_fconj, tc_HOL_Obool, tc_HOL_Obool ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= V_x (hAPP (c_Product__Type_Ofst T_a T_b) (hAPP (hAPP (c_Product__Type_OPair T_a T_b) V_x) V_y))) ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.75 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.75 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.75 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus _let_0))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (hAPP _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) V_B_2)) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) (hAPP (hAPP (c_COMBB _let_0 _let_0 T_c) _let_1) V_B_2))) ))) 5.50/5.75 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.75 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.75 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_a) _let_0))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_b) V_a))) (= _let_0 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_a) V_b))) )) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.50/5.75 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.75 ( c_Int_OMin, c_Int_OMin ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (forall ((T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (= _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) _let_0))) )) 5.50/5.75 ( tc_Nat_Onat ) 5.50/5.75 ( tc_Int_Oint ) 5.50/5.75 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (forall ((V_xys_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (hAPP (c_Set_Oimage _let_0 T_b (c_Product__Type_Ofst T_b T_c)) (hAPP (c_List_Oset _let_0) V_xys_2)) (c_Map_Odom T_b T_c (c_Map_Omap__of T_b T_c V_xys_2))) )) 5.50/5.75 ( c_Com_Obodies, tc_Com_Ocom, tc_Com_Opname ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_1 (c_Groups_Oone__class_Oone T_a))) (forall ((V_m $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Ocomm__semiring__1 T_a)) (= (hAPP (hAPP _let_0 V_m) V_m) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (hAPP (hAPP _let_0 _let_1) _let_1)) V_m))) ))) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (= V_x_2 (c_Set_Othe__elem T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.75 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.75 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.75 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (or (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2)) (= V_y_2 V_x_2)) (not (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2))))) )) 5.50/5.75 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.75 ) 5.50/5.75 (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)) ) 5.50/5.75 ( (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 ) 5.50/5.75 ( (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 ) 5.50/5.75 ) 5.50/5.75 (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))) ) 5.50/5.75 ( tc_Com_Ocom, tc_Com_Opname ) 5.50/5.75 ( tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.75 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.75 ( (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) ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_member T_b))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 B_y) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) B_y) V_x_2))) )) (not (hBOOL (hAPP (hAPP _let_0 V_x_2) V_A_2))) (= V_x_2 (c_Big__Operators_Olinorder__class_OMax T_b V_A_2))) )) 5.50/5.75 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.75 ) 5.50/5.75 (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 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_x) V_N_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) B_x) B_m))) )) ))) ) 5.50/5.75 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2)) _let_1)) (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)))) ))) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v_H))) (forall ((V_v_H $$unsorted)) (or (hBOOL (hAPP c_Nat__Numeral_Oneg _let_0)) (= (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) V_v_H)) (hAPP c_Int_Onat (c_Divides_Odiv__class_Omod tc_Int_Oint (c_Groups_Oone__class_Oone tc_Int_Oint) _let_0)))) )) 5.50/5.75 ( c_Int_OPls ) 5.50/5.75 ( (c_Int_OBit1 c_Int_OPls) ) 5.50/5.75 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.50/5.75 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.50/5.75 ( c_Int_OMin ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) (forall ((V_v_H $$unsorted)) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v_H)))) (= _let_0 (c_Divides_Odiv__class_Omod tc_Nat_Onat _let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v_H)))) )) 5.50/5.75 ( c_Int_OPls ) 5.50/5.75 ( (c_Int_OBit1 c_Int_OPls) ) 5.50/5.75 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.50/5.75 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.50/5.75 ( c_Int_OMin ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_N_2 $$unsorted) (V_h_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (= (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))) (= (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)))) )) 5.50/5.75 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 5.50/5.75 ) 5.50/5.75 (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))) ) 5.50/5.75 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_u_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_l_2)) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_l_2 V_u_2)))) ) 5.50/5.75 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((T_b $$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))) ) 5.50/5.75 ( tc_Nat_Onat ) 5.50/5.75 ( tc_HOL_Obool ) 5.50/5.75 ( tc_Int_Oint ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (= V_A_2 (c_Complete__Lattice_OSup__class_OSup (tc_fun T_b tc_HOL_Obool) (hAPP (hAPP (c_Equiv__Relations_Oquotient T_b) V_A_2) V_r_2)))) ) 5.50/5.75 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.75 ) 5.50/5.75 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (forall ((V_y_2 $$unsorted) (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 T_b) (hAPP _let_0 V_x_2)) (hAPP _let_0 V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_x_2) V_y_2)))) )) 5.50/5.75 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 5.50/5.75 ) 5.50/5.75 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_k) (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) c_Int_OMin) V_k)) ) 5.50/5.76 ( c_Int_OPls ) 5.50/5.76 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.50/5.76 ( c_Int_OMin ) 5.50/5.76 ) 5.50/5.76 (instantiation (forall ((T_b $$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)))) ) 5.50/5.76 ( tc_Nat_Onat ) 5.50/5.76 ( tc_Int_Oint ) 5.50/5.76 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.76 ( (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (tc_fun T_b T_c))) (forall ((T_c $$unsorted) (T_b $$unsorted)) (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))))) )) 5.50/5.76 ( tc_HOL_Obool, tc_Com_Ocom ) 5.50/5.76 ( tc_HOL_Obool, tc_Nat_Onat ) 5.50/5.76 ( tc_HOL_Obool, tc_HOL_Obool ) 5.50/5.76 ( tc_HOL_Obool, tc_Int_Oint ) 5.50/5.76 ( tc_HOL_Obool, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.76 ( tc_HOL_Obool, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.76 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.50/5.76 ( tc_HOL_Obool, tc_Product__Type_Ounit ) 5.50/5.76 ( tc_Int_Oint, tc_Int_Oint ) 5.50/5.76 ( (tc_fun tc_Int_Oint tc_HOL_Obool), tc_Int_Oint ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (c_Option_Ooption_OSome T_b))) (forall ((V_a_H_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (= (hAPP _let_0 V_a_2) (hAPP _let_0 V_a_H_2)) (= V_a_H_2 V_a_2)) )) 5.50/5.76 ( skv_10, skv_10, tc_Com_Ocom ) 5.50/5.76 ) 5.50/5.76 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (= V_m (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_n))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_n)) ) 5.50/5.76 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.50/5.76 ) 5.50/5.76 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) (= (c_Groups_Osgn__class_Osgn T_a V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (c_Groups_Oone__class_Oone T_a)))) ) 5.50/5.76 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.76 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP _let_0 V_a))) (not (hBOOL (hAPP _let_0 V_b))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)))) )) 5.50/5.76 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Int_Oint))) (forall ((V_k $$unsorted)) (= (c_Int_OBit1 V_k) (hAPP (hAPP _let_0 (hAPP (hAPP _let_0 (c_Groups_Oone__class_Oone tc_Int_Oint)) V_k)) V_k)) )) 5.50/5.76 ( c_Int_OPls ) 5.50/5.76 ( (c_Int_OBit1 c_Int_OPls) ) 5.50/5.76 ( c_Int_OMin ) 5.50/5.76 ) 5.50/5.76 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) V_z) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_z) V_z))) ) 5.50/5.76 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (let ((_let_2 (c_Rings_Odvd__class_Odvd tc_Nat_Onat))) (let ((_let_3 (tc_fun tc_Nat_Onat _let_0))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (c_Orderings_Oorder_Ostrict__mono tc_Nat_Onat T_b (hAPP (hAPP (c_COMBS tc_Nat_Onat _let_1 _let_1) (hAPP (hAPP (c_COMBB _let_3 (tc_fun _let_1 _let_1) tc_Nat_Onat) (c_COMBS tc_Nat_Onat tc_HOL_Obool tc_HOL_Obool)) (hAPP (hAPP (c_COMBB _let_1 _let_3 tc_Nat_Onat) (hAPP (c_COMBB tc_HOL_Obool _let_0 tc_Nat_Onat) c_fconj)) _let_2))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Nat_Onat) (hAPP (c_COMBB tc_HOL_Obool tc_HOL_Obool tc_Nat_Onat) c_fNot)) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) _let_2))) V_f_2)) (hBOOL (hAPP (hAPP _let_2 V_y_2) V_x_2)) (not (hBOOL (hAPP (hAPP _let_2 V_x_2) V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (hAPP V_f_2 V_x_2)) (hAPP V_f_2 V_y_2)))) ))))) 5.50/5.76 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 5.50/5.76 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint), tc_Int_Oint ) 5.50/5.76 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 5.50/5.76 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 5.50/5.76 ( (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)))))), (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 ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_a_2 $$unsorted) (V_ba_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_ba_2)) (hAPP _let_1 V_a_2))) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_ba_2)))) ))) 5.50/5.76 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.50/5.76 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.76 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.76 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_x_2))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_3 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP _let_1 _let_2)))) (let ((_let_4 (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP _let_1 V_A_2)))) (let ((_let_5 (= _let_2 _let_3))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or _let_5 (= _let_4 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_x_2) (c_Big__Operators_Olattice__class_OInf__fin T_b _let_3)))) (or (not _let_5) (= V_x_2 _let_4)))) ))))))) 5.50/5.76 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.76 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.76 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.76 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 _let_2) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) B_x) B_y)) (hAPP (hAPP _let_1 B_x) (hAPP (hAPP _let_1 B_y) _let_2)))) )) (hBOOL (hAPP (hAPP _let_0 (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)) V_A_2))) )))) 5.50/5.76 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.76 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.50/5.76 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted)) (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))) )) 5.50/5.76 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 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) ) 5.50/5.76 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 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) ) 5.50/5.76 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.76 ) 5.50/5.76 (instantiation (forall ((V_l $$unsorted)) (or (not (c_List_Onat__list V_l)) (= V_l (c_List_Oembed__list (c_List_Oreturn__list V_l)))) ) 5.50/5.76 ( (c_List_Olist_ONil tc_Int_Oint) ) 5.50/5.76 ) 5.50/5.76 (instantiation (forall ((V_xs_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (hAPP (c_List_Ofoldl T_b T_b (c_Lattices_Osemilattice__sup__class_Osup T_b) (c_Orderings_Obot__class_Obot T_b)) V_xs_2) (c_Complete__Lattice_OSup__class_OSup T_b (hAPP (c_List_Oset T_b) V_xs_2)))) ) 5.50/5.76 ( c_Com_Obodies, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.76 ) 5.50/5.76 (instantiation (forall ((V_a_2 $$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))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (= V_a_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_a_2) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)))) ) 5.50/5.76 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) _let_1)))) (let ((_let_3 (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2))) (let ((_let_4 (= _let_1 _let_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (and (or _let_4 (= _let_3 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) (c_Big__Operators_Olattice__class_OSup__fin T_b _let_2)))) (or (not _let_4) (= V_x_2 _let_3)))) )))))) 5.50/5.76 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (or (and (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_1) V_w_2))) (not (hBOOL (hAPP (hAPP _let_0 _let_1) V_z_2)))) (= (hBOOL (hAPP (hAPP _let_0 V_w_2) V_z_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Int_Onat V_w_2)) (hAPP c_Int_Onat V_z_2))))) ))) 5.50/5.76 ( c_Int_OPls, c_Int_OMin ) 5.50/5.76 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.76 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.76 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.76 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.76 ( c_Int_OMin, c_Int_OMin ) 5.50/5.76 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.76 ) 5.50/5.76 (instantiation (forall ((V_b $$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))) ) 5.50/5.76 ( (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 ) 5.50/5.76 ) 5.50/5.76 (instantiation (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))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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) (= (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)) (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)))) )))) 5.50/5.76 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.76 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.76 ( (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)) ) 5.50/5.76 ) 5.50/5.76 (instantiation (forall ((V_R_2 $$unsorted) (T_b $$unsorted)) (= (c_Transitive__Closure_Ortrancl T_b V_R_2) (c_Transitive__Closure_Ortrancl T_b (c_Transitive__Closure_Otrancl T_b V_R_2))) ) 5.50/5.76 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ominus__class_Ominus T_b))) (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (not (= (hAPP (hAPP _let_1 V_ca_2) V_d_2) (hAPP (hAPP _let_1 V_a_2) V_ba_2))) (= (hBOOL (hAPP (hAPP _let_0 V_ca_2) V_d_2)) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_ba_2)))) ))) 5.50/5.76 ( (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 ) 5.50/5.76 ) 5.50/5.76 (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))))) ) 5.50/5.76 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.76 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.76 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.76 ) 5.50/5.76 (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)))))) ) 5.50/5.76 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.76 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.76 ( (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) ) 5.50/5.76 ( (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) ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2))) (let ((_let_2 (c_Lattices_Osemilattice__sup__class_Osup T_b))) (let ((_let_3 (c_Finite__Set_Ofinite T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP _let_3 V_A_2))) (not (hBOOL (hAPP _let_3 V_B_2))) (= (c_Orderings_Obot__class_Obot _let_0) _let_1) (= (hAPP (hAPP _let_2 (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_2 (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_1)))) ))))) 5.50/5.76 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.76 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.76 ( (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)) ) 5.50/5.76 ) 5.50/5.76 (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)))) ) 5.50/5.76 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.76 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.76 ( (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) ) 5.50/5.76 ( (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) ) 5.50/5.76 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.76 ) 5.50/5.76 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__sup__class_Osup T_b)) V_x_2) V_A_2))) ) 5.50/5.76 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.76 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.76 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.76 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.76 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.76 ) 5.50/5.76 (instantiation (forall ((V_l_2 $$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)) ) 5.50/5.76 ( (c_List_Olist_ONil tc_Int_Oint) ) 5.50/5.76 ) 5.50/5.76 (instantiation (forall ((V_n_2 $$unsorted)) (= (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_n_2) (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Nat_OSuc V_n_2))) ) 5.50/5.76 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.76 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.50/5.76 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.50/5.76 ) 5.50/5.76 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero T_b)) V_a_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) V_a_2)))) )) 5.50/5.77 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.77 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_u_2 $$unsorted)) (= V_u_2 (hAPP (c_Finite__Set_Ocard tc_Nat_Onat) (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) V_u_2))) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (tc_fun T_d tc_HOL_Obool))) (let ((_let_2 (tc_fun T_d (tc_fun T_b tc_HOL_Obool)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_d $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_c _let_2 _let_0) (hAPP (hAPP (c_COMBB _let_1 (tc_fun _let_2 _let_0) T_c) _let_0) V_B_2)) V_C_2)) (hAPP (hAPP _let_0 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_1) V_A_2) V_B_2)) V_C_2))) )))) 5.50/5.77 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (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, tc_Nat_Onat ) 5.50/5.77 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (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, tc_Nat_Onat ) 5.50/5.77 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (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, tc_Nat_Onat ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Ocomm__ring__1 T_a)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_x) V_y) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_x) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_y)))) ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (c_COMBI T_b))) (forall ((V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) (hAPP (c_List_Oset T_b) V_xs_2))) (= (c_List_Olinorder__class_Oinsort__insert__key T_b T_b _let_0 V_x_2 V_xs_2) (hAPP (hAPP (c_List_Olinorder__class_Oinsort__key T_b T_b _let_0) V_x_2) V_xs_2))) )) 5.50/5.77 ( c_Com_Obodies, skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (hAPP (hAPP _let_0 V_n) V_m) (hAPP (hAPP _let_0 V_m) V_n)) )) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless T_a) V_x))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP _let_0 V_y))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_z))) (hBOOL (hAPP _let_0 V_z))) )) 5.50/5.77 ( c_Int_OPls, c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.77 ( c_Int_OMin, c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_k_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) (hAPP c_Nat_OSuc V_k_2)) (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_k_2)) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.77 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.50/5.77 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_h_2 $$unsorted) (V_g_2 $$unsorted) (T_e $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_d $$unsorted)) (= (hAPP (c_Fun_Ocomp T_e T_c T_b (hAPP (c_Fun_Ocomp T_d T_c T_e V_f_2) V_g_2)) V_h_2) (hAPP (c_Fun_Ocomp T_d T_c T_b V_f_2) (hAPP (c_Fun_Ocomp T_e T_d T_b V_g_2) V_h_2))) ) 5.50/5.77 ( skv_2, skv_3, skv_4, skv_5, skv_6, skv_7, skv_8 ) 5.50/5.77 ) 5.50/5.77 (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))) ) 5.50/5.77 ( 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)) ) 5.50/5.77 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.77 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_n $$unsorted)) (= (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_n)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) V_n)) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.77 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (forall ((V_Pa_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_Hilbert__Choice_OEps _let_0 (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c tc_HOL_Obool) V_Pa_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_Pa_2) (c_Product__Type_Ofst T_b T_c))) (c_Product__Type_Osnd T_b T_c)))) )) 5.50/5.77 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.77 ( (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 ) 5.50/5.77 ( (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 ) 5.50/5.77 ( (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT), tc_Com_Ocom, tc_Com_Opname ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_List_Oset T_b) (c_List_Olist_ONil T_b))) ) 5.50/5.77 ( tc_Com_Ocom ) 5.50/5.77 ( tc_Nat_Onat ) 5.50/5.77 ( tc_HOL_Obool ) 5.50/5.77 ( tc_Int_Oint ) 5.50/5.77 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.77 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.77 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.50/5.77 ( tc_Product__Type_Ounit ) 5.50/5.77 ( (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hBOOL (hAPP (hAPP (c_member T_b) (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) V_A_2))) ) 5.50/5.77 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.77 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.50/5.77 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (c_Fun_Oid (tc_prod T_b T_c)) (c_Product__Type_Oapfst T_b T_b T_c (c_Fun_Oid T_b))) ) 5.50/5.77 ( tc_Com_Ocom, tc_Com_Opname ) 5.50/5.77 ( tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.77 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.77 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_w_2) V_z_2)) (not (forall ((B_n $$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)))) ))) ) 5.50/5.77 ( c_Int_OPls, c_Int_OMin ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.77 ( (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) ) 5.50/5.77 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.77 ( c_Int_OMin, c_Int_OMin ) 5.50/5.77 ( (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) ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)) (hBOOL (hAPP (hAPP _let_0 (c_Groups_Osgn__class_Osgn T_b V_a_2)) _let_1)))) ))) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (c_Int_Oiszero T_a (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OPls))) ) 5.50/5.77 ( tc_Nat_Onat ) 5.50/5.77 ( tc_Int_Oint ) 5.50/5.77 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Smallcheck_Osmall T_2)) (not (class_Smallcheck_Osmall T_1)) (class_Smallcheck_Osmall (tc_prod T_2 T_1))) ) 5.50/5.77 ( tc_Com_Ocom, tc_Com_Opname ) 5.50/5.77 ( tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.77 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.77 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oab__group__add T_b)) (= (= (c_Groups_Ozero__class_Ozero T_b) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_ba_2)) (= V_ba_2 V_a_2))) ) 5.50/5.77 ( (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 ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Orderings_Otop__class_Otop T_b) (c_Complete__Lattice_OInf__class_OInf T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 5.50/5.77 ( tc_Com_Ocom ) 5.50/5.77 ( tc_Nat_Onat ) 5.50/5.77 ( tc_HOL_Obool ) 5.50/5.77 ( tc_Int_Oint ) 5.50/5.77 ( (tc_fun tc_HOL_Obool tc_HOL_Obool) ) 5.50/5.77 ( (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 5.50/5.77 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.77 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.77 ( (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.50/5.77 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.77 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.50/5.77 ( tc_Product__Type_Ounit ) 5.50/5.77 ( (tc_fun tc_Product__Type_Ounit tc_HOL_Obool) ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_b))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_b)) (= (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 T_b) (hAPP _let_0 V_m_2)) (hAPP _let_0 V_n_2))))) )) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)))) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.77 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.77 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.77 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2)) (= V_A_2 (hAPP (c_Set_Oimage T_c T_b (c_Fun_Othe__inv__into T_b T_c V_A_2 V_f_2)) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) ) 5.50/5.77 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.77 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 5.50/5.77 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 5.50/5.77 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (let ((_let_1 (c_Set_Oimage _let_0 T_b (c_Product__Type_Ofst T_b T_c)))) (let ((_let_2 (c_List_Oset _let_0))) (forall ((V_ys_2 $$unsorted) (V_xs_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (= (c_Map_Omap__of T_b T_c V_ys_2) (c_Map_Omap__of T_b T_c V_xs_2))) (= (hAPP _let_1 (hAPP _let_2 V_ys_2)) (hAPP _let_1 (hAPP _let_2 V_xs_2)))) )))) 5.50/5.77 ( c_Com_Obodies, c_Com_Obodies, tc_Com_Ocom, tc_Com_Opname ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone tc_Nat_Onat))) (forall ((V_v $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_v) 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) V_v)))) )) 5.50/5.77 ( c_Int_OPls ) 5.50/5.77 ( (c_Int_OBit1 c_Int_OPls) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.77 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.50/5.77 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.50/5.77 ( c_Int_OMin ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (forall ((V_v $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_v) c_Int_OPls)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 V_v)) (hAPP _let_0 (c_Int_Osucc V_v)))) )) 5.50/5.77 ( c_Int_OPls ) 5.50/5.77 ( (c_Int_OBit1 c_Int_OPls) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.77 ( c_Int_OMin ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_k_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (hAPP _let_0 V_m_2) (hAPP _let_0 V_n_2)) (= V_n_2 V_m_2)) )) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (c_Relation_ORange T_c T_b))) (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert T_b) V_ba_2) (hAPP _let_0 V_r_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert (tc_prod T_c T_b)) (hAPP (hAPP (c_Product__Type_OPair T_c T_b) V_a_2) V_ba_2)) V_r_2))) )) 5.50/5.77 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.77 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.77 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite (tc_prod T_b T_b)) V_r_2))) (= (c_Wellfounded_Oacyclic T_b V_r_2) (c_Wellfounded_Owf T_b V_r_2))) ) 5.50/5.77 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.77 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.50/5.77 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 5.50/5.77 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (c_Groups_Oabs__class_Oabs T_a))) (let ((_let_1 (c_Groups_Ominus__class_Ominus T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (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)))) ))) 5.50/5.77 ( (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 ) 5.50/5.77 ( (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 ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_i_2 $$unsorted) (V_Pa_2 $$unsorted)) (= (hBOOL (hAPP V_Pa_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_Pa_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_Pa_2 (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))))) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Nat_OSuc ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Code__Numeral_Oof__nat ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Set_Oinsert tc_Nat_Onat) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 5.50/5.77 ( (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)) ) 5.50/5.77 ( (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)) ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat_OSuc ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Code__Numeral_Oof__nat ) 5.50/5.77 ( (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)) ) 5.50/5.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Nat_OSuc ) 5.50/5.77 ( (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) ) 5.50/5.77 ( (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) ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_w_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) V_w_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_w_2)) (c_Nat_Osemiring__1__class_ONats T_b)))) ) 5.50/5.77 ( c_Int_OPls, tc_Nat_Onat ) 5.50/5.77 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.77 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.50/5.77 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.50/5.77 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.50/5.77 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.50/5.77 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.50/5.77 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.50/5.77 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.50/5.77 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.50/5.77 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (c_Orderings_Oord__class_Oless T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Fields_Olinordered__field__inverse__zero T_a)) (not (forall ((B_z $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_1 (c_Groups_Ozero__class_Ozero T_a)) B_z))) (not (hBOOL (hAPP (hAPP _let_1 B_z) (c_Groups_Oone__class_Oone T_a)))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) B_z) V_x)) V_y))) )) (hBOOL (hAPP (hAPP _let_0 V_x) V_y))) ))) 5.50/5.77 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.77 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.77 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.77 ) 5.50/5.77 (instantiation (let ((_let_0 (hAPP (c_member T_b) V_x_2))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_x_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (hBOOL (hAPP _let_0 V_A_2)) (hBOOL (hAPP _let_0 V_B_2)) (= (= (hAPP _let_1 V_A_2) (hAPP _let_1 V_B_2)) (= V_B_2 V_A_2))) ))) 5.50/5.77 ( (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_c)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b T_c) V_A_2) V_f_2) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_c (hAPP (hAPP (c_COMBB T_c (tc_fun T_c T_c) T_b) (c_Lattices_Osemilattice__inf__class_Oinf T_c)) V_f_2)) (c_Orderings_Otop__class_Otop T_c)) V_A_2))) ) 5.50/5.77 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_A_2) V_A_2)) ) 5.50/5.77 ( c_FunDef_Opair__less, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.50/5.77 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.77 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z))) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (hAPP c_Int_Onat V_z)) (hAPP (c_Int_Oring__1__class_Oof__int T_a) V_z))) ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 5.50/5.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.50/5.