0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : do_CVC4 %s 0.03/0.23 % Computer : n164.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 05:49:55 CDT 2018 0.03/0.23 % CPUTime : 0.80/1.01 %----Proving without arithmetic mode 0.80/1.01 ------- cvc4-fof casc j9 : /export/starexec/sandbox2/benchmark/theBenchmark.p at ... 0.80/1.01 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 21.19/23.90 --- Run --no-e-matching --full-saturate-quant at 20... 41.48/45.86 --- Run --finite-model-find --uf-ss=no-minimal at 15... 56.72/62.28 --- Run --multi-trigger-when-single --full-saturate-quant at 5... 61.96/68.70 --- Run --trigger-sel=max --full-saturate-quant at 5... 67.19/75.07 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5... 72.41/81.43 --- Run --multi-trigger-cache --full-saturate-quant at 10... 82.66/93.20 --- Run --prenex-quant=none --full-saturate-quant at 15... 97.07/107.67 % SZS status Theorem for theBenchmark 97.07/107.67 % SZS output start Proof for theBenchmark 97.07/107.67 (skolem (forall ((B_h $$unsorted)) (not (c_Fun_Obij__betw tc_Nat_Onat tc_Com_Opname B_h (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Finite__Set_Ocard tc_Com_Opname) v_U)) v_U)) ) 97.07/107.67 ( skv_1 ) 97.07/107.67 ) 97.07/107.67 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.67 ( skv_2 ) 97.07/107.67 ) 97.07/107.67 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.67 ( skv_3 ) 97.07/107.67 ) 97.07/107.67 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Int_Oint) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.67 ( skv_4 ) 97.07/107.67 ) 97.07/107.67 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_member t_a) (hAPP v_mgt__call v_pn)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.67 ( skv_5 ) 97.07/107.67 ) 97.07/107.67 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.67 ( skv_6 ) 97.07/107.67 ) 97.07/107.67 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.67 ( skv_7 ) 97.07/107.67 ) 97.07/107.67 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.67 ( skv_8 ) 97.07/107.67 ) 97.07/107.67 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.67 ( skv_9 ) 97.07/107.67 ) 97.07/107.67 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.67 ( skv_10 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_f $$unsorted)) (not (c_Fun_Obij__betw tc_Com_Opname tc_Com_Opname B_f v_U v_U)) ) 97.07/107.67 ( skv_11 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.67 ( skv_12 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.67 ( skv_13 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.67 ( skv_14 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_member t_a) (hAPP v_mgt__call v_pn)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.67 ( skv_15 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.67 ( skv_16 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.67 ( skv_17 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.67 ( skv_18 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.67 ( skv_19 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (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_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.67 ( skv_20 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_h $$unsorted)) (not (c_Fun_Obij__betw tc_Com_Opname tc_Nat_Onat B_h v_U (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Finite__Set_Ocard tc_Com_Opname) v_U)))) ) 97.07/107.67 ( skv_21 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) B_n))) (not (= (c_Groups_Oone__class_Oone tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) ) 97.07/107.67 ( skv_22 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_h $$unsorted)) (not (c_Fun_Obij__betw tc_Nat_Onat tc_Com_Opname B_h (c_SetInterval_Oord__class_OatLeastAtMost tc_Nat_Onat (c_Groups_Oone__class_Oone tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard tc_Com_Opname) v_U)) v_U)) ) 97.07/107.67 ( skv_23 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_n $$unsorted)) (not (= (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))) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.07/107.67 ( skv_24 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_AA $$unsorted)) (or (not (= v_G (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) B_AA))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun tc_Com_Opname tc_HOL_Obool)) B_AA) v_U)))) ) 97.07/107.67 ( skv_25 ) 97.07/107.67 ) 97.07/107.67 (skolem (forall ((B_n $$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)))) ) 97.07/107.67 ( skv_26 ) 97.07/107.67 ) 97.07/107.67 (skolem (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((B_n $$unsorted)) (not (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Int_Opred _let_0)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) )) 97.07/107.68 ( skv_27 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((B_n $$unsorted)) (not (= (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 _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)))) )) 97.07/107.68 ( skv_28 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((B_n $$unsorted)) (not (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) _let_0) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) )) 97.07/107.68 ( skv_29 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((B_n $$unsorted)) (not (= (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 _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)))) )) 97.07/107.68 ( skv_30 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((B_n $$unsorted)) (not (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) _let_0) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) )) 97.07/107.68 ( skv_31 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_n $$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))))) ) 97.07/107.68 ( skv_32 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((B_n $$unsorted)) (not (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Int_Opred _let_0)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Nat_OSuc B_n))))) )) 97.07/107.68 ( skv_33 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_k $$unsorted)) (not (= (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP c_Nat_OSuc v_n)) B_k))) ) 97.07/107.68 ( skv_34 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_x $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_HOL_Obool) (hAPP (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G) B_x)) (hAPP (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U) B_x))) ) 97.07/107.68 ( skv_35 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_n $$unsorted) (B_f $$unsorted)) (not (= v_U (hAPP (c_Set_Oimage tc_Nat_Onat tc_Com_Opname B_f) (hAPP (c_Set_OCollect tc_Nat_Onat) (hAPP (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat)) B_n))))) ) 97.07/107.68 ( skv_36 skv_37 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Nat_OSuc v_n)))) (forall ((B_k $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_k) (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U))))) (not (forall ((B_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) B_i) B_k))) (not (hBOOL (hAPP _let_0 B_i)))) )) (not (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) B_k) (c_Groups_Oone__class_Oone tc_Nat_Onat)))))) )) 97.07/107.68 ( skv_38 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_x $$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))))) ) 97.07/107.68 ( skv_39 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member tc_Product__Type_Ounit) B_x) (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool))))) ) 97.07/107.68 ( skv_40 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_x) (c_Orderings_Otop__class_Otop _let_0)))) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) B_x))) )) 97.07/107.68 ( skv_41 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_x) (c_Orderings_Otop__class_Otop _let_0)))) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) B_x))) )) 97.07/107.68 ( skv_42 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_x) (c_Orderings_Otop__class_Otop _let_0)))) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) B_x))) )) 97.07/107.68 ( skv_43 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)))) (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_x) _let_0))) (= _let_0 (hAPP (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) B_x))) )) 97.07/107.68 ( skv_44 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member t_a) B_x) v_G))) ) 97.07/107.68 ( skv_45 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_x $$unsorted)) (= B_x (hAPP c_Nat_OSuc (hAPP (c_Hilbert__Choice_Oinv__into tc_Nat_Onat tc_Nat_Onat (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) c_Nat_OSuc) B_x))) ) 97.07/107.68 ( skv_46 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((B_x $$unsorted)) (= B_x (hAPP _let_0 (hAPP (c_Hilbert__Choice_Oinv__into tc_Nat_Onat tc_Int_Oint (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) _let_0) B_x))) )) 97.07/107.68 ( skv_47 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_x $$unsorted)) (= B_x (hAPP c_Int_Onat (hAPP (c_Hilbert__Choice_Oinv__into tc_Int_Oint tc_Nat_Onat (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)) c_Int_Onat) B_x))) ) 97.07/107.68 ( skv_48 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_x $$unsorted)) (= B_x (hAPP v_mgt__call (hAPP (c_Hilbert__Choice_Oinv__into tc_Com_Opname t_a (c_Orderings_Otop__class_Otop (tc_fun tc_Com_Opname tc_HOL_Obool)) v_mgt__call) B_x))) ) 97.07/107.68 ( skv_49 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member t_a) B_x) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)))) ) 97.07/107.68 ( skv_50 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member tc_Com_Opname) B_x) v_U))) ) 97.07/107.68 ( skv_51 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun _let_0 tc_HOL_Obool)) B_y) (hAPP _let_1 c_Int_Ointrel)))) (hBOOL (hAPP _let_1 (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.68 ( skv_52 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.07/107.68 ( skv_53 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U))) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.68 ( skv_54 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U))) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.68 ( skv_55 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Finite__Set_Ocard t_a) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.68 ( skv_56 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.68 ( skv_57 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.68 ( skv_58 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.68 ( skv_59 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.68 ( skv_60 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP _let_0 (hAPP _let_0 