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.50/5.77 ) 5.50/5.77 (instantiation (forall ((V_xs_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ocomm__monoid__add T_b)) (not (hBOOL (hAPP (c_List_Odistinct T_b) V_xs_2))) (= (hAPP (c_List_Omonoid__add__class_Olistsum T_b) V_xs_2) (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__add__class_Osetsum T_b T_b) (c_COMBI T_b)) (hAPP (c_List_Oset T_b) V_xs_2)))) ) 5.50/5.78 ( c_Com_Obodies, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_c))) (forall ((V_B_2 $$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 _let_0 (hAPP V_B_2 B_x)))) ) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tc_fun T_c tc_HOL_Obool)) V_A_2) V_B_2))))) )) 5.50/5.78 ( (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 ) 5.50/5.78 ( (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 ) 5.50/5.78 ( (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 ) 5.50/5.78 ) 5.50/5.78 (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))) ) 5.50/5.78 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.78 ( (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 ) 5.50/5.78 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 5.50/5.78 ( (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 ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (hAPP _let_0 V_m)) (hAPP _let_0 V_n)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m) V_n))) )) 5.50/5.78 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.50/5.78 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((V_a_2 $$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_OInf__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__inf__class_Oinf T_b)) V_a_2) V_A_2))) ) 5.50/5.78 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.78 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.78 ( (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) ) 5.50/5.78 ( (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) ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Oone__class_Oone T_a))) ) 5.50/5.78 ( tc_Nat_Onat ) 5.50/5.78 ( tc_Int_Oint ) 5.50/5.78 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Int_Oring__1__class_OInts T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (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_ba_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_ba_2)) _let_1))) ))) 5.50/5.78 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_a_2) V_A_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)))) )) 5.50/5.78 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.78 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.78 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.78 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((V_x_2 $$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)))) ) 5.50/5.78 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.78 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.78 ( (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) ) 5.50/5.78 ( (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) ) 5.50/5.78 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (c_Lattices_Osemilattice__inf__class_Oinf T_b))) (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 $$unsorted)) (= (hAPP (hAPP _let_0 (hAPP V_h_2 B_x)) (hAPP V_h_2 B_y)) (hAPP V_h_2 (hAPP (hAPP _let_0 B_x) B_y))) )) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (= V_N_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP V_h_2 (c_Big__Operators_Olattice__class_OInf__fin T_b V_N_2)) (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (c_Set_Oimage T_b T_b V_h_2) V_N_2)))) )) 5.50/5.78 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((V_t $$unsorted) (V_n $$unsorted) (V_s $$unsorted) (V_c $$unsorted)) (or (not (c_Natural_Oevaln V_c V_s V_n V_t)) (hBOOL (hAPP (hAPP (c_Natural_Oevalc V_c) V_s) V_t))) ) 5.50/5.78 ( v_s2, v_na, v_s1, (c_Com_Ocom_OWhile v_ba v_ca) ) 5.50/5.78 ( v_s1, v_na, v_s0, v_ca ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Obounded__lattice T_1)) (class_Lattices_Obounded__lattice (tc_fun T_2 T_1))) ) 5.50/5.78 ( tc_Com_Ocom, tc_HOL_Obool ) 5.50/5.78 ( tc_Nat_Onat, tc_HOL_Obool ) 5.50/5.78 ( tc_HOL_Obool, tc_HOL_Obool ) 5.50/5.78 ( tc_Int_Oint, tc_HOL_Obool ) 5.50/5.78 ( tc_Int_Oint, tc_Int_Oint ) 5.50/5.78 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.50/5.78 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.50/5.78 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.50/5.78 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.50/5.78 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((V_u_2 $$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 (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)) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_u_2))) ) 5.50/5.78 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.78 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.78 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.78 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.78 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.78 ) 5.50/5.78 (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))) ) 5.50/5.78 ( tc_Com_Ocom, tc_HOL_Obool ) 5.50/5.78 ( tc_Nat_Onat, tc_HOL_Obool ) 5.50/5.78 ( tc_HOL_Obool, tc_HOL_Obool ) 5.50/5.78 ( tc_Int_Oint, tc_HOL_Obool ) 5.50/5.78 ( tc_Int_Oint, tc_Int_Oint ) 5.50/5.78 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.50/5.78 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.50/5.78 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.50/5.78 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.50/5.78 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (hAPP (c_Set_Oimage T_b T_b V_f_2) V_A_2))) (forall ((V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) _let_0) V_A_2))) (not (c_Fun_Oinj__on T_b T_b V_f_2 V_A_2)) (= V_A_2 _let_0)) )) 5.50/5.78 ( c_Nat_OSuc, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((V_a_2 $$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))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP (c_Finite__Set_Ofold1 T_b (c_Orderings_Oord__class_Omin T_b)) V_A_2)) V_a_2))) ) 5.50/5.78 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_Opred (c_Int_OBit0 V_k)) (c_Int_OBit1 (c_Int_Opred V_k))) ) 5.50/5.78 ( c_Int_OPls ) 5.50/5.78 ( (c_Int_OBit1 c_Int_OPls) ) 5.50/5.78 ( c_Int_OMin ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Fields_Ofield__inverse__zero T_a)) (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x) (hAPP (hAPP (c_Rings_Oinverse__class_Odivide T_a) V_x) (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OMin)))) ) 5.50/5.78 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.78 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.78 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ocancel__ab__semigroup__add T_a)) (not (= (hAPP _let_0 V_c) (hAPP _let_0 V_b))) (= V_c V_b)) )) 5.50/5.78 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((T_b $$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))) ) 5.50/5.78 ( tc_Nat_Onat ) 5.50/5.78 ( tc_Int_Oint ) 5.50/5.78 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (c_Groups_Ominus__class_Ominus T_b))) (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oab__group__add T_b)) (not (= (hAPP (hAPP _let_0 V_a_2) V_ba_2) (hAPP (hAPP _let_0 V_ca_2) V_d_2))) (= (= V_d_2 V_ca_2) (= V_ba_2 V_a_2))) )) 5.50/5.78 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Finite__Set_Ofinite T_1)) (not (class_Finite__Set_Ofinite T_2)) (class_Finite__Set_Ofinite (tc_prod T_2 T_1))) ) 5.50/5.78 ( tc_Com_Ocom, tc_Com_Opname ) 5.50/5.78 ( tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.78 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.78 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (forall ((V_z $$unsorted)) (= V_z (hAPP _let_0 (hAPP _let_0 V_z))) )) 5.50/5.78 ( c_Int_OPls ) 5.50/5.78 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_0))))) (let ((_let_2 (= (c_Orderings_Obot__class_Obot _let_0) _let_1))) (let ((_let_3 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_4 (c_Big__Operators_Olattice_OInf__fin T_b _let_3 V_A_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (and (or (not _let_2) (= V_x_2 _let_4)) (or _let_2 (= _let_4 (hAPP (hAPP _let_3 V_x_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_3 _let_1)))))) )))))) 5.50/5.78 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((V_y_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (c_Groups_Oone__class_Oone T_b)) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_OBit1 c_Int_OPls)) V_y_2)))) ) 5.50/5.78 ( c_Int_OPls, tc_Nat_Onat ) 5.50/5.78 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.78 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.50/5.78 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.50/5.78 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.50/5.78 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.50/5.78 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.50/5.78 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.50/5.78 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.50/5.78 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.50/5.78 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (= _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2)) (and (= V_A_2 _let_0) (= V_B_2 _let_0))) )) 5.50/5.78 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.78 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.78 ( (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)) ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone T_a))) (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) _let_0) _let_0))) )) 5.50/5.78 ( tc_Nat_Onat ) 5.50/5.78 ( tc_Int_Oint ) 5.50/5.78 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((V_A_2 $$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)) ) 5.50/5.78 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) V_a_2)) (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero T_b)) V_a_2)))) )) 5.50/5.78 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.78 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.78 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.78 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.50/5.78 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.78 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (forall ((V_X_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite (tc_prod tc_Nat_Onat tc_Nat_Onat)) V_X_2))) (hBOOL (hAPP (hAPP (c_member (tc_prod _let_0 _let_0)) (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Orderings_Obot__class_Obot _let_0)) V_X_2)) c_FunDef_Omax__weak))) )) 5.50/5.78 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= V_a_2 (c_Complete__Lattice_OSup__class_OSup T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 5.50/5.78 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.78 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.78 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.78 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (T_d $$unsorted) (T_c $$unsorted)) (= (c_Product__Type_Oapsnd T_c T_d T_b V_f_2) (c_Product__Type_Omap__pair T_b T_b T_c T_d (c_Fun_Oid T_b) V_f_2)) ) 5.50/5.78 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint, tc_Int_Oint, tc_Int_Oint ) 5.50/5.78 ) 5.50/5.78 (instantiation (forall ((V_x_2 $$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))) (= (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)))) ) 5.50/5.78 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.78 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.78 ( (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) ) 5.50/5.78 ( (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) ) 5.50/5.78 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (forall ((V_m $$unsorted)) (= (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) V_m) (c_Divides_Odivmod__nat V_m _let_0)) )) 5.50/5.78 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (class_Int_Oring__char__0 T_b)) (= (= (hAPP _let_0 V_x_2) (hAPP _let_0 V_y_2)) (= V_y_2 V_x_2))) )) 5.50/5.78 ( c_Int_OPls, (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.50/5.78 ( c_Int_OPls, (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.50/5.78 ( c_Int_OPls, (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.50/5.78 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.50/5.78 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.50/5.78 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.50/5.78 ( (c_Int_OBit1 c_Int_OPls), c_Int_OMin, tc_Int_Oint ) 5.50/5.78 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Nat_Onat ) 5.50/5.78 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 5.50/5.78 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.50/5.78 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.50/5.78 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.50/5.78 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.50/5.78 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.50/5.78 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.50/5.78 ( c_Int_OMin, (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.50/5.78 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.78 ) 5.50/5.78 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (forall ((V_Pa_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_HOL_OThe _let_0 (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c tc_HOL_Obool) V_Pa_2)) (c_HOL_OThe _let_0 (hAPP (hAPP (c_COMBS _let_0 T_c tc_HOL_Obool) (hAPP (hAPP (c_COMBB T_b (tc_fun T_c tc_HOL_Obool) _let_0) V_Pa_2) (c_Product__Type_Ofst T_b T_c))) (c_Product__Type_Osnd T_b T_c)))) )) 5.50/5.78 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.78 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.78 ( (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint _let_0))) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hAPP (hAPP (c_COMBC tc_Int_Oint tc_Int_Oint _let_0) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool)) (hAPP (hAPP (c_COMBB (tc_fun tc_Int_Oint tc_Int_Oint) _let_1 tc_Int_Oint) (hAPP (c_COMBB tc_Int_Oint _let_0 tc_Int_Oint) c_fequal)) c_Nitpick_Oint__gcd))) (c_Groups_Oone__class_Oone tc_Int_Oint))))), tc_Int_Oint, tc_Int_Oint ) 5.50/5.79 ( (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT), tc_Com_Ocom, tc_Com_Opname ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (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)))) )) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (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)))) ))) 5.50/5.79 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus T_a))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Ocomm__semiring__1 T_a)) (= (hAPP (hAPP _let_0 V_a) V_c) (hAPP (hAPP _let_0 V_c) V_a))) )) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Oab__semigroup__idem__mult 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) (hAPP (c_Finite__Set_Ofold1 T_b _let_0) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)))) )) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.79 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.79 ( (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) ) 5.50/5.79 ( (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) ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Otop__class_Otop _let_0))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_c) B_x) V_A_2))) (= _let_1 (hAPP V_B_2 B_x))) ) (= _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) V_B_2))) ))) 5.50/5.79 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (c_Finite__Set_Ofold1 T_b (c_Lattices_Osemilattice__sup__class_Osup T_b)) V_A_2) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2))) ) 5.50/5.79 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.79 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.50/5.79 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_x_2))) (not (hBOOL (hAPP _let_0 V_y_2))) (= (= (hAPP c_Int_Onat V_y_2) (hAPP c_Int_Onat V_x_2)) (= V_y_2 V_x_2))) )) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.50/5.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.50/5.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.50/5.79 ( c_Int_OMin, c_Int_OMin ) 5.50/5.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.50/5.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olinorder__class_OMin T_b V_A_2) (hAPP (c_Finite__Set_Ofold1 T_b (c_Orderings_Oord__class_Omin T_b)) V_A_2))) ) 5.50/5.79 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.79 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.50/5.79 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((T_b $$unsorted) (T_c $$unsorted)) (= (c_Product__Type_Oapsnd T_c T_c T_b (c_Fun_Oid T_c)) (c_Fun_Oid (tc_prod T_b T_c))) ) 5.50/5.79 ( tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.79 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.79 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.79 ( tc_Com_Opname, tc_Com_Ocom ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_x $$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)))) ) 5.50/5.79 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( (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 ) 5.50/5.79 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.79 ( (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 ) 5.50/5.79 ) 5.50/5.79 (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) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x)) V_x))) ) 5.50/5.79 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( c_Int_OMin, tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)))) (forall ((T_b $$unsorted)) (= _let_0 (c_Transitive__Closure_Otrancl T_b _let_0)) )) 5.50/5.79 ( tc_Nat_Onat ) 5.50/5.79 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.79 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Groups_Ocomm__monoid__add T_c)) (not (c_Fun_Oinj__on T_b T_c V_f_2 V_B_2)) (= (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__add__class_Osetsum T_c T_c) (c_Fun_Oid T_c)) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_B_2)) (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__add__class_Osetsum T_b T_c) V_f_2) V_B_2))) ) 5.50/5.79 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.50/5.79 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 5.50/5.79 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 5.50/5.79 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (= V_x_2 (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.79 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.79 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.79 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (c_Orderings_Oord__class_Omax T_b) (c_Orderings_Oord_Omax T_b (c_Orderings_Oord__class_Oless__eq T_b)))) ) 5.50/5.79 ( tc_Nat_Onat ) 5.50/5.79 ( tc_HOL_Obool ) 5.50/5.79 ( tc_Int_Oint ) 5.50/5.79 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.79 ) 5.50/5.79 (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))) ) 5.50/5.79 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.79 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.50/5.79 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Groups_Osgn__class_Osgn T_a V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (= _let_0 (c_Groups_Osgn__class_Osgn T_a _let_0))) )) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless T_a) V_z))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_y) V_x))) (not (hBOOL (hAPP _let_0 V_y))) (hBOOL (hAPP _let_0 V_x))) )) 5.50/5.79 ( (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 ) 5.50/5.79 ( c_Int_OMin, c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_ba_2)) (c_Groups_Ozero__class_Ozero T_b))) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_ba_2)))) )) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_ba_2 $$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_ba_2)))) (hBOOL (hAPP (hAPP (c_Product__Type_Ocurry T_b T_c tc_HOL_Obool V_f_2) V_a_2) V_ba_2))) ) 5.50/5.79 ( (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)) ) 5.50/5.79 ( (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)) ) 5.50/5.79 ( (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_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_0 _let_0))) ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((B_Z $$unsorted)) (or (not (v_P B_Z v_s1)) (and (not (hBOOL (hAPP v_b v_s2))) (v_P B_Z v_s2))) ) 5.50/5.79 ( skv_1 ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_member T_b))) (forall ((V_x_2 $$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))) (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 B_y) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) B_y))) )) (not (hBOOL (hAPP (hAPP _let_0 V_x_2) V_A_2))) (= V_x_2 (c_Big__Operators_Olinorder__class_OMin T_b V_A_2))) )) 5.50/5.79 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (let ((_let_1 (c_Groups_Oone__class_Oone T_a))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) _let_1) _let_1)) (hAPP _let_0 V_w)) (hAPP _let_0 (c_Int_OBit0 V_w)))) ))) 5.50/5.79 ( c_Int_OPls, tc_Nat_Onat ) 5.50/5.79 ( c_Int_OPls, tc_Int_Oint ) 5.50/5.79 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.50/5.79 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.50/5.79 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (= (and (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) V_ba_2)) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_ba_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_b) V_a_2)) V_ba_2)))) )) 5.50/5.79 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.50/5.79 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.50/5.79 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_x))) (not (hBOOL (hAPP _let_0 V_y))) (= (hAPP c_Int_Onat (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_x) V_y)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP c_Int_Onat V_x)) (hAPP c_Int_Onat V_y)))) )) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_s2 $$unsorted) (V_c1 $$unsorted) (V_s1 $$unsorted) (V_n $$unsorted) (V_s0 $$unsorted) (V_c0 $$unsorted)) (or (not (c_Natural_Oevaln V_c0 V_s0 V_n V_s1)) (not (c_Natural_Oevaln V_c1 V_s1 V_n V_s2)) (c_Natural_Oevaln (c_Com_Ocom_OSemi V_c0 V_c1) V_s0 V_n V_s2)) ) 5.50/5.79 ( v_s2, (c_Com_Ocom_OWhile v_ba v_ca), v_s1, v_na, v_s0, v_ca ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_n $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (= (hAPP (c_Int_Oring__1__class_Oof__int T_a) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) V_n))) ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.50/5.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.50/5.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (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)))) ))) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) (= V_y (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y))) ) 5.50/5.79 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Osemilattice__sup (tc_fun T_2 T_1))) ) 5.50/5.79 ( tc_Com_Ocom, tc_HOL_Obool ) 5.50/5.79 ( tc_Nat_Onat, tc_HOL_Obool ) 5.50/5.79 ( tc_HOL_Obool, tc_HOL_Obool ) 5.50/5.79 ( tc_Int_Oint, tc_HOL_Obool ) 5.50/5.79 ( tc_Int_Oint, tc_Int_Oint ) 5.50/5.79 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.50/5.79 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.50/5.79 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.50/5.79 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.50/5.79 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_n_2 $$unsorted)) (= (hAPP (c_List_Oset tc_Nat_Onat) (c_List_Oupt (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_n_2)) (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) V_n_2)) ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_k) (c_Groups_Oone__class_Oone tc_Int_Oint)) (c_Int_Osucc V_k)) ) 5.50/5.79 ( c_Int_OPls ) 5.50/5.79 ( c_Int_OMin ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (= V_x_2 (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.79 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.79 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.79 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone T_a))) (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (= _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) _let_0))) )) 5.50/5.79 ( tc_Nat_Onat ) 5.50/5.79 ( tc_Int_Oint ) 5.50/5.79 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (forall ((V_X_2 $$unsorted)) (or (= _let_1 V_X_2) (hBOOL (hAPP (hAPP (c_member (tc_prod _let_0 _let_0)) (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) V_X_2) _let_1)) c_FunDef_Omin__strict))) ))) 5.50/5.79 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_x_2 $$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)) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Orderings_Oord__class_Omin 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)))) ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.50/5.79 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.79 ( (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) ) 5.50/5.79 ( (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) ) 5.50/5.79 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_i_2) V_k_2)) (hBOOL (hAPP (hAPP (c_member T_b) V_i_2) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_k_2))))) ) 5.50/5.79 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.79 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.79 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Relation_ODomain T_b T_b))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (hAPP _let_0 (c_Transitive__Closure_Otrancl T_b V_r_2)) (hAPP _let_0 V_r_2)) )) 5.50/5.79 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP _let_0 (c_Map_Odom T_b T_c V_f_2)))) (hBOOL (hAPP _let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (not (forall ((B_x $$unsorted)) (not (= (hAPP V_f_2 B_x) (c_Option_Ooption_ONone T_c))) ))) )) 5.50/5.79 ( c_Com_Obody, tc_Com_Ocom, tc_Com_Opname ) 5.50/5.79 ) 5.50/5.79 (instantiation (let ((_let_0 (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= _let_0 (hAPP (hAPP (c_Set_Oinsert T_c) (hAPP V_f_2 V_x_2)) _let_0))) )) 5.50/5.79 ( 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 ) 5.50/5.79 ) 5.50/5.79 (instantiation (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (= V_ba_2 V_a_2) (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_ba_2)) (c_Relation_OId T_b)))) ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.79 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.50/5.79 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.80 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.50/5.80 ) 5.50/5.80 (instantiation (forall ((T_b $$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))) ) 5.50/5.80 ( tc_Nat_Onat ) 5.50/5.80 ( tc_Int_Oint ) 5.50/5.80 ( tc_Code__Numeral_Ocode__numeral ) 5.50/5.80 ) 5.50/5.80 (instantiation (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (forall ((V_Y_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite (tc_prod tc_Nat_Onat tc_Nat_Onat)) V_Y_2))) (= _let_1 V_Y_2) (hBOOL (hAPP (hAPP (c_member (tc_prod _let_0 _let_0)) (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) _let_1) V_Y_2)) c_FunDef_Omax__strict))) ))) 5.50/5.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 5.50/5.80 ) 5.50/5.80 (instantiation (forall ((V_u_2 $$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 (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)) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_l_2))) ) 5.50/5.80 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.50/5.80 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.80 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.50/5.80 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.50/5.80 ) 5.50/5.80 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Ozero__class_Ozero T_a)) V_a))) (not (hBOOL (hAPP _let_0 V_b))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)))) )) 5.50/5.80 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.50/5.80 ) 5.50/5.80 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_r_2)) (c_Wellfounded_Owf (tc_fun T_b tc_HOL_Obool) (c_Wellfounded_Omin__ext T_b V_r_2))) ) 5.50/5.80 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.80 ( c_FunDef_Opair__leq, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.80 ) 5.50/5.80 (instantiation (let ((_let_0 (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted)) (= (= (hAPP _let_0 V_B_2) (hAPP _let_0 V_A_2)) (= V_B_2 V_A_2)) )) 5.50/5.80 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 5.50/5.80 ) 5.50/5.80 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Finite__Set_Ofinite T_2)) (not (class_Finite__Set_Ofinite T_1)) (class_Finite__Set_Ofinite (tc_fun T_2 T_1))) ) 5.50/5.80 ( tc_HOL_Obool, tc_Com_Ocom ) 5.50/5.80 ( tc_HOL_Obool, tc_Nat_Onat ) 5.50/5.80 ( tc_HOL_Obool, tc_HOL_Obool ) 5.50/5.80 ( tc_HOL_Obool, tc_Int_Oint ) 5.50/5.80 ( tc_HOL_Obool, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.80 ( tc_HOL_Obool, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.50/5.80 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.50/5.80 ( tc_HOL_Obool, tc_Product__Type_Ounit ) 5.50/5.80 ( tc_Int_Oint, tc_Int_Oint ) 5.50/5.80 ( (tc_fun tc_Int_Oint tc_HOL_Obool), tc_Int_Oint ) 5.50/5.80 ) 5.50/5.80 (instantiation (forall ((V_x_2 $$unsorted) (V_Pa_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_Pa_2 (hAPP c_Int_OAbs__Integ B_y)))) )) (hBOOL (hAPP V_Pa_2 V_x_2))) ) 5.50/5.80 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 5.50/5.80 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 5.50/5.80 ( c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 5.50/5.80 ( c_Int_OPls, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 5.50/5.80 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 5.50/5.80 ( c_Int_OPls, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 5.50/5.80 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 5.50/5.80 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 5.50/5.80 ( (c_Int_OBit1 c_Int_OPls), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert tc_Nat_Onat) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( 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)) ) 5.50/5.80 ( c_fequal, (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 5.50/5.80 ( c_fequal, (c_COMBB tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool) tc_Int_Oint) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Nat__Numeral_Oneg ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_Onat ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 5.50/5.80 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat__Numeral_Oneg ) 5.50/5.80 ( (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))))) ) 5.50/5.80 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 5.50/5.80 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 5.50/5.80 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Nat_OSuc ) 5.50/5.80 ( (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) ) 5.50/5.80 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 5.50/5.80 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 5.50/5.80 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 5.50/5.80 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), c_Code__Numeral_Oof__nat ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 5.50/5.80 ( c_Int_Onat, (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint c_Code__Numeral_Oof__nat) ) 5.50/5.80 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 5.50/5.80 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 5.50/5.80 ( (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) ) 5.50/5.80 ( c_fconj, (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) ) 5.50/5.80 ( c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 5.50/5.80 ( c_fTrue, (c_COMBK tc_HOL_Obool tc_Nat_Onat) ) 5.50/5.80 ( (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))) ) 5.50/5.80 ( (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) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Nat_Onat) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( c_Int_OMin, (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 5.50/5.80 ( c_Int_OMin, (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 5.50/5.80 ( c_Int_OMin, (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 5.50/5.80 ( c_Int_OMin, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 5.50/5.80 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OMin) ) 5.50/5.80 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) ) 5.50/5.80 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OMin) ) 5.50/5.80 ( c_Int_OMin, (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) c_Int_OPls) ) 5.50/5.80 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc ) 5.50/5.80 ( (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) ) 5.50/5.80 ( c_Com_OWT, (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_Onat ) 5.50/5.80 ( (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) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Oint__of ) 5.50/5.80 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (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))) ) 5.50/5.80 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) c_Int_OMin), c_Nat__Numeral_Oneg ) 5.50/5.80 ( 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))) ) 5.50/5.80 ( c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)) ) 5.50/5.80 ( c_Com_Ocom_OSKIP, (c_Nat_Osize__class_Osize tc_Com_Ocom) ) 5.50/5.80 ( c_Com_Ocom_OSKIP, c_Com_OWT ) 5.50/5.80 ( 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)) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool), (let ((_let_0 (tc_fun tc_Int_Oint (tc_fun tc_Int_Oint tc_HOL_Obool)))) (c_COMBB _let_0 _let_0 tc_Int_Oint)) ) 5.50/5.80 ( v_s0, v_ba ) 5.50/5.80 ( (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))) ) 5.50/5.80 ( 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)))) ) 5.50/5.80 ( v_s2, v_b ) 5.50/5.80 ( (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))) ) 5.50/5.