B_y)))) )) 97.07/107.68 ( skv_61 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_n $$unsorted)) (or (not (= (c_Groups_Oone__class_Oone tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n))) (hBOOL (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_n))) ) 97.07/107.68 ( skv_62 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_2 (tc_fun _let_1 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_2) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_1) (c_Orderings_Otop__class_Otop _let_2)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (hAPP c_Int_OAbs__Integ B_y)))) )))) 97.07/107.68 ( skv_63 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.07/107.68 ( skv_64 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (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)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.68 ( skv_65 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop _let_0)))) (hBOOL (hAPP (hAPP (c_COMBB tc_Nat_Onat _let_0 tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.07/107.68 ( skv_66 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (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))) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.68 ( skv_67 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.68 ( skv_68 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.68 ( skv_69 ) 97.07/107.68 ) 97.07/107.68 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.68 ( skv_70 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_0) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)) (c_Orderings_Otop__class_Otop _let_0)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Orderings_Obot__class_Obot _let_0)) (hAPP c_Int_OAbs__Integ B_y)))) )) 97.07/107.68 ( skv_71 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Orderings_Obot__class_Obot _let_0)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.07/107.68 ( skv_72 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (forall ((B_y $$unsorted)) (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member _let_0) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)) (c_Orderings_Otop__class_Otop _let_0)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Set_Oinsert (tc_prod _let_0 _let_0)) (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) _let_0) _let_0)) (hAPP c_Int_OAbs__Integ B_y))))) )) 97.07/107.68 ( skv_73 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (forall ((B_y $$unsorted)) (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Set_Oinsert (tc_prod _let_0 _let_0)) (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) _let_0) _let_0)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y))))) )) 97.07/107.68 ( skv_74 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))))) (forall ((B_y $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (or (not (hBOOL (hAPP (hAPP (c_member _let_0) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_0)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (hAPP c_Int_OAbs__Integ B_y))))) ))) 97.07/107.68 ( skv_75 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (forall ((B_y $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y))))) )) 97.07/107.68 ( skv_76 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0)))) (hAPP c_Int_OAbs__Integ B_y)))) )))) 97.07/107.68 ( skv_77 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0)))) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )))) 97.07/107.68 ( skv_78 ) 97.07/107.68 ) 97.07/107.68 (skolem (let ((_let_0 (tc_fun (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) tc_HOL_Obool))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))))) (forall ((B_y $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omax__ext _let_0 (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))) (hAPP c_Int_OAbs__Integ B_y)))))) ))) 97.07/107.69 ( skv_79 ) 97.07/107.69 ) 97.07/107.69 (skolem (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))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ))) 97.07/107.69 ( skv_80 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_81 ) 97.07/107.69 ) 97.07/107.69 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.69 ( skv_82 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP c_Nat_OSuc (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_83 ) 97.07/107.69 ) 97.07/107.69 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP c_Nat_OSuc (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.69 ( skv_84 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_85 ) 97.07/107.69 ) 97.07/107.69 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.69 ( skv_86 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP c_Int_Onat (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_87 ) 97.07/107.69 ) 97.07/107.69 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP c_Int_Onat (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.69 ( skv_88 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Finite__Set_Ocard tc_HOL_Obool) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_89 ) 97.07/107.69 ) 97.07/107.69 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Finite__Set_Ocard tc_HOL_Obool) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.69 ( skv_90 ) 97.07/107.69 ) 97.07/107.69 (skolem (forall ((B_n $$unsorted)) (or (not (= (c_Groups_Oone__class_Oone tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n))) (hBOOL (hAPP c_Nat_OSuc B_n))) ) 97.07/107.69 ( skv_91 ) 97.07/107.69 ) 97.07/107.69 (skolem (forall ((B_n $$unsorted)) (or (not (= (c_Groups_Oone__class_Oone tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n))) (hBOOL (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) B_n))) ) 97.07/107.69 ( skv_92 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0)))) (hAPP c_Int_OAbs__Integ B_y)))) )))) 97.07/107.69 ( skv_93 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0)))) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )))) 97.07/107.69 ( skv_94 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_fun (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) tc_HOL_Obool))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))))) (forall ((B_y $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omin__ext _let_0 (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))) (hAPP c_Int_OAbs__Integ B_y)))))) ))) 97.07/107.69 ( skv_95 ) 97.07/107.69 ) 97.07/107.69 (skolem (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))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ))) 97.07/107.69 ( skv_96 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (forall ((B_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_i) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) B_i) (c_Groups_Oone__class_Oone tc_Nat_Onat)))) (hAPP _let_0 B_i)))) (c_Groups_Oone__class_Oone tc_Int_Oint)))) )) 97.07/107.69 ( skv_97 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (forall ((B_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_i) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) (hAPP c_Int_OAbs__Integ (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) B_i) (c_Groups_Oone__class_Oone tc_Nat_Onat)))) (hAPP c_Int_OAbs__Integ B_i)))) (c_Groups_Oone__class_Oone tc_Int_Oint)))) ))) 97.07/107.69 ( skv_98 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (forall ((B_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_i) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) B_i) (c_Groups_Oone__class_Oone tc_Nat_Onat)))) (hAPP _let_0 B_i)))) (c_Groups_Oone__class_Oone tc_Int_Oint)))) )) 97.07/107.69 ( skv_99 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (let ((_let_1 (c_Groups_Oone__class_Oone tc_Int_Oint))) (forall ((B_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_i) _let_1))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) B_i) (c_Groups_Oone__class_Oone tc_Nat_Onat)))) (hAPP _let_0 B_i)))) _let_1))) ))) 97.07/107.69 ( skv_100 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (forall ((B_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_i) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) B_i) (c_Groups_Oone__class_Oone tc_Nat_Onat)))) (hAPP _let_0 B_i)))) (c_Groups_Oone__class_Oone tc_Int_Oint)))) )) 97.07/107.69 ( skv_101 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_102 ) 97.07/107.69 ) 97.07/107.69 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.07/107.69 ( skv_103 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_104 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_105 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_106 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_107 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_108 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP c_Int_OAbs__Integ (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_109 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_110 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_111 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_112 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_113 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_114 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP v_mgt__call (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_115 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_116 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_117 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_118 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_member tc_Com_Opname) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.69 ( skv_119 ) 97.07/107.69 ) 97.07/107.69 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Nat_Osize__class_Osize tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.70 ( skv_120 ) 97.07/107.70 ) 97.07/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Set_OCollect _let_0) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.70 ( skv_121 ) 97.07/107.70 ) 97.07/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.70 ( skv_122 ) 97.07/107.70 ) 97.07/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.07/107.70 ( skv_123 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_124 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_2) (c_Orderings_Otop__class_Otop _let_2)) (hAPP c_Int_OAbs__Integ B_y)))) )))) 97.17/107.70 ( skv_125 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_126 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_127 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Set_Oinsert t_a) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_128 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_0) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)) (c_Orderings_Otop__class_Otop _let_0)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (hAPP c_Int_OAbs__Integ B_y)))) )) 