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)) ) 5.50/5.80 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Orderings_Obot__class_Obot _let_0))) ) 5.50/5.80 ( (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))) ) 5.50/5.80 ( (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))) ) 5.50/5.80 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_0 _let_0))) ) 5.50/5.80 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (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_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))) (hAPP (hAPP (c_Product__Type_OPair (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_0) _let_0))) ) 5.50/5.80 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 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)))) ) 5.50/5.80 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 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)))) ) 5.50/5.80 ( c_FunDef_Omax__weak, (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_0 _let_0) c_FunDef_Omax__strict)) ) 5.50/5.80 ( (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))) ) 5.50/5.80 ( c_FunDef_Omin__weak, (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (hAPP (c_Product__Type_OPair _let_0 _let_0) c_FunDef_Omin__strict)) ) 5.50/5.80 ( v_s1, v_b ) 5.50/5.80 ( 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))) ) 5.50/5.80 ( (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))) ) 5.50/5.80 ( c_FunDef_Omax__strict, (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( c_fFalse, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 5.50/5.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), (c_Finite__Set_Ocard tc_HOL_Obool) ) 5.50/5.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Finite__Set_Ocard tc_Product__Type_Ounit) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (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 ) 5.50/5.80 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), (c_Finite__Set_Ofinite tc_Com_Opname) ) 5.50/5.80 ( c_Com_Obodies, (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) ) 5.50/5.80 ( (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) ) 5.50/5.80 ( (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) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Int_Oint) ) 5.50/5.80 ( (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) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (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) ) 5.50/5.80 ( (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_fun tc_Int_Oint tc_HOL_Obool)))) (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (c_COMBC tc_Int_Oint tc_Int_Oint tc_HOL_Obool))) ) 5.50/5.80 ( (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)) ) 5.50/5.80 ( (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)))))) ) 5.50/5.80 ( (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) ) 5.60/5.80 ( (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT), (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool) ) 5.60/5.80 ( (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (hAPP (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)) skv_9) ) 5.60/5.80 ( (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)) ) 5.60/5.80 ( (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)) ) 5.60/5.80 ( (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)) ) 5.60/5.80 ( (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)) ) 5.60/5.80 ( (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 ) 5.60/5.80 ( skv_2, (c_Fun_Ocomp skv_4 skv_8 skv_6 skv_3) ) 5.60/5.80 ( skv_2, (c_Fun_Ocomp skv_4 skv_7 skv_6 (hAPP (c_Fun_Ocomp skv_8 skv_7 skv_4 skv_5) skv_3)) ) 5.60/5.80 ( skv_3, (c_Fun_Ocomp skv_8 skv_7 skv_4 skv_5) ) 5.60/5.80 ( (hAPP (c_Fun_Ocomp skv_4 skv_8 skv_6 skv_3) skv_2), (c_Fun_Ocomp skv_8 skv_7 skv_6 skv_5) ) 5.60/5.80 ( skv_9, (hAPP (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool) (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT)) ) 5.60/5.80 ( skv_9, (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)) ) 5.60/5.80 ( skv_10, c_Com_OWT ) 5.60/5.80 ( skv_10, (c_Option_Ooption_OSome tc_Com_Ocom) ) 5.60/5.80 ( skv_11, c_Com_Obody ) 5.60/5.80 ) 5.60/5.80 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) (= V_x (hAPP (hAPP (c_Orderings_Oord__class_Omax T_a) V_x) V_y))) ) 5.60/5.80 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.60/5.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.80 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.80 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.80 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.80 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.60/5.80 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.80 ) 5.60/5.80 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ominus__class_Ominus T_b))) (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (not (= (hAPP (hAPP _let_1 V_ca_2) V_d_2) (hAPP (hAPP _let_1 V_a_2) V_ba_2))) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) V_ba_2)) (hBOOL (hAPP (hAPP _let_0 V_ca_2) V_d_2)))) ))) 5.60/5.80 ( (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 ) 5.60/5.80 ) 5.60/5.80 (instantiation (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))) (forall ((T_b $$unsorted)) (= (hAPP (c_Set_OCollect _let_0) (hAPP (hAPP (c_COMBB _let_1 tc_HOL_Obool _let_0) (c_HOL_OEx T_b)) (hAPP (hAPP (c_COMBC _let_0 _let_2 _let_1) (hAPP (hAPP (c_COMBB (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_2 _let_1) _let_0) (c_COMBB _let_0 tc_HOL_Obool T_b)) c_fequal)) (hAPP (hAPP (c_COMBS T_b T_b _let_0) (c_Product__Type_OPair T_b T_b)) (c_COMBI T_b))))) (c_Relation_OId T_b)) )))) 5.60/5.80 ( tc_Nat_Onat ) 5.60/5.80 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.81 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.60/5.81 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_2 (hBOOL (hAPP (hAPP _let_1 V_v_2) V_v_H_2)))) (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP _let_0 V_v_2)) (hAPP _let_0 V_v_H_2))) (and _let_2 (or (not _let_2) (hBOOL (hAPP (hAPP _let_1 c_Int_OPls) V_v_H_2))))) )))) 5.60/5.81 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.81 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.81 ( c_Int_OMin, c_Int_OMin ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_n_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Oring__1 T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_b) V_n_2)) (c_Int_Oring__1__class_OInts T_b)))) ) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.60/5.81 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.60/5.81 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless T_b) (c_Groups_Ozero__class_Ozero T_b)))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP _let_0 V_a_2)) (hBOOL (hAPP _let_0 (c_Groups_Osgn__class_Osgn T_b V_a_2))))) )) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (forall ((V_x_2 $$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_member T_b) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_1))))) (hAPP _let_0 V_A_2)))) ))) 5.60/5.81 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (= V_a_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_a_2) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)))) ) 5.60/5.81 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (c_Finite__Set_Ocard T_b) V_A_2) (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__add__class_Osetsum T_b tc_Nat_Onat) (hAPP (c_COMBK tc_Nat_Onat T_b) (c_Groups_Oone__class_Oone tc_Nat_Onat))) V_A_2)) ) 5.60/5.81 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 5.60/5.81 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (= (c_Option_Oset T_b (hAPP (c_Option_Ooption_OSome T_b) V_x_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.81 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.81 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.81 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.81 ( skv_10, tc_Com_Ocom ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m))) (forall ((V_m $$unsorted)) (= _let_0 (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) _let_0)) )) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.81 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.60/5.81 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_z $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_0) V_z))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_z)))) )) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.60/5.81 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.81 ( c_Int_OMin ) 5.60/5.81 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_k) c_Int_OMin) (c_Int_Osucc V_k)) ) 5.60/5.81 ( c_Int_OPls ) 5.60/5.81 ( c_Int_OMin ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) c_Int_OMin))) (forall ((V_l $$unsorted)) (= (c_Int_OBit1 (hAPP _let_0 V_l)) (hAPP _let_0 (c_Int_OBit0 V_l))) )) 5.60/5.81 ( c_Int_OPls ) 5.60/5.81 ( (c_Int_OBit1 c_Int_OPls) ) 5.60/5.81 ( c_Int_OMin ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_y_2 $$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)))) (= (= (hAPP V_f_2 V_y_2) (hAPP V_f_2 V_x_2)) (= V_y_2 V_x_2))) ) 5.60/5.81 ( (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_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 5.60/5.81 ( (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))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) (hAPP (c_Set_Oimage T_b T_b V_f_2) V_A_2)))) (c_Fun_Oinj__on T_b T_b V_f_2 V_A_2)) ) 5.60/5.81 ( c_Nat_OSuc, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_a) V_b)))) (let ((_let_2 (c_Divides_OposDivAlg V_a V_b))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) V_b))) (and (or _let_1 (= (hAPP (c_Divides_Oadjust V_b) (c_Divides_OposDivAlg V_a (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)))) V_b))) _let_2)) (or (not _let_1) (= _let_2 (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) _let_0) V_a))))) )))) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls ) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.60/5.81 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.81 ( c_Int_OMin, c_Int_OMin ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (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)))) ))) 5.60/5.81 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.60/5.81 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (hBOOL (hAPP (hAPP (c_member T_b) V_i_2) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_k_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_i_2) V_k_2)))) ) 5.60/5.81 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.60/5.81 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (c_Orderings_Obot__class_Obot T_a) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x)) V_x))) ) 5.60/5.81 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)) V_a))) (= V_a (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a))) ) 5.60/5.81 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (c_Groups_Oone__class_Oone T_a) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit1 c_Int_OPls)))) ) 5.60/5.81 ( tc_Nat_Onat ) 5.60/5.81 ( tc_Int_Oint ) 5.60/5.81 ( tc_Code__Numeral_Ocode__numeral ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (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)))) ))) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= (hAPP c_Nat_OSuc (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_1))))) (hAPP _let_0 V_A_2))) ))) 5.60/5.81 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Rings_Odvd__class_Odvd tc_Nat_Onat))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (c_Orderings_Oorder_Omono tc_Nat_Onat T_b _let_0 V_f_2)) (not (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP V_f_2 V_x_2)) (hAPP V_f_2 V_y_2)))) )) 5.60/5.81 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, (c_Int_Onumber__class_Onumber__of tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))), c_Int_OAbs__Integ, tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oab__group__add T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) V_a) (c_Groups_Ozero__class_Ozero T_a))) ) 5.60/5.81 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_1 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_v $$unsorted)) (or (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v))) (= (hAPP c_Nat_OSuc (hAPP (hAPP _let_1 (hAPP _let_0 V_v)) V_n)) (hAPP (hAPP _let_1 (hAPP _let_0 (c_Int_Osucc V_v))) V_n))) ))) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), c_Int_OPls ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Int_OBit1 c_Int_OPls) ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_v $$unsorted)) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v)))) (= (hAPP c_Nat_OSuc (hAPP (hAPP _let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v)) V_n)) (hAPP (hAPP _let_0 (c_Groups_Oone__class_Oone tc_Nat_Onat)) V_n))) )) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Int_OBit1 c_Int_OPls) ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((T_a $$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) c_Int_OMin)) (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OMin))) ) 5.60/5.81 ( tc_Nat_Onat ) 5.60/5.81 ( tc_Int_Oint ) 5.60/5.81 ( tc_Code__Numeral_Ocode__numeral ) 5.60/5.81 ) 5.60/5.81 (instantiation (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))) (forall ((V_k_2 $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) (hAPP _let_1 V_k_2)) (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) _let_2) (c_Orderings_Obot__class_Obot _let_0))) (hAPP _let_1 _let_2)) )))) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.81 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.60/5.81 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (c_Groups_Ozero__class_Ozero T_a) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) V_a))) ) 5.60/5.81 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_w_2 $$unsorted)) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w_2)))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 V_w_2)))) ) 5.60/5.81 ( c_Int_OPls ) 5.60/5.81 ( (c_Int_OBit1 c_Int_OPls) ) 5.60/5.81 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.60/5.81 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.60/5.81 ( c_Int_OMin ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (forall ((V_w_2 $$unsorted)) (or (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w_2))) (= (hAPP _let_0 (c_Int_OBit1 V_w_2)) (hAPP (hAPP (c_HOL_OLet tc_Nat_Onat tc_Nat_Onat) (hAPP _let_0 V_w_2)) (hAPP (hAPP (c_COMBB tc_Nat_Onat tc_Nat_Onat tc_Nat_Onat) c_Nat_OSuc) (hAPP (hAPP (c_COMBS tc_Nat_Onat tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oplus__class_Oplus tc_Nat_Onat)) (c_COMBI tc_Nat_Onat)))))) )) 5.60/5.81 ( c_Int_OPls ) 5.60/5.81 ( (c_Int_OBit1 c_Int_OPls) ) 5.60/5.81 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.60/5.81 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.60/5.81 ( c_Int_OMin ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((T_b $$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))))) ) 5.60/5.81 ( tc_Nat_Onat ) 5.60/5.81 ( tc_Int_Oint ) 5.60/5.81 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.81 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((T_b $$unsorted)) (= (hAPP (c_Set_OCollect T_b) (hAPP (c_COMBK tc_HOL_Obool T_b) c_fFalse)) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) ) 5.60/5.81 ( tc_Com_Ocom ) 5.60/5.81 ( tc_Nat_Onat ) 5.60/5.81 ( tc_HOL_Obool ) 5.60/5.81 ( tc_Int_Oint ) 5.60/5.81 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.81 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.81 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.60/5.81 ( tc_Product__Type_Ounit ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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))) )) 5.60/5.81 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.81 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.81 ( (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)) ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted)) (= _let_0 (hAPP (c_List_Orotate1 T_a) _let_0)) )) 5.60/5.81 ( tc_Nat_Onat ) 5.60/5.81 ( tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (let ((_let_1 (hAPP _let_0 V_u))) (let ((_let_2 (hAPP _let_0 V_v))) (let ((_let_3 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) _let_1) _let_2)))) (let ((_let_4 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) _let_1) _let_2))) (forall ((V_v $$unsorted) (V_u $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (not (class_Int_Onumber T_b)) (and (or _let_3 (= _let_2 _let_4)) (or (not _let_3) (= _let_1 _let_4)))) )))))) 5.60/5.81 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.60/5.81 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Int_Oint ) 5.60/5.81 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 5.60/5.81 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_m $$unsorted)) (= (hAPP _let_0 (hAPP c_Nat_OSuc V_m)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) (hAPP _let_0 V_m))) )) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.81 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.60/5.81 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_y_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (not (class_Int_Onumber__ring T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) c_Int_OPls) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (c_Groups_Ozero__class_Ozero T_b)) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_y_2))))) ) 5.60/5.81 ( c_Int_OPls, tc_Nat_Onat ) 5.60/5.81 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.81 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.60/5.81 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.60/5.81 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.60/5.81 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.60/5.81 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.60/5.81 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.60/5.81 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.60/5.81 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.60/5.81 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_xs_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) (hAPP (c_List_Oset T_b) V_xs_2))) (= V_xs_2 (c_List_Oremove1 T_b V_x_2 V_xs_2))) ) 5.60/5.81 ( c_Com_Obodies, skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_a_2 $$unsorted) (V_ba_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_ba_2) V_a_2))) (= (c_SetInterval_Oord__class_OatLeastAtMost T_b V_a_2 V_ba_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 5.60/5.81 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.81 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Complete__Lattice_OInf__class_OInf T_b V_A_2)) V_x_2))) ) 5.60/5.81 ( (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) _let_0))) )) 5.60/5.81 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((T_b $$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)))) ) 5.60/5.81 ( tc_Nat_Onat ) 5.60/5.81 ( tc_Int_Oint ) 5.60/5.81 ( tc_Code__Numeral_Ocode__numeral ) 5.60/5.81 ( (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.81 ) 5.60/5.81 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (and (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_b) _let_0))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_a) V_b)))) (= (c_Divides_OposDivAlg V_a V_b) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) _let_0) V_a))) )) 5.60/5.81 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.60/5.