97.17/107.70 ( skv_129 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_0) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)) (c_Orderings_Otop__class_Otop _let_0)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Set_Oinsert (tc_prod _let_0 _let_0)) (hAPP c_Int_OAbs__Integ B_y)))) )) 97.17/107.70 ( skv_130 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_0) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)) (c_Orderings_Otop__class_Otop _let_0)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Product__Type_OPair _let_0 _let_0) (hAPP c_Int_OAbs__Integ B_y)))) )) 97.17/107.70 ( skv_131 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_132 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_133 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Set_Oinsert tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_134 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_135 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Set_Oimage tc_Nat_Onat tc_Nat_Onat c_Nat_OSuc) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_136 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_137 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) c_Code__Numeral_Onat__of) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_138 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_139 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_140 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_141 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Set_Oinsert _let_0) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_142 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_143 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_member t_a) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_144 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_145 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_146 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_COMBK tc_HOL_Obool tc_Nat_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_147 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_148 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Nat_Osize__class_Osize tc_HOL_Obool) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_149 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Finite__Set_Ocard tc_Product__Type_Ounit) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_150 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_fun (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) tc_HOL_Obool))) (forall ((B_y $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Product__Type_OPair _let_0 _let_0) (hAPP c_Int_OAbs__Integ B_y)))))) )) 97.17/107.70 ( skv_151 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Equiv__Relations_Oquotient _let_0))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP _let_2 (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP _let_2 (hAPP c_Int_OAbs__Integ B_y)))) )))) 97.17/107.70 ( skv_152 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_153 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_154 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat _let_2) (c_Orderings_Otop__class_Otop _let_2)) (hAPP c_Int_OAbs__Integ B_y)))) )))) 97.17/107.70 ( skv_155 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)) (hAPP c_Int_OAbs__Integ B_y)))) ))) 97.17/107.70 ( skv_156 ) 97.17/107.70 ) 97.17/107.70 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.70 ( skv_157 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Set_Oinsert (tc_prod _let_0 _let_0)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.17/107.70 ( skv_158 ) 97.17/107.70 ) 97.17/107.70 (skolem (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat)) B_x))) ) 97.17/107.70 ( skv_159 ) 97.17/107.70 ) 97.17/107.70 (skolem (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)) B_x))) ) 97.17/107.70 ( skv_160 ) 97.17/107.70 ) 97.17/107.70 (skolem (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)))) (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member tc_Product__Type_Ounit) B_x) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)) _let_0) _let_0)))) )) 97.17/107.70 ( skv_161 ) 97.17/107.70 ) 97.17/107.70 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.70 ( skv_162 ) 97.17/107.70 ) 97.17/107.70 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.70 ( skv_163 ) 97.17/107.70 ) 97.17/107.70 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.70 ( skv_164 ) 97.17/107.70 ) 97.17/107.70 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.70 ( skv_165 ) 97.17/107.70 ) 97.17/107.70 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.70 ( skv_166 ) 97.17/107.70 ) 97.17/107.70 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP c_Int_OAbs__Integ (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_167 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_168 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_169 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_170 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_171 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_172 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP v_mgt__call (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_173 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_174 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_175 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_176 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_member tc_Com_Opname) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_177 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Nat_Osize__class_Osize tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_178 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_179 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_180 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop _let_0)))) (hBOOL (hAPP (c_COMBB tc_Nat_Onat _let_0 tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.17/107.71 ( skv_181 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop _let_0)))) (hBOOL (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.17/107.71 ( skv_182 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Otop__class_Otop _let_0))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) _let_1))) (hBOOL (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR tc_Nat_Onat _let_0) _let_1) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ))) 97.17/107.71 ( skv_183 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_184 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_185 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Set_Oinsert t_a) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_186 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.17/107.71 ( skv_187 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Product__Type_OPair _let_0 _let_0) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.17/107.71 ( skv_188 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_189 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.17/107.71 ( skv_190 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Set_Oinsert tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_191 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_192 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Set_Oimage tc_Nat_Onat tc_Nat_Onat c_Nat_OSuc) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_193 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Fun_Ocomp tc_Nat_Onat tc_Int_Oint tc_Code__Numeral_Ocode__numeral (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_194 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (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) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_195 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_196 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_197 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.17/107.71 ( skv_198 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_199 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_member t_a) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_200 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_201 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_202 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_COMBK tc_HOL_Obool tc_Nat_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_203 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_204 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Nat_Osize__class_Osize tc_HOL_Obool) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_205 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Finite__Set_Ocard tc_Product__Type_Ounit) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_206 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (tc_fun (tc_prod (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Product__Type_OPair _let_0 _let_0) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.17/107.71 ( skv_207 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_208 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ) 97.17/107.71 ( skv_209 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop _let_0)))) (hBOOL (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat _let_0) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) 97.17/107.71 ( skv_210 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Otop__class_Otop _let_0))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) _let_1))) (hBOOL (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI tc_Nat_Onat _let_0) _let_1) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) ))) 97.17/107.71 ( skv_211 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint _let_0) (hAPP _let_0 B_y)))) )) 97.17/107.71 ( skv_212 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n))) (forall ((B_n $$unsorted)) (or (not (= _let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) (hBOOL _let_0)) )) 97.17/107.71 ( skv_213 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n))) (forall ((B_n $$unsorted)) (or (not (= (c_Groups_Oone__class_Oone tc_Int_Oint) _let_0)) (hBOOL _let_0)) )) 97.17/107.71 ( skv_214 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_n $$unsorted)) (or (not (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) (hBOOL (hAPP c_Nat_OSuc B_n))) ) 97.17/107.71 ( skv_215 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n))) (forall ((B_n $$unsorted)) (or (not (= _let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) (hBOOL _let_0)) )) 97.17/107.71 ( skv_216 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_n $$unsorted)) (or (not (= (c_Groups_Oone__class_Oone tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n))) (hBOOL (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) B_n))) ) 97.17/107.71 ( skv_217 ) 97.17/107.71 ) 97.17/107.71 (skolem (forall ((B_n $$unsorted)) (or (not (= (c_Groups_Oone__class_Oone tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n))) (hBOOL (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) B_n))) ) 97.17/107.71 ( skv_218 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)))) (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Int_Oint) B_y) (hAPP (c_Set_Oimage tc_Nat_Onat tc_Int_Oint _let_0) _let_1)))) (hBOOL (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP (c_Hilbert__Choice_Oinv__into tc_Nat_Onat tc_Int_Oint _let_1 _let_0) B_y)))) ))) 97.17/107.71 ( skv_219 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (c_Set_Oinsert tc_Com_Opname))) (forall ((B_x $$unsorted) (B_y $$unsorted)) (hBOOL (hAPP (hAPP (c_member tc_Com_Opname) (hAPP (hAPP (c_Orderings_Oord__class_Omax tc_Com_Opname) B_x) B_y)) (hAPP (hAPP _let_0 B_x) (hAPP (hAPP _let_0 B_y) (c_Orderings_Obot__class_Obot (tc_fun tc_Com_Opname tc_HOL_Obool)))))) )) 97.17/107.71 ( skv_220 skv_221 ) 97.17/107.71 ) 97.17/107.71 (skolem (let ((_let_0 (c_Set_Oinsert tc_Com_Opname))) (forall ((B_x $$unsorted) (B_y $$unsorted)) (hBOOL (hAPP (hAPP (c_member tc_Com_Opname) (hAPP (hAPP (c_Orderings_Oord__class_Omin tc_Com_Opname) B_x) B_y)) (hAPP (hAPP _let_0 B_x) (hAPP (hAPP _let_0 B_y) (c_Orderings_Obot__class_Obot (tc_fun tc_Com_Opname tc_HOL_Obool)))))) )) 97.17/107.71 ( skv_222 skv_223 ) 97.17/107.71 ) 97.17/107.71 (instantiation (forall ((V_n $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_n) V_n))) ) 97.17/107.71 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 97.17/107.71 ) 97.17/107.71 (instantiation (let ((_let_0 (c_Fun_Oid T_b))) (forall ((T_b $$unsorted)) (= _let_0 (c_Hilbert__Choice_Oinv__into T_b T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) _let_0)) )) 97.17/107.71 ( tc_Nat_Onat ) 97.17/107.71 ( tc_HOL_Obool ) 97.17/107.71 ( tc_Int_Oint ) 97.17/107.71 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.71 ( t_a ) 97.17/107.71 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.71 ( tc_Product__Type_Ounit ) 97.17/107.71 ) 97.17/107.71 (instantiation (forall ((V_n $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Nat_OSuc V_n)))))) ) 97.17/107.71 ( v_n ) 97.17/107.71 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.17/107.71 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.17/107.71 ) 97.17/107.71 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) V_B_2)) (and (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_B_2)) (hBOOL (hAPP (hAPP _let_0 V_A_2) V_B_2)))) )) 97.17/107.71 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (hAPP v_mgt__call v_pn), t_a ) 97.17/107.71 ) 97.17/107.71 (instantiation (forall ((V_v_2 $$unsorted)) (= (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v_2)) (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred V_v_2))))) ) 97.17/107.71 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.71 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.71 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.71 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.71 ) 97.17/107.71 (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)))) ) 97.17/107.71 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.71 ) 97.17/107.71 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Nat_Onat))) (forall ((V_m_2 $$unsorted) (V_na_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_na_2) V_m_2))) (hBOOL (hAPP (hAPP _let_0 V_m_2) V_na_2))) )) 97.17/107.71 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.17/107.71 ) 97.17/107.71 (instantiation (forall ((T_b $$unsorted)) (c_Finite__Set_Ofun__left__comm__idem T_b (tc_fun T_b tc_HOL_Obool) (c_Set_Oinsert T_b)) ) 97.17/107.71 ( tc_Nat_Onat ) 97.17/107.71 ( tc_HOL_Obool ) 97.17/107.71 ( tc_Int_Oint ) 97.17/107.71 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.71 ( t_a ) 97.17/107.71 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.71 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.71 ( tc_Product__Type_Ounit ) 97.17/107.71 ) 97.17/107.71 (instantiation (forall ((V_m_2 $$unsorted) (V_na_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Nat_OSuc V_na_2)) V_m_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_na_2) V_m_2))) ) 97.17/107.71 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), v_n ) 97.17/107.71 ) 97.17/107.71 (instantiation (forall ((V_n $$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))))) ) 97.17/107.71 ( v_n ) 97.17/107.71 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.17/107.71 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.17/107.71 ) 97.17/107.71 (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)) (= (and (not (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP _let_1 V_x_2) V_y_2)) (c_Transitive__Closure_Ortrancl T_b V_r_2)))) (c_Wellfounded_Oacyclic T_b V_r_2)) (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))) ))) 97.17/107.71 ( (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 ) 97.17/107.71 ( (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 ) 97.17/107.71 ( (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))), (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) ) 97.17/107.71 ) 97.17/107.71 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_Fun_Obij__betw T_b T_c V_f_2 _let_0 _let_1) (and (c_Fun_Oinj__on T_b T_c V_f_2 _let_0) (= _let_1 (hAPP (c_Set_Oimage T_b T_c V_f_2) _let_0)))) ))) 97.17/107.72 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.17/107.72 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.17/107.72 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.17/107.72 ( v_mgt__call, t_a, tc_Com_Opname ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (= V_m (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_n)) V_n)) ) 97.17/107.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_n) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) V_m))) ) 97.17/107.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_r_2 $$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)) ) 97.17/107.72 ( (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) (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 ) 97.17/107.72 ( (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 ) 97.17/107.72 ( (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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 ) 97.17/107.72 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_k_2 $$unsorted)) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_k_2))) ) 97.17/107.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_i_2 $$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))) ) 97.17/107.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.17/107.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_OBit0 V_k1_2)) (c_Int_OBit1 V_k2_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_k1_2) V_k2_2))) ) 97.17/107.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.72 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.72 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.72 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.72 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_n $$unsorted)) (not (= V_n (hAPP c_Nat_OSuc V_n))) ) 97.17/107.72 ( v_n ) 97.17/107.72 ) 97.17/107.72 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (and (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_A_2) V_B_2)) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2))) (hBOOL (hAPP (hAPP (c_member (tc_prod _let_0 _let_0)) (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) V_A_2) V_B_2)) (c_Wellfounded_Ofinite__psubset T_b)))) )) 97.17/107.72 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.72 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _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)) ) 97.17/107.72 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _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)) ) 97.17/107.72 ) 97.17/107.72 (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))) ))))) 97.17/107.72 ( tc_Nat_Onat, tc_Nat_Onat ) 97.17/107.72 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.72 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.72 ) 97.17/107.72 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((T_b $$unsorted)) (c_Fun_Obij__betw T_b T_b (c_Fun_Oid T_b) _let_0 _let_0) )) 97.17/107.72 ( tc_Nat_Onat ) 97.17/107.72 ( tc_HOL_Obool ) 97.17/107.72 ( tc_Int_Oint ) 97.17/107.72 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.72 ( t_a ) 97.17/107.72 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.72 ( tc_Product__Type_Ounit ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_k_2 $$unsorted)) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) V_k_2))) ) 97.17/107.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.72 ) 97.17/107.72 (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))) )) 97.17/107.72 ( v_pn, tc_Com_Opname ) 97.17/107.72 ( (hAPP v_mgt__call v_pn), t_a ) 97.17/107.72 ) 97.17/107.72 (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)))) )) 97.17/107.72 ( (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) (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 ) 97.17/107.72 ) 97.17/107.72 (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))) ) 97.17/107.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.72 ) 97.17/107.72 (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)) (= (and (not (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP _let_1 V_x_2) V_y_2)) (c_Transitive__Closure_Ortrancl T_b V_r_2)))) (c_Wellfounded_Owf T_b V_r_2)) (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))) ))) 97.17/107.72 ( (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 ) 97.17/107.72 ( (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 ) 97.17/107.72 ( (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))), (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) ) 97.17/107.72 ) 97.17/107.72 (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))) ) 97.17/107.72 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.72 ) 97.17/107.72 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_na_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_na_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) V_na_2))) )) 97.17/107.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_m $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m) (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Nat_Onat) V_m) V_m))) ) 97.17/107.72 ( (hAPP c_Nat_OSuc v_n) ) 97.17/107.72 ) 97.17/107.72 (instantiation (let ((_let_0 (hAPP (c_Rings_Odvd__class_Odvd tc_Nat_Onat) V_k_2))) (forall ((V_na_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 V_na_2)) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_na_2) V_k_2)))) )) 97.17/107.72 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_m $$unsorted)) (not (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP c_Nat_OSuc V_m))) ) 97.17/107.72 ( v_n ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) V_A_2)) ) 97.17/107.72 ( v_G, t_a ) 97.17/107.72 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a ) 97.17/107.72 ) 97.17/107.72 (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)))) ) 97.17/107.72 ( v_pn, tc_Com_Opname ) 97.17/107.72 ( (hAPP v_mgt__call v_pn), t_a ) 97.17/107.72 ) 97.17/107.72 (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))))) ) 97.17/107.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.72 ( (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)) ) 97.17/107.72 ( (hAPP v_mgt__call v_pn), t_a ) 97.17/107.72 ( (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) ) 97.17/107.72 ( (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) ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Oantisym T_b (c_Relation_OId T_b)) ) 97.17/107.72 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Relation_Osym T_b (hAPP (c_Set_OCollect (tc_prod T_b T_b)) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_b tc_HOL_Obool) V_r_2))) (c_Predicate_Osymp T_b V_r_2)) ) 97.17/107.72 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.72 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= V_a (hAPP (c_Product__Type_Ofst T_a T_b) (hAPP (hAPP (c_Product__Type_OPair T_a T_b) V_a) V_b))) ) 97.17/107.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.17/107.72 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.17/107.72 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.72 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.72 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.72 ) 97.17/107.72 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n)) (hAPP c_Nat_OSuc V_m))) ) 97.17/107.72 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.17/107.72 ) 97.17/107.72 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Otop__class_Otop _let_0))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) _let_1)) ))) 97.17/107.72 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.72 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.73 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.73 ) 97.17/107.73 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_na_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP _let_0 V_m_2)) (hAPP _let_0 V_na_2)))) )) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.73 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.73 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.17/107.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Osingle__valued T_b T_b (c_Relation_OId T_b)) ) 97.17/107.73 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_x_2 $$unsorted)) (= (c_Nat__Transfer_Ois__nat V_x_2) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_x_2))) ) 97.17/107.73 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_n $$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))) ) 97.17/107.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Nat_OSuc V_n)))) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.73 ( v_n ) 97.17/107.73 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.17/107.73 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Int_OBit1 V_k1_2)) (c_Int_OBit0 V_k2_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_k1_2) V_k2_2))) ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.73 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.73 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_A_2 $$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)))) ) 97.17/107.73 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 97.17/107.73 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((T_b $$unsorted)) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 97.17/107.73 ( tc_Nat_Onat ) 97.17/107.73 ( tc_HOL_Obool ) 97.17/107.73 ( tc_Int_Oint ) 97.17/107.73 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.73 ( t_a ) 97.17/107.73 ( tc_Com_Opname ) 97.17/107.73 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.73 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.73 ( tc_Product__Type_Ounit ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_m $$unsorted)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_m)) ) 97.17/107.73 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.17/107.73 ) 97.17/107.73 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (forall ((V_w_2 $$unsorted)) (= (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP _let_0 V_w_2))) (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP _let_0 (c_Int_OBit0 V_w_2))))) )) 97.17/107.73 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.73 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.73 ) 97.17/107.73 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$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)))) )) 97.17/107.73 ( tc_Nat_Onat ) 97.17/107.73 ( tc_HOL_Obool ) 97.17/107.73 ( tc_Int_Oint ) 97.17/107.73 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.73 ( t_a ) 97.17/107.73 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.73 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.73 ( tc_Product__Type_Ounit ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Relation_Otrans T_b (hAPP (c_Set_OCollect (tc_prod T_b T_b)) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_b tc_HOL_Obool) V_r_2))) (c_Predicate_Otransp T_b V_r_2)) ) 97.17/107.73 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.73 ( (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 ) 97.17/107.73 ) 97.17/107.73 (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)))) ))))) 97.17/107.73 ( c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_z_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) (hAPP c_Int_Onat V_z_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2)) V_z_2))) ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.73 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_b (hAPP (c_Product__Type_Osnd T_b T_a) (hAPP (hAPP (c_Product__Type_OPair T_b T_a) V_a) V_b))) ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.17/107.73 ( (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)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.73 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.73 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.73 ) 97.17/107.73 (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))) ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.73 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.73 ( (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) ) 97.17/107.73 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.73 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_B_2))) ) 97.17/107.73 ( v_G, (hAPP v_mgt__call v_pn), t_a ) 97.17/107.73 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.73 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.73 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.73 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.73 ) 97.17/107.73 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP c_Int_Onat V_w_2)) (hAPP c_Int_Onat V_z_2))) (and (hBOOL (hAPP (hAPP _let_0 V_w_2) V_z_2)) (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_2)))) )) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.73 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.73 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_z_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) 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))) ) 97.17/107.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.17/107.73 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_w_2 $$unsorted) (V_z_2 $$unsorted)) (= (and (not (= V_w_2 V_z_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_z_2) V_w_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_z_2) V_w_2))) ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Orefl__on T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) ) 97.17/107.73 ( tc_Nat_Onat ) 97.17/107.73 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.73 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_x_2) V_y_2)) (c_List_Omeasures T_b (c_List_Olist_ONil (tc_fun T_b tc_Nat_Onat)))))) ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.73 ( (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)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.73 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.73 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_x_2 $$unsorted)) (= (not (hBOOL (hAPP c_Nat__Numeral_Oneg V_x_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_x_2))) ) 97.17/107.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_Opred V_k_2)) V_l_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_k_2) V_l_2))) ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.73 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.73 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.73 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.73 ) 97.17/107.73 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_b_2)) (c_Relation_OId T_b))) (= V_b_2 V_a_2)) ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.73 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.73 ( (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)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.73 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.74 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.74 ) 97.17/107.74 (instantiation (forall ((T_b $$unsorted)) (c_Wellfounded_OwfP T_b (hAPP (c_COMBK (tc_fun T_b tc_HOL_Obool) T_b) (hAPP (c_COMBK tc_HOL_Obool T_b) c_fFalse))) ) 97.17/107.74 ( tc_Nat_Onat ) 97.17/107.74 ( tc_HOL_Obool ) 97.17/107.74 ( tc_Int_Oint ) 97.17/107.74 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.74 ( t_a ) 97.17/107.74 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.74 ( tc_Product__Type_Ounit ) 97.17/107.74 ) 97.17/107.74 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (and (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2)) (not (= V_B_2 V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_A_2) V_B_2))) )) 97.17/107.74 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.17/107.74 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a ) 97.17/107.74 ) 97.17/107.74 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (forall ((V_w_2 $$unsorted)) (= (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP _let_0 V_w_2))) (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP _let_0 (c_Int_OBit1 V_w_2))))) )) 97.17/107.74 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.74 ) 97.17/107.74 (instantiation (let ((_let_0 (c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted)) (= _let_0 (hAPP (c_List_Otl T_a) _let_0)) )) 97.17/107.74 ( tc_Nat_Onat ) 97.17/107.74 ( tc_Int_Oint ) 97.17/107.74 ) 97.17/107.74 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Orefl__on T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) (c_Relation_OId T_b)) ) 97.17/107.74 ( tc_Nat_Onat ) 97.17/107.74 ( tc_HOL_Obool ) 97.17/107.74 ( tc_Int_Oint ) 97.17/107.74 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.74 ( t_a ) 97.17/107.74 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.74 ( tc_Product__Type_Ounit ) 97.17/107.74 ) 97.17/107.74 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite (tc_prod T_b T_b)))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP _let_0 (c_Transitive__Closure_Otrancl T_b V_r_2))) (hBOOL (hAPP _let_0 V_r_2))) )) 97.17/107.74 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc))), tc_Nat_Onat ) 97.17/107.74 ) 97.17/107.74 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (forall ((V_A_2 $$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))) )) 97.17/107.74 ( v_G, (hAPP v_mgt__call v_pn), t_a ) 97.17/107.74 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.74 ( (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) ) 97.17/107.74 ( (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) ) 97.17/107.74 ( (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)) ) 97.17/107.74 ) 97.17/107.74 (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_Owf T_b V_r_2) (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)))) ))))) 97.17/107.74 ( (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) (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 ) 97.17/107.74 ( (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 ) 97.17/107.74 ( (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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 ) 97.17/107.74 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.74 ) 97.17/107.74 (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))) ) 97.17/107.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.74 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.74 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.74 ) 97.17/107.74 (instantiation (forall ((T_b $$unsorted)) (c_Wellfounded_Owf (tc_fun T_b tc_HOL_Obool) (c_Wellfounded_Ofinite__psubset T_b)) ) 97.17/107.74 ( tc_Nat_Onat ) 97.17/107.74 ( tc_HOL_Obool ) 97.17/107.74 ( tc_Int_Oint ) 97.17/107.74 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.74 ( t_a ) 97.17/107.74 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.74 ( tc_Product__Type_Ounit ) 97.17/107.74 ) 97.17/107.74 (instantiation (let ((_let_0 (hAPP (c_Product__Type_Ofst (tc_fun (tc_prod T_b T_b) tc_HOL_Obool) (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_Pa_2))) (forall ((V_Pa_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) (= (c_FunDef_Oreduction__pair T_b V_Pa_2) (and (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_Wellfounded_Owf T_b _let_0)))) )) 97.17/107.74 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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))))))) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) _let_3)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) _let_3) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1)))))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.74 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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))))))) (hAPP (hAPP (c_Product__Type_OPair _let_1 _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) _let_3)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) _let_3) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1)))))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.74 ) 97.17/107.74 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (c_Relation_Osym T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (hAPP (c_Relation_Oconverse T_b T_b) V_r_2))) ) 97.17/107.74 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.74 ) 97.17/107.74 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) _let_0)) (= V_A_2 _let_0)) )) 97.17/107.74 ( v_G, t_a ) 97.17/107.74 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a ) 97.17/107.74 ) 97.17/107.74 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (forall ((V_G_2 $$unsorted) (V_F_2 $$unsorted) (T_b $$unsorted)) (= (and (hBOOL (hAPP _let_0 V_F_2)) (hBOOL (hAPP _let_0 V_G_2))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_F_2) V_G_2)))) )) 97.17/107.74 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.74 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.74 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.74 ) 97.17/107.74 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Osym T_b (c_Relation_OId T_b)) ) 97.17/107.74 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.74 ) 97.17/107.74 (instantiation (forall ((V_a_2 $$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))) ) 97.17/107.74 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.17/107.74 ( (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)) ) 97.17/107.74 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.17/107.74 ( (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) ) 97.17/107.74 ( (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) ) 97.17/107.74 ) 97.17/107.74 (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))) )) 97.17/107.74 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.74 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.74 ) 97.17/107.74 (instantiation (forall ((V_z_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP c_Int_Onat V_z_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_z_2))) ) 97.17/107.74 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.74 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.17/107.74 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.74 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.74 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.74 ) 97.17/107.74 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (= (or (hBOOL (hAPP _let_0 V_m_2)) (hBOOL (hAPP _let_0 V_na_2))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m_2) V_na_2)))) )) 97.17/107.74 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.74 ) 97.17/107.74 (instantiation (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_j) V_i)) V_i))) ) 97.17/107.75 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w_2) V_z_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_w_2) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_z_2) (c_Groups_Oone__class_Oone tc_Int_Oint))))) ) 97.17/107.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.75 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.75 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((V_w $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_w) V_w)) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.75 ) 97.17/107.75 (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))))) )) 97.17/107.75 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.17/107.75 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.17/107.75 ( (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) ) 97.17/107.75 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.75 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.75 ) 97.17/107.75 (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_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))) (let ((_let_3 (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat))) (let ((_let_4 (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel))) (let ((_let_5 (c_Set_Oinsert _let_1))) (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_4 (hAPP (hAPP _let_5 (hAPP (hAPP _let_3 V_x_2) V_y_2)) _let_2)))) (hAPP c_Int_OAbs__Integ (hAPP _let_4 (hAPP (hAPP _let_5 (hAPP (hAPP _let_3 V_u_2) V_v_2)) _let_2))))) (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)))) ))))))) 97.17/107.75 ( (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) ) 97.17/107.75 ( (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) ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((V_n $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Nat_OSuc V_n)) V_n))) ) 97.17/107.75 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.75 ( v_n ) 97.17/107.75 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.17/107.75 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.17/107.75 ) 97.17/107.75 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$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))) )) 97.17/107.75 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (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)) ) 97.17/107.75 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.17/107.75 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.17/107.75 ) 97.17/107.75 (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))) ) 97.17/107.75 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.75 ) 97.17/107.75 (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))) )) 97.17/107.75 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.75 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.75 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.75 ) 97.17/107.75 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat))) (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP c_Nat_OSuc V_na_2)) V_m_2)) (not (hBOOL (hAPP (hAPP _let_0 V_m_2) V_na_2)))) )) 97.17/107.75 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.17/107.75 ( v_n, (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.17/107.75 ) 97.17/107.75 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (forall ((V_na_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_na_2) _let_0)) (= _let_0 V_na_2)) )) 97.17/107.75 ( (hAPP c_Nat_OSuc v_n) ) 97.17/107.75 ) 97.17/107.75 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat))) (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP c_Nat_OSuc V_m_2)) V_na_2)) (hBOOL (c_Nat_Onat_Onat__case tc_HOL_Obool c_fFalse (hAPP _let_0 V_m_2) V_na_2))) )) 97.17/107.75 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), v_n ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_na_2)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) V_na_2)) (= V_na_2 V_m_2))) ) 97.17/107.75 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.17/107.75 ) 97.17/107.75 (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))))) ) 97.17/107.