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.81 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.81 ( c_Int_OMin, c_Int_OMin ) 5.60/5.81 ) 5.60/5.81 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_a) V_b)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_b) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (= (c_Divides_OposDivAlg V_a V_b) (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))))) ) 5.60/5.82 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( c_Int_OMin, c_Int_OMin ) 5.60/5.82 ) 5.60/5.82 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_x_2) V_A_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.60/5.82 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.82 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.82 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.82 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((V_m_2 $$unsorted) (V_w_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_w_2))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w_2) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP c_Int_Onat V_w_2)) V_m_2)))) ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Int_OMin ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Complete__Lattice_OSup__class_OSup T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))) (c_Orderings_Otop__class_Otop T_b))) ) 5.60/5.82 ( tc_Com_Ocom ) 5.60/5.82 ( tc_Nat_Onat ) 5.60/5.82 ( tc_HOL_Obool ) 5.60/5.82 ( tc_Int_Oint ) 5.60/5.82 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.82 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.82 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 5.60/5.82 ( tc_Product__Type_Ounit ) 5.60/5.82 ) 5.60/5.82 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (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))) )) 5.60/5.82 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( c_Int_OMin, c_Int_OMin ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2))) (= (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2))) (= V_y_2 V_x_2))) ) 5.60/5.82 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.60/5.82 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ) 5.60/5.82 (instantiation (let ((_let_0 (hBOOL (hAPP V_a1_2 V_a2_2)))) (let ((_let_1 (c_Com_Ocom_OWhile V_a1_2 V_a3_2))) (forall ((V_a6_2 $$unsorted) (V_a4_2 $$unsorted) (V_a2_2 $$unsorted) (V_a3_2 $$unsorted) (V_a1_2 $$unsorted)) (= (or (and _let_0 (not (forall ((B_s1 $$unsorted)) (or (not (c_Natural_Oevaln _let_1 B_s1 V_a4_2 V_a6_2)) (not (c_Natural_Oevaln V_a3_2 V_a2_2 V_a4_2 B_s1))) ))) (and (not _let_0) (= V_a6_2 V_a2_2))) (c_Natural_Oevaln _let_1 V_a2_2 V_a4_2 V_a6_2)) ))) 5.60/5.82 ( v_s2, v_na, v_s1, v_c, v_b ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((V_b $$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))) ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Groups_Ominus T_1)) (class_Groups_Ominus (tc_fun T_2 T_1))) ) 5.60/5.82 ( tc_Com_Ocom, tc_HOL_Obool ) 5.60/5.82 ( tc_Nat_Onat, tc_HOL_Obool ) 5.60/5.82 ( tc_HOL_Obool, tc_HOL_Obool ) 5.60/5.82 ( tc_Int_Oint, tc_HOL_Obool ) 5.60/5.82 ( tc_Int_Oint, tc_Int_Oint ) 5.60/5.82 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.60/5.82 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.60/5.82 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.60/5.82 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.60/5.82 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.60/5.82 ) 5.60/5.82 (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))) ) 5.60/5.82 ( (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 ) 5.60/5.82 ( (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 ) 5.60/5.82 ) 5.60/5.82 (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))) ) 5.60/5.82 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.60/5.82 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 5.60/5.82 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 5.60/5.82 ( (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.60/5.82 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Otop T_1)) (class_Orderings_Otop (tc_fun T_2 T_1))) ) 5.60/5.82 ( tc_Com_Ocom, tc_HOL_Obool ) 5.60/5.82 ( tc_Nat_Onat, tc_HOL_Obool ) 5.60/5.82 ( tc_HOL_Obool, tc_HOL_Obool ) 5.60/5.82 ( tc_Int_Oint, tc_HOL_Obool ) 5.60/5.82 ( tc_Int_Oint, tc_Int_Oint ) 5.60/5.82 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.60/5.82 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.60/5.82 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.60/5.82 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.60/5.82 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.60/5.82 ) 5.60/5.82 (instantiation (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)))) (forall ((V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (= (hAPP _let_0 (hAPP (hAPP _let_1 V_a_2) _let_2)) (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) _let_2)))) (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_ba_2) V_A_2))) (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_ba_2)) V_r_2))) )))) 5.60/5.82 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_z) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OMin)) V_z))) ) 5.60/5.82 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.82 ) 5.60/5.82 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (c_Finite__Set_Ofold1 T_b (c_Groups_Otimes__class_Otimes T_b)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oab__semigroup__mult 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_Groups_Otimes__class_Otimes T_b) (hAPP _let_3 V_A_2)) (hAPP _let_3 V_B_2)) (hAPP _let_3 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2)))) ))))) 5.60/5.82 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.82 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.82 ( (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)) ) 5.60/5.82 ) 5.60/5.82 (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)))))) ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.82 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.82 ( (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) ) 5.60/5.82 ( (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) ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((V_y_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) V_y_2) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (= V_y_2 (hAPP c_Code__Numeral_Onat__of (hAPP c_Code__Numeral_Oof__nat V_y_2)))) ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((V_h_2 $$unsorted) (T_c $$unsorted) (V_F_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_F_2))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (hAPP (c_Set_Oimage T_b T_c V_h_2) V_F_2)))) ) 5.60/5.82 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.60/5.82 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.60/5.82 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.60/5.82 ) 5.60/5.82 (instantiation (let ((_let_0 (tc_fun T_c tc_HOL_Obool))) (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (c_Orderings_Otop__class_Otop (tc_fun (tc_prod T_b T_c) tc_HOL_Obool)) (hAPP (hAPP (c_Product__Type_OSigma T_b T_c) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))) (hAPP (c_COMBK _let_0 T_b) (c_Orderings_Otop__class_Otop _let_0)))) )) 5.60/5.82 ( tc_Com_Ocom, tc_Com_Opname ) 5.60/5.82 ( tc_Nat_Onat, tc_Nat_Onat ) 5.60/5.82 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.82 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.60/5.82 ) 5.60/5.82 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Fields_Olinordered__field T_a)) (not (forall ((B_e $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)) B_e))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_y) B_e)))) )) (hBOOL (hAPP _let_0 V_y))) )) 5.60/5.82 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.60/5.82 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) V_a) (c_Groups_Ozero__class_Ozero T_a))) ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 5.60/5.82 ) 5.60/5.82 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_z))) (hBOOL (hAPP (hAPP _let_0 V_x) V_z))) )) 5.60/5.82 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.60/5.82 ( c_Int_OMin, c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((V_n_2 $$unsorted)) (= (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))) (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_n_2)) ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.82 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.60/5.82 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (c_Groups_Ozero__class_Ozero T_a)) V_a))) ) 5.60/5.82 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 5.60/5.82 ) 5.60/5.82 (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)) ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.60/5.82 ) 5.60/5.82 (instantiation (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (forall ((V_d_2 $$unsorted)) (= (hAPP (c_Set_OCollect (tc_prod tc_Int_Oint tc_Int_Oint)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Int_Oint tc_Int_Oint tc_HOL_Obool) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_d_2)))) (c_Orderings_Oord__class_Oless tc_Int_Oint)))) (c_Int_Oint__ge__less__than2 V_d_2)) )) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( c_Int_OMin ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((T_b $$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))) ) 5.60/5.82 ( tc_Nat_Onat ) 5.60/5.82 ( tc_Int_Oint ) 5.60/5.82 ( tc_Code__Numeral_Ocode__numeral ) 5.60/5.82 ) 5.60/5.82 (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))))) ))) ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( c_Int_OMin ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (= V_b V_a) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_b) V_a))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_b) V_a))) ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.60/5.82 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.60/5.82 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.82 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.60/5.82 ) 5.60/5.82 (instantiation (let ((_let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n))) (forall ((V_n $$unsorted)) (= _let_0 (hAPP (c_Int_Oring__1__class_Oof__int tc_Int_Oint) _let_0)) )) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.82 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.82 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.60/5.82 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.82 ) 5.60/5.82 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat))) (forall ((V_k_2 $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) V_k_2) (hAPP _let_0 V_k_2)) (hAPP _let_0 (hAPP c_Nat_OSuc V_k_2))) )) 5.60/5.82 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.82 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.60/5.82 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.60/5.82 ) 5.60/5.82 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (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_x_2 _let_0) (= V_y_2 _let_0)))) )) 5.60/5.82 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.60/5.82 ( (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.60/5.82 ( (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)) ) 5.60/5.82 ) 5.60/5.82 (instantiation (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Finite__Set_Ofun__left__comm T_b T_c V_f_2)) (c_Finite__Set_Ofun__left__comm T_d T_c (hAPP (hAPP (c_COMBB T_b (tc_fun T_c T_c) T_d) V_f_2) V_g_2))) ) 5.60/5.82 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint, c_fconj, tc_HOL_Obool, tc_HOL_Obool ) 5.60/5.82 ) 5.60/5.82 (instantiation (let ((_let_0 (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint))) (let ((_let_1 (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_List_Oupto__rel))) (forall ((V_Pa_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP _let_1 (hAPP (hAPP _let_0 V_a0_2) V_a1_2)))) (not (forall ((B_i $$unsorted) (B_j $$unsorted)) (or (not (hBOOL (hAPP _let_1 (hAPP (hAPP _let_0 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_Pa_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_Pa_2 B_i) B_j))) )) (hBOOL (hAPP (hAPP V_Pa_2 V_a0_2) V_a1_2))) ))) 5.60/5.82 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OPls, c_Int_OMin ) 5.60/5.82 ( (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) ) 5.60/5.82 ( (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) ) 5.60/5.82 ( (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) ) 5.60/5.82 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 5.60/5.82 ( (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) ) 5.60/5.82 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.60/5.82 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.60/5.82 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.82 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), c_Int_OMin, c_Int_OMin ) 5.60/5.82 ( (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) ) 5.60/5.82 ( (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) ) 5.60/5.82 ( (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) ) 5.60/5.82 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), (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)) ) 5.60/5.82 ( (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)) ) 5.60/5.83 ( (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)) ) 5.60/5.83 ( (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 ) 5.60/5.83 ( (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) ) 5.60/5.83 ( (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)) ) 5.60/5.83 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 5.60/5.83 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_prod (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_1 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair (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_1) _let_1)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))), (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) c_FunDef_Opair__leq) ) 5.60/5.83 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_0 _let_0))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (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_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_0) _let_0)) ) 5.60/5.83 ( (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)) ) 5.60/5.83 ( (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)) ) 5.60/5.83 ( (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)) ) 5.60/5.83 ( (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)) ) 5.60/5.83 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omax__weak, c_FunDef_Omax__strict ) 5.60/5.83 ( (let ((_let_0 (tc_fun (tc_prod (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_HOL_Obool))) (c_Product__Type_OPair _let_0 _let_0)), c_FunDef_Omin__weak, c_FunDef_Omin__strict ) 5.60/5.83 ( (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) ) 5.60/5.83 ( (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 ) 5.60/5.83 ( (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 ) 5.60/5.83 ( (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)))) ) 5.60/5.83 ( (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)))) ) 5.60/5.83 ( (let ((_let_0 (tc_fun tc_Int_Oint (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))) (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) ) 5.60/5.83 ( (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) ) 5.60/5.83 ( (c_Product__Type_Oprod_Oprod__case tc_Com_Opname tc_Com_Ocom tc_HOL_Obool), skv_9, (hAPP (c_COMBK (tc_fun tc_Com_Ocom tc_HOL_Obool) tc_Com_Opname) c_Com_OWT) ) 5.60/5.83 ( (c_member (tc_prod tc_Com_Opname tc_Com_Ocom)), (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9 ) 5.60/5.83 ( (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 ) 5.60/5.83 ( (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 ) 5.60/5.83 ) 5.60/5.83 (instantiation (forall ((B_n $$unsorted) (BOUND_VARIABLE_122084 $$unsorted) (BOUND_VARIABLE_122085 $$unsorted) (BOUND_VARIABLE_122086 $$unsorted)) (or (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_Hoare__Mirabelle_Otriple t_a)) B_x) v_G))) (c_Hoare__Mirabelle_Otriple__valid t_a B_n B_x)) )) (not (v_P BOUND_VARIABLE_122084 BOUND_VARIABLE_122085)) (not (hBOOL (hAPP v_b BOUND_VARIABLE_122085))) (not (c_Natural_Oevaln v_c BOUND_VARIABLE_122085 B_n BOUND_VARIABLE_122086)) (v_P BOUND_VARIABLE_122084 BOUND_VARIABLE_122086)) ) 5.60/5.83 ( v_na, skv_1, v_s0, v_s1 ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (let ((_let_1 (c_Groups_Oone__class_Oone T_a))) (let ((_let_2 (c_Groups_Osgn__class_Osgn T_a V_x))) (let ((_let_3 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) _let_0) V_x)))) (let ((_let_4 (= V_x _let_0))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Osgn__if T_a)) (and (or _let_4 (and (or _let_3 (= _let_2 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) _let_1))) (or (not _let_3) (= _let_1 _let_2)))) (or (not _let_4) (= _let_0 _let_2)))) )))))) 5.60/5.83 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.83 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.83 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_x_2))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_3 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP _let_1 _let_2)))) (let ((_let_4 (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP _let_1 V_A_2)))) (let ((_let_5 (= _let_2 _let_3))) (forall ((V_x_2 $$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))) (and (or _let_5 (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) (c_Big__Operators_Olattice__class_OSup__fin T_b _let_3)) _let_4)) (or (not _let_5) (= V_x_2 _let_4)))) ))))))) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.60/5.83 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.83 ( (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) ) 5.60/5.83 ( (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) ) 5.60/5.83 ) 5.60/5.83 (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))) ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.60/5.83 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.83 ( (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))) ) 5.60/5.83 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) (forall ((V_n $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_n))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) (c_Groups_Oone__class_Oone tc_Nat_Onat))) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))))))) )) 5.60/5.83 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (c_Nat_Osize__class_Osize tc_Com_Ocom))) (forall ((V_com_2 $$unsorted) (V_fun_2 $$unsorted)) (= (hAPP _let_0 (c_Com_Ocom_OWhile V_fun_2 V_com_2)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP _let_0 V_com_2)) (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) )) 5.60/5.83 ( v_c, v_b ) 5.60/5.83 ) 5.60/5.83 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_b)) (not (class_Orderings_Olinorder T_b)) (= (c_Lattices_Osemilattice__inf__class_Oinf T_b) (c_Orderings_Oord__class_Omin T_b))) ) 5.60/5.83 ( tc_Nat_Onat ) 5.60/5.83 ( tc_HOL_Obool ) 5.60/5.83 ( tc_Int_Oint ) 5.60/5.83 ( tc_Code__Numeral_Ocode__numeral ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_k_2))) (= (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_i_2) V_k_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_k_2) V_i_2)))) )) 5.60/5.83 ( c_Int_OPls, c_Int_OMin ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ( (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) ) 5.60/5.83 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ( c_Int_OMin, c_Int_OMin ) 5.60/5.83 ( (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) ) 5.60/5.83 ) 5.60/5.83 (instantiation (forall ((V_a_2 $$unsorted) (V_ba_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_b)) (= (= V_ba_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_ba_2) V_a_2)) (= V_a_2 (c_Groups_Ozero__class_Ozero T_b)))) ) 5.60/5.83 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.83 ) 5.60/5.83 (instantiation (forall ((V_xs_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Complete__Lattice_OInf__class_OInf T_b (hAPP (c_List_Oset T_b) V_xs_2)) (hAPP (c_List_Ofoldl T_b T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b) (c_Orderings_Otop__class_Otop T_b)) V_xs_2))) ) 5.60/5.83 ( c_Com_Obodies, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Int_Oring__1__class_OInts T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (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_ba_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_ba_2)) _let_1))) ))) 5.60/5.83 ( (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 ) 5.60/5.83 ) 5.60/5.83 (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))) ) 5.60/5.83 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin ) 5.60/5.83 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ( c_Int_OMin, c_Int_OMin ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_v $$unsorted) (T_a $$unsorted)) (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)))) )) 5.60/5.83 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (hAPP (c_Set_Oinsert T_b) V_k_2) (c_Orderings_Obot__class_Obot _let_0)))) (forall ((V_k_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) _let_1) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_k_2)))) ))) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.83 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.83 ( (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) ) 5.60/5.83 ( (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) ) 5.60/5.83 ) 5.60/5.83 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (= V_r_2 (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) (hAPP (c_Relation_Oconverse T_b T_b) V_r_2)) V_r_2))) ) 5.60/5.83 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.83 ) 5.60/5.83 (instantiation (forall ((V_A_2 $$unsorted)) (or (not (c_Nat__Transfer_Onat__set V_A_2)) (= (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Int_Oint) 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))))) ) 5.60/5.83 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 5.60/5.83 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= V_a (hAPP _let_0 (hAPP _let_0 V_a)))) )) 5.60/5.83 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.83 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.83 ) 5.60/5.83 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_l_2 V_u_2)) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_u_2)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_l_2))) ) 5.60/5.83 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.83 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.83 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.83 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.83 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.60/5.83 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.83 ) 5.60/5.83 (instantiation (forall ((V_x_2 $$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))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)))) ) 5.60/5.83 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.83 ) 5.60/5.83 (instantiation (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (hBOOL (hAPP (hAPP (c_member T_b) V_i_2) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_k_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_k_2) V_i_2)))) ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.60/5.83 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.60/5.83 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_z $$unsorted) (V_z_H $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_H))) (not (hBOOL (hAPP (hAPP _let_0 V_z_H) V_z))) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP c_Int_Onat V_z)) (hAPP c_Int_Onat V_z_H)) (hAPP c_Int_Onat (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_z) V_z_H)))) )) 5.60/5.83 ( c_Int_OPls, c_Int_OMin ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ( c_Int_OMin, c_Int_OMin ) 5.60/5.83 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ) 5.60/5.83 (instantiation (forall ((V_b $$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)))) ) 5.60/5.83 ( (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 ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ocancel__semigroup__add T_a)) (not (= (hAPP _let_0 V_c) (hAPP _let_0 V_b))) (= V_c V_b)) )) 5.60/5.83 ( (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 ) 5.60/5.83 ) 5.60/5.83 (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))) ) 5.60/5.83 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 V_i))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (or (not (hBOOL (hAPP _let_1 V_j))) (not (hBOOL (hAPP (hAPP _let_0 V_j) V_k))) (hBOOL (hAPP _let_1 V_k))) ))) 5.60/5.83 ( c_Int_OPls, c_Int_OMin, c_Int_OMin ) 5.60/5.83 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ( c_Int_OMin, c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.83 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, c_Int_OMin ) 5.60/5.83 ) 5.60/5.83 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Oord T_1)) (class_Orderings_Oord (tc_fun T_2 T_1))) ) 5.60/5.83 ( tc_Com_Ocom, tc_HOL_Obool ) 5.60/5.83 ( tc_Nat_Onat, tc_HOL_Obool ) 5.60/5.83 ( tc_HOL_Obool, tc_HOL_Obool ) 5.60/5.83 ( tc_Int_Oint, tc_HOL_Obool ) 5.60/5.83 ( tc_Int_Oint, tc_Int_Oint ) 5.60/5.83 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.60/5.83 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.60/5.83 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.60/5.83 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.60/5.83 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_N_2 $$unsorted) (V_h_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (= (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)))) )) 5.60/5.83 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))))) (let ((_let_1 (c_Power_Opower__class_Opower T_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (= (hAPP (hAPP _let_1 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) _let_0) (hAPP (hAPP _let_1 V_a) _let_0))) ))) 5.60/5.83 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.83 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.83 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_1 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP _let_0 V_v)) (hAPP _let_0 V_v_H)))) (let ((_let_2 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_v_H) c_Int_OPls)))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_v) c_Int_OPls)) (and (or (not _let_2) (= (hAPP _let_0 V_v) _let_1)) (or _let_2 (= _let_1 (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_v) V_v_H)))))) )))) 5.60/5.83 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls) ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_1 (hAPP _let_0 V_v_H))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_v) c_Int_OPls))) (= _let_1 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP _let_0 V_v)) _let_1))) ))) 5.60/5.83 ( (c_Int_OBit1 c_Int_OPls), (c_Int_OBit1 c_Int_OPls) ) 5.60/5.83 ) 5.60/5.83 (instantiation (let ((_let_0 (c_Product__Type_OPair T_b T_c))) (forall ((V_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (and (= V_b_H_2 V_ba_2) (= V_a_H_2 V_a_2)) (= (hAPP (hAPP _let_0 V_a_H_2) V_b_H_2) (hAPP (hAPP _let_0 V_a_2) V_ba_2))) )) 5.60/5.83 ( (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 ) 5.60/5.83 ( (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 ) 5.60/5.84 ( (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_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 5.60/5.84 ( (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) ) 5.60/5.84 ( c_FunDef_Omax__weak, c_FunDef_Omax__strict, c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.60/5.84 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, c_FunDef_Omax__weak, c_FunDef_Omax__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.60/5.84 ( c_FunDef_Omin__weak, c_FunDef_Omin__strict, c_FunDef_Omin__weak, c_FunDef_Omin__strict, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oab__semigroup__mult T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2)) (= (hAPP (c_Finite__Set_Ofold1 T_b _let_0) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_a_2) V_A_2))) )) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.60/5.84 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.84 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.84 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.84 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (forall ((V_Pa_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_A_2))) (not (hBOOL (hAPP V_Pa_2 V_A_2))) (not (forall ((B_a $$unsorted) (B_A $$unsorted)) (or (not (hBOOL (hAPP _let_0 B_A))) (not (hBOOL (hAPP (hAPP (c_member T_b) B_a) B_A))) (not (hBOOL (hAPP V_Pa_2 B_A))) (hBOOL (hAPP V_Pa_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus (tc_fun T_b tc_HOL_Obool)) B_A) (hAPP (hAPP (c_Set_Oinsert T_b) B_a) _let_1))))) )) (hBOOL (hAPP V_Pa_2 _let_1))) ))) 5.60/5.84 ( (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 ) 5.60/5.84 ( (c_Finite__Set_Ofinite tc_Int_Oint), (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 5.60/5.84 ( (c_Finite__Set_Ofinite tc_Com_Opname), (c_Map_Odom tc_Com_Opname tc_Com_Ocom c_Com_Obody), tc_Com_Opname ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_xs_2 $$unsorted) (T_b $$unsorted)) (or (not (= (hAPP (c_Nat_Osize__class_Osize (tc_List_Olist T_b)) V_xs_2) (hAPP (c_Finite__Set_Ocard T_b) (hAPP (c_List_Oset T_b) V_xs_2)))) (hBOOL (hAPP (c_List_Odistinct T_b) V_xs_2))) ) 5.60/5.84 ( c_Com_Obodies, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.84 ) 5.60/5.84 (instantiation (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))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Fields_Olinordered__field T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) V_b))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Rings_Oinverse__class_Odivide T_a) (hAPP (hAPP _let_1 V_a) V_b)) (hAPP (hAPP _let_1 _let_2) _let_2))) V_b))) )))) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (forall ((V_x_2 $$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_member T_b) V_x_2) V_A_2))) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP _let_0 V_A_2)) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_1)))))) ))) 5.60/5.84 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_k $$unsorted)) (= (hAPP c_Code__Numeral_Onat__of (hAPP (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) V_k)) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_k)) ) 5.60/5.84 ( c_Int_OPls ) 5.60/5.84 ( (c_Int_OBit1 c_Int_OPls) ) 5.60/5.84 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.60/5.84 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (= V_m_2 V_n_2) (= (hAPP c_Code__Numeral_Oof__nat V_n_2) (hAPP c_Code__Numeral_Oof__nat V_m_2))) ) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_Finite__Set_Ofold1 T_b (c_Groups_Otimes__class_Otimes T_b)))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (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 (c_Groups_Otimes__class_Otimes T_b) V_x_2) (hAPP _let_0 V_A_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.60/5.84 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.84 ( (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) ) 5.60/5.84 ( (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) ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_v $$unsorted)) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v)))) (= (c_Groups_Oone__class_Oone tc_Nat_Onat) (hAPP c_Nat_OSuc (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v)))) ) 5.60/5.84 ( c_Int_OPls ) 5.60/5.84 ( (c_Int_OBit1 c_Int_OPls) ) 5.60/5.84 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.60/5.84 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.60/5.84 ( c_Int_OMin ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (forall ((V_v $$unsorted)) (or (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v))) (= (hAPP c_Nat_OSuc (hAPP _let_0 V_v)) (hAPP _let_0 (c_Int_Osucc V_v)))) )) 5.60/5.84 ( c_Int_OPls ) 5.60/5.84 ( (c_Int_OBit1 c_Int_OPls) ) 5.60/5.84 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)) ) 5.60/5.84 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)) ) 5.60/5.84 ( c_Int_OMin ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_R_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (c_Relation_OImage T_c T_b V_R_2) (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) ) 5.60/5.84 ( c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_u_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq 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))) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Int_Oint _let_0) V_u_2))) )) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.60/5.84 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.84 ( c_Int_OMin ) 5.60/5.84 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_Set_Oimage T_b T_c V_f_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (= (= V_B_2 V_A_2) (= (hAPP _let_0 V_A_2) (hAPP _let_0 V_B_2)))) )) 5.60/5.84 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 5.60/5.84 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 5.60/5.84 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) (= (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a))) ) 5.60/5.84 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_n $$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)))) ) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.84 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.60/5.84 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (let ((_let_1 (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_b) V_n_2))) (let ((_let_2 (c_Groups_Oplus__class_Oplus T_b))) (let ((_let_3 (c_Groups_Oone__class_Oone T_b))) (forall ((V_n_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Ocomm__semiring__1 T_b)) (= (hAPP (hAPP _let_0 (hAPP (hAPP _let_2 _let_3) _let_3)) (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__add__class_Osetsum tc_Nat_Onat T_b) (c_Nat_Osemiring__1__class_Oof__nat T_b)) (c_SetInterval_Oord__class_OatLeastAtMost tc_Nat_Onat (c_Groups_Oone__class_Oone tc_Nat_Onat) V_n_2))) (hAPP (hAPP _let_0 _let_1) (hAPP (hAPP _let_2 _let_1) _let_3)))) ))))) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.60/5.84 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 5.60/5.84 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= V_a (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) V_b))) ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) V_B_2))) (= (hAPP (c_Finite__Set_Ocard (tc_sum T_b T_c)) (c_Sum__Type_OPlus T_b T_c V_A_2 V_B_2)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)) (hAPP (c_Finite__Set_Ocard T_c) V_B_2)))) ) 5.60/5.84 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit, (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (not (class_Int_Onumber__ring T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_x_2)) (c_Groups_Ozero__class_Ozero T_b))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_x_2) c_Int_OPls)))) ) 5.60/5.84 ( c_Int_OPls, tc_Nat_Onat ) 5.60/5.84 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.84 ( c_Int_OPls, tc_Code__Numeral_Ocode__numeral ) 5.60/5.84 ( (c_Int_OBit1 c_Int_OPls), tc_Nat_Onat ) 5.60/5.84 ( (c_Int_OBit1 c_Int_OPls), tc_Int_Oint ) 5.60/5.84 ( (c_Int_OBit1 c_Int_OPls), tc_Code__Numeral_Ocode__numeral ) 5.60/5.84 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.60/5.84 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.60/5.84 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Nat_Onat ) 5.60/5.84 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), tc_Int_Oint ) 5.60/5.84 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_r_2)) (c_Wellfounded_Oacyclic T_b V_r_2)) ) 5.60/5.84 ( c_FunDef_Opair__less, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.84 ( c_Wellfounded_Opred__nat, tc_Nat_Onat ) 5.60/5.84 ( c_Wellfounded_Oless__than, tc_Nat_Onat ) 5.60/5.84 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_z))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) (not (hBOOL (hAPP _let_0 V_y))) (hBOOL (hAPP _let_0 V_x))) )) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (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))) ))) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_a_2)) V_ba_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_ba_2)) V_a_2)))) ))) 5.60/5.84 ( c_Int_OPls, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( c_Int_OPls, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( c_Int_OPls, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.60/5.84 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.60/5.84 ( c_Int_OPls, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OPls, tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_OMin, tc_Int_Oint ) 5.60/5.84 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, tc_Int_Oint ) 5.60/5.84 ( c_Int_OMin, c_Int_OPls, tc_Int_Oint ) 5.60/5.84 ( c_Int_OMin, (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), c_Int_OPls, tc_Int_Oint ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (hAPP (c_Set_Oinsert T_b) V_a_2))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$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 _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP _let_0 (c_Orderings_Obot__class_Obot _let_1)))))) ))) 5.60/5.84 ( (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OatMost tc_Nat_Onat))) (let ((_let_1 (hAPP c_Nat_OSuc V_k_2))) (forall ((V_k_2 $$unsorted)) (= (hAPP _let_0 _let_1) (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) _let_1) (hAPP _let_0 V_k_2))) ))) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.84 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.60/5.84 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OatLeast T_b))) (forall ((V_u_2 $$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_OatLeastLessThan T_b V_l_2) V_u_2)) (hAPP _let_0 V_u_2)) (hAPP _let_0 V_l_2))) )) 5.60/5.84 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( (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 ) 5.60/5.84 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.60/5.84 ( (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 ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) _let_1))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_b) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_1))) ))) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_x_2 $$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_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)))) ) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.60/5.84 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.84 ( (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) ) 5.60/5.84 ( (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) ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (= (hAPP (c_Int_Oring__1__class_Oof__int T_a) (c_Groups_Oone__class_Oone tc_Int_Oint)) (c_Groups_Oone__class_Oone T_a))) ) 5.60/5.84 ( tc_Nat_Onat ) 5.60/5.84 ( tc_Int_Oint ) 5.60/5.84 ( tc_Code__Numeral_Ocode__numeral ) 5.60/5.84 ) 5.60/5.84 (instantiation (forall ((V_y $$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))) ) 5.60/5.84 ( c_Int_OPls, c_Int_OMin, tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( (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 ) 5.60/5.84 ( c_Int_OMin, (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( c_Int_OMin, c_Int_OMin, tc_Int_Oint ) 5.60/5.84 ( (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 ) 5.60/5.84 ) 5.60/5.84 (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) V_z) (hAPP (c_Int_Onumber__class_Onumber__of T_a) c_Int_OMin)))) ) 5.60/5.84 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.84 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.84 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 V_A_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.60/5.84 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.84 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.84 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 5.60/5.84 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.84 ) 5.60/5.84 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))))) (let ((_let_1 (c_Divides_Odiv__class_Odiv tc_Nat_Onat))) (forall ((V_m $$unsorted)) (= (hAPP (hAPP _let_1 (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_m))) _let_0) (hAPP c_Nat_OSuc (hAPP (hAPP _let_1 V_m) _let_0))) ))) 5.60/5.84 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.84 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 5.60/5.84 ) 5.60/5.84 (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))) ) 5.60/5.85 ( (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 ) 5.60/5.85 ) 5.60/5.85 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (let ((_let_1 (c_Big__Operators_Olattice_OSup__fin T_b _let_0 V_A_2))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_2))))) (let ((_let_4 (= (c_Orderings_Obot__class_Obot _let_2) _let_3))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (and (or (not _let_4) (= V_x_2 _let_1)) (or _let_4 (= _let_1 (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 _let_3)))))) )))))) 5.60/5.85 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.85 ) 5.60/5.85 (instantiation (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Nat_Onat _let_1))) (let ((_let_3 (tc_fun _let_1 _let_1))) (let ((_let_4 (tc_fun tc_Nat_Onat _let_3))) (forall ((V_z_2 $$unsorted)) (= (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)) )))))) 5.60/5.85 ( c_Int_OPls ) 5.60/5.85 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 5.60/5.85 ( c_Int_OMin ) 5.60/5.85 ) 5.60/5.85 (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))) ) 5.60/5.85 ( tc_Com_Ocom, tc_HOL_Obool ) 5.60/5.85 ( tc_Nat_Onat, tc_HOL_Obool ) 5.60/5.85 ( tc_HOL_Obool, tc_HOL_Obool ) 5.60/5.85 ( tc_Int_Oint, tc_HOL_Obool ) 5.60/5.85 ( tc_Int_Oint, tc_Int_Oint ) 5.60/5.85 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.60/5.85 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.60/5.85 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.60/5.85 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.60/5.85 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.60/5.85 ) 5.60/5.85 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Opreorder T_1)) (class_Orderings_Opreorder (tc_fun T_2 T_1))) ) 5.60/5.85 ( tc_Com_Ocom, tc_HOL_Obool ) 5.60/5.85 ( tc_Nat_Onat, tc_HOL_Obool ) 5.60/5.85 ( tc_HOL_Obool, tc_HOL_Obool ) 5.60/5.85 ( tc_Int_Oint, tc_HOL_Obool ) 5.60/5.85 ( tc_Int_Oint, tc_Int_Oint ) 5.60/5.85 ( tc_Int_Oint, (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.60/5.85 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 5.60/5.85 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.60/5.85 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 5.60/5.85 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 5.60/5.85 ) 5.60/5.85 (instantiation (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (forall ((V_m_2 $$unsorted)) (= (hAPP c_Int_OAbs__Integ (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_m_2) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))))) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2)) )) 5.60/5.85 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.85 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.85 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.60/5.85 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.85 ) 5.60/5.85 (instantiation (let ((_let_0 (c_member (tc_prod T_b T_b)))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (let ((_let_2 (c_Transitive__Closure_Otrancl T_b V_r_2))) (let ((_let_3 (hAPP _let_1 V_a_2))) (forall ((V_ca_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_3 V_ba_2)) _let_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_ca_2)) _let_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_3 V_ca_2)) _let_2))) ))))) 5.60/5.85 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Wellfounded_Opred__nat, (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.85 ) 5.60/5.85 (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)))) ) 5.60/5.85 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 5.60/5.85 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.85 ) 5.60/5.85 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (c_Orderings_Otop__class_Otop T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (c_Orderings_Obot__class_Obot T_a)))) ) 5.60/5.85 ( tc_Nat_Onat ) 5.60/5.85 ( tc_HOL_Obool ) 5.60/5.85 ( tc_Int_Oint ) 5.60/5.85 ( (tc_fun tc_HOL_Obool tc_HOL_Obool) ) 5.60/5.85 ( (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 5.60/5.85 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 5.60/5.85 ( (tc_fun tc_Int_Oint tc_HOL_Obool) ) 5.60/5.85 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 5.60/5.85 ( (tc_fun tc_Product__Type_Ounit tc_HOL_Obool) ) 5.60/5.85 ) 5.60/5.85 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (c_Groups_Ozero__class_Ozero T_a) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)))) ) 5.60/5.85 ( c_Int_OPls, tc_Int_Oint ) 5.60/5.85 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 5.60/5.85 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.85 ( c_Int_OMin, tc_Int_Oint ) 5.60/5.85 ) 5.60/5.85 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_x_2 $$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_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)))) )) 5.60/5.85 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 5.60/5.85 ( (let ((_let_0 (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_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_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 5.60/5.85 ( (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) ) 5.60/5.85 ( (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) ) 5.60/5.85 ) 5.60/5.85 (instantiation (let ((_let_0 (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (hAPP _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_2)))))) (let ((_let_4 (hAPP _let_1 V_A_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or _let_0 (= _let_3 _let_4)) (or (not _let_0) (= _let_3 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) _let_4) (c_Groups_Oone__class_Oone tc_Nat_Onat)))))) )))))) 5.60/5.85 ( skv_9, (hAPP (c_List_Oset (tc_prod tc_Com_Opname tc_Com_Ocom)) c_Com_Obodies), (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.85 ) 5.60/5.85 (instantiation (let ((_let_0 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_w_2)))) (forall ((V_w_2 $$unsorted) (V_m_2 $$unsorted)) (= (and (or (not _let_0) (= V_w_2 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2))) (or _let_0 (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_m_2))) (= V_m_2 (hAPP c_Int_Onat V_w_2))) )) 5.60/5.85 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 5.60/5.85 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.85 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 5.60/5.85 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls))) ) 5.60/5.85 ) 5.60/5.85 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (let ((_let_2 (c_Groups_Oplus__class_Oplus T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) (c_Int_Oring__1__class_OInts T_b)))) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_2 (hAPP (hAPP _let_2 (c_Groups_Oone__class_Oone T_b)) V_a_2)) V_a_2)) _let_1)))) )))) 5.60/5.85 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 5.60/5.85 ( skv_9, (tc_prod tc_Com_Opname tc_Com_Ocom) ) 5.60/5.85 ) 5.60/5.85 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (let ((_let_1 (hAPP _let_0 V_u))) (let ((_let_2 (hAPP _let_0 V_v))) (let ((_let_3 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) _let_1) _let_2)))) (let ((_let_4 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) _let_1) _let_2))) (forall ((V_v $$unsorted) (V_u $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (not (class_Int_Onumber T_b)) (and (or _let_3 (= _let_1 _let_4)) (or (not _let_3) (= _let_2 _let_4)))) )))))) 5.60/5.85 ( c_Int_OPls, c_Int_OPls, tc_Int_Oint ) 5.60/5.85 ( (c_Int_OBit1 c_Int_OPls), c_Int_OPls, tc_Int_Oint ) 5.60/5.85 ( (c_Int_OBit0 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 5.60/5.85 ( (c_Int_OBit1 (c_Int_OBit1 c_Int_OPls)), c_Int_OPls, tc_Int_Oint ) 5.60/5.85 ) 5.60/5.85 % SZS output end Proof for theBenchmark 5.60/5.87 EOF