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.75 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.75 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.75 ) 97.17/107.75 (instantiation (let ((_let_0 (c_Relation_OId T_b))) (forall ((T_b $$unsorted)) (= _let_0 (hAPP (c_Relation_Oconverse T_b T_b) _let_0)) )) 97.17/107.75 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((T_a $$unsorted)) (hBOOL (hAPP (c_List_Odistinct T_a) (c_List_Olist_ONil T_a))) ) 97.17/107.75 ( tc_Nat_Onat ) 97.17/107.75 ( tc_Int_Oint ) 97.17/107.75 ) 97.17/107.75 (instantiation (let ((_let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n))) (forall ((V_n $$unsorted)) (= _let_0 (hAPP (c_Int_Oring__1__class_Oof__int tc_Int_Oint) _let_0)) )) 97.17/107.75 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.75 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Oantisym T_b (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) ) 97.17/107.75 ( tc_Nat_Onat ) 97.17/107.75 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.75 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.75 ) 97.17/107.75 (instantiation (let ((_let_0 (hAPP (c_Groups_Otimes__class_Otimes tc_Nat_Onat) V_m))) (forall ((V_m $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m) (hAPP _let_0 (hAPP _let_0 V_m)))) )) 97.17/107.75 ( (hAPP c_Nat_OSuc v_n) ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((V_Z_2 $$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)))) ) 97.17/107.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.17/107.75 ) 97.17/107.75 (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_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))) (let ((_let_3 (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat))) (let ((_let_4 (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel))) (let ((_let_5 (c_Set_Oinsert _let_1))) (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_4 (hAPP (hAPP _let_5 (hAPP (hAPP _let_3 V_x_2) V_y_2)) _let_2)))) (hAPP c_Int_OAbs__Integ (hAPP _let_4 (hAPP (hAPP _let_5 (hAPP (hAPP _let_3 V_u_2) V_v_2)) _let_2)))))) ))))))) 97.17/107.75 ( (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) ) 97.17/107.75 ( (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) ) 97.17/107.75 ( (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) ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((V_k $$unsorted)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_k)) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.75 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((T_b $$unsorted)) (c_Wellfounded_Owf T_b (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) ) 97.17/107.75 ( tc_Nat_Onat ) 97.17/107.75 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.75 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.75 ) 97.17/107.75 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2)) (hBOOL (hAPP (hAPP (c_member _let_0) V_A_2) (hAPP (c_Set_OPow T_b) V_B_2)))) )) 97.17/107.75 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.17/107.75 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a ) 97.17/107.75 ) 97.17/107.75 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= V_A_2 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (c_Set_Oinsert T_b)) (c_Orderings_Obot__class_Obot _let_0)))) )) 97.17/107.75 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.17/107.75 ) 97.17/107.75 (instantiation (let ((_let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m))) (forall ((V_m $$unsorted)) (= _let_0 (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) _let_0)) )) 97.17/107.75 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.75 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Otrans T_b (c_Relation_OId T_b)) ) 97.17/107.75 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((V_n $$unsorted)) (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n)))) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (and (c_Relation_Orefl__on T_b V_A_2 V_r_2) (c_Relation_Otrans T_b V_r_2) (c_Relation_Osym T_b V_r_2)) (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) ) 97.17/107.75 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.75 ) 97.17/107.75 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$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)) )) 97.17/107.75 ( tc_Nat_Onat ) 97.17/107.75 ( tc_HOL_Obool ) 97.17/107.75 ( tc_Int_Oint ) 97.17/107.75 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.75 ( t_a ) 97.17/107.75 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.75 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.75 ( tc_Product__Type_Ounit ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((V_z_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP c_Int_Onat V_z_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z_2))) ) 97.17/107.75 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.75 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.17/107.75 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.75 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.75 ) 97.17/107.75 (instantiation (forall ((V_u_2 $$unsorted)) (= V_u_2 (hAPP (c_Finite__Set_Ocard tc_Nat_Onat) (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) V_u_2))) ) 97.17/107.76 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (class_Nat_Osize (tc_prod T_2 T_1)) ) 97.17/107.76 ( tc_Nat_Onat, tc_Nat_Onat ) 97.17/107.76 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.76 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (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))) (c_Wellfounded_OwfP T_b V_r_2)) ) 97.17/107.76 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.76 ( (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 ) 97.17/107.76 ) 97.17/107.76 (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)) ) 97.17/107.76 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.76 ( (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 ) 97.17/107.76 ) 97.17/107.76 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (forall ((V_z $$unsorted)) (= V_z (hAPP _let_0 (hAPP _let_0 V_z))) )) 97.17/107.76 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.17/107.76 ) 97.17/107.76 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) (c_Orderings_Otop__class_Otop _let_0))) )) 97.17/107.76 ( v_G, t_a ) 97.17/107.76 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) (hAPP c_Nat_OSuc V_na_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_na_2))) ) 97.17/107.76 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_n) (hAPP c_Nat_OSuc V_n))) ) 97.17/107.76 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.76 ( v_n ) 97.17/107.76 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.17/107.76 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.17/107.76 ) 97.17/107.76 (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)))) ) 97.17/107.76 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((T_b $$unsorted)) (c_Relation_Otrans (tc_fun T_b tc_HOL_Obool) (c_Wellfounded_Ofinite__psubset T_b)) ) 97.17/107.76 ( tc_Nat_Onat ) 97.17/107.76 ( tc_HOL_Obool ) 97.17/107.76 ( tc_Int_Oint ) 97.17/107.76 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.76 ( t_a ) 97.17/107.76 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.76 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.76 ( tc_Product__Type_Ounit ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Relation_Oantisym T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (c_Relation_OId T_b))) (c_Relation_Oantisym T_b V_r_2)) ) 97.17/107.76 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.76 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.76 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.76 ) 97.17/107.76 (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))) ))) 97.17/107.76 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (hBOOL (hAPP V_A_2 V_x_2))) ) 97.17/107.76 ( v_U, v_pn, tc_Com_Opname ) 97.17/107.76 ( v_G, (hAPP v_mgt__call v_pn), t_a ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n)) V_m)) ) 97.17/107.76 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= V_f_2 (hAPP (c_Fun_Ocomp T_b T_c T_b V_f_2) (c_Fun_Oid T_b))) ) 97.17/107.76 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.17/107.76 ) 97.17/107.76 (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))) ) 97.17/107.76 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_na_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_na_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_na_2)))) ) 97.17/107.76 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.76 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.76 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.76 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.76 ) 97.17/107.76 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((T_b $$unsorted)) (= _let_0 (hAPP (c_Set_Oimage T_b T_b (c_Fun_Oid T_b)) _let_0)) )) 97.17/107.76 ( tc_Nat_Onat ) 97.17/107.76 ( tc_HOL_Obool ) 97.17/107.76 ( tc_Int_Oint ) 97.17/107.76 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.76 ( t_a ) 97.17/107.76 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.76 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.76 ( tc_Product__Type_Ounit ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_n $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP c_Nat_OSuc V_n))) ) 97.17/107.76 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.76 ( v_n ) 97.17/107.76 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.17/107.76 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (c_Groups_Ozero__class_Ozero T_a) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) V_a))) ) 97.17/107.76 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.17/107.76 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 97.17/107.76 ) 97.17/107.76 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless T_a) V_z))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) (not (hBOOL (hAPP _let_0 V_y))) (hBOOL (hAPP _let_0 V_x))) )) 97.17/107.76 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_S_2 $$unsorted)) (= (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Int_Oint) B_x) V_S_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) B_x))) ) (c_Nat__Transfer_Onat__set V_S_2)) ) 97.17/107.76 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_na_2 $$unsorted)) (= (= V_na_2 (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_na_2)) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.76 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.76 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.76 ) 97.17/107.76 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (let ((_let_2 (c_Orderings_Otop__class_Otop (tc_fun T_d tc_HOL_Obool)))) (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Obij__betw T_b T_c V_f_2 _let_0 _let_1)) (not (c_Fun_Obij__betw T_c T_d V_g_2 _let_1 _let_2)) (c_Fun_Obij__betw T_b T_d (hAPP (c_Fun_Ocomp T_c T_d T_b V_g_2) V_f_2) _let_0 _let_2)) )))) 97.17/107.76 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, c_Code__Numeral_Onat__of, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral ) 97.17/107.76 ( c_Int_Onat, tc_Nat_Onat, (c_Groups_Oabs__class_Oabs tc_Int_Oint), tc_Int_Oint, tc_Int_Oint ) 97.17/107.76 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral, c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.17/107.76 ) 97.17/107.76 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (c_Finite__Set_Ofold1 T_b (c_Groups_Otimes__class_Otimes T_b)))) (let ((_let_3 (c_Finite__Set_Ofinite T_b))) (forall ((V_B_2 $$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 _let_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_b) (hAPP _let_2 V_A_2)) (hAPP _let_2 V_B_2)))) ))))) 97.17/107.76 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.76 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.76 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.76 ) 97.17/107.76 (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 (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_Orderings_Olinorder 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_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_0 (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMax T_b V_B_2)))) ))))) 97.17/107.76 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.76 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.76 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.76 ) 97.17/107.76 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (hAPP c_Nat_OSuc (hAPP (hAPP _let_0 V_m) V_n)) (hAPP (hAPP _let_0 (hAPP c_Nat_OSuc V_m)) V_n)) )) 97.17/107.76 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.76 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_a) (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a)))) ) 97.17/107.76 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.76 ( (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.17/107.76 ( v_G, (tc_fun t_a tc_HOL_Obool) ) 97.17/107.76 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.17/107.76 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.17/107.76 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((T_b $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_c) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP V_f_2 V_x_2)) (hAPP (c_Set_Oimage T_c T_b V_f_2) V_A_2)))) ) 97.17/107.76 ( t_a, v_U, tc_Com_Opname, v_pn, v_mgt__call ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) (= V_y (hAPP (hAPP (c_Orderings_Oord__class_Omin T_a) V_x) V_y))) ) 97.17/107.76 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.76 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.17/107.76 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.76 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.17/107.76 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.17/107.76 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.17/107.76 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.76 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.76 ) 97.17/107.76 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= V_x_2 (c_Big__Operators_Olattice_OSup__fin T_b (c_Orderings_Oord__class_Omax T_b) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 97.17/107.76 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.76 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.76 ( (hAPP v_mgt__call v_pn), t_a ) 97.17/107.76 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.76 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.76 ) 97.17/107.76 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (c_COMBC T_b _let_0 tc_HOL_Obool) (c_member T_b)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBS T_b tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_b) c_fdisj) (hAPP _let_1 V_A_2))) (hAPP _let_1 V_B_2))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)) ))) 97.17/107.76 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.77 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.77 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.17/107.77 ) 97.17/107.77 (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)) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.77 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.77 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.77 ) 97.17/107.77 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_u_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_0) V_u_2))) (= (hAPP (c_Set_Oimage tc_Nat_Onat tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint)) (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) (hAPP c_Int_Onat V_u_2))) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Int_Oint _let_0) V_u_2))) )) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.17/107.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.77 ) 97.17/107.77 (instantiation (forall ((V_na_2 $$unsorted) (V_Pa_2 $$unsorted)) (or (hBOOL (hAPP V_Pa_2 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (not (hBOOL (hAPP V_Pa_2 V_na_2))) (not (forall ((B_k $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_k) V_na_2))) (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)))))) ))) ) 97.17/107.77 ( 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)) ) 97.17/107.77 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 97.17/107.77 ( c_fequal, (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_Onat ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert tc_Nat_Onat) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (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))) ) 97.17/107.77 ( c_Int_Onat, (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)) ) 97.17/107.77 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.17/107.77 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 97.17/107.77 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) ) 97.17/107.77 ( v_U, (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) ) 97.17/107.77 ( v_U, (hAPP (c_member tc_Com_Opname) v_pn) ) 97.17/107.77 ( v_U, (c_Finite__Set_Ofinite tc_Com_Opname) ) 97.17/107.77 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (c_Finite__Set_Ocard t_a) ) 97.17/107.77 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) v_G) ) 97.17/107.77 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (c_Groups_Ominus__class_Ominus tc_Nat_Onat) ) 97.17/107.77 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Nat_OSuc v_n)) ) 97.17/107.77 ( v_n, c_Nat_OSuc ) 97.17/107.77 ( (hAPP c_Nat_OSuc v_n), (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) ) 97.17/107.77 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U))) ) 97.17/107.77 ( v_G, (c_Finite__Set_Ocard t_a) ) 97.17/107.77 ( v_G, (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) ) 97.17/107.77 ( v_G, (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (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) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( 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)) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (hAPP (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) ) 97.17/107.77 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) ) 97.17/107.77 ( v_pn, v_mgt__call ) 97.17/107.77 ( v_pn, (c_member tc_Com_Opname) ) 97.17/107.77 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Nat_OSuc ) 97.17/107.77 ( (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) ) 97.17/107.77 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (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) ) 97.17/107.77 ( (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), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (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))) ) 97.17/107.77 ( (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))) ) 97.17/107.77 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (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))) ) 97.17/107.77 ( (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))) ) 97.17/107.77 ( (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))) ) 97.17/107.77 ( (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_Set_Oinsert (tc_prod _let_0 _let_0))) ) 97.17/107.77 ( (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))), (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))) ) 97.17/107.77 ( (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))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0))))))) ) 97.17/107.77 ( (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))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0))))))) ) 97.17/107.77 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.17/107.77 ( 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)))) ) 97.17/107.77 ( (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))) ) 97.17/107.77 ( (hAPP v_mgt__call v_pn), (c_Set_Oinsert t_a) ) 97.17/107.77 ( (hAPP v_mgt__call v_pn), (c_member t_a) ) 97.17/107.77 ( c_fTrue, (c_COMBK tc_HOL_Obool tc_Nat_Onat) ) 97.17/107.77 ( c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (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_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (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 ) 97.17/107.77 ( c_fFalse, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 97.17/107.77 ( (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_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 97.17/107.77 ( (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)) ) 97.17/107.77 ( (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 ) 97.17/107.77 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Finite__Set_Ocard tc_Product__Type_Ounit) ) 97.17/107.77 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) ) 97.17/107.77 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), (c_Finite__Set_Ocard tc_HOL_Obool) ) 97.17/107.77 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (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))) ) 97.17/107.77 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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))) ) 97.17/107.77 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (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))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))))) ) 97.17/107.77 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.77 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 97.17/107.77 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 97.17/107.77 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 97.17/107.77 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.17/107.77 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), c_Int_Onat ) 97.17/107.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), c_Nat__Numeral_Oneg ) 97.17/107.77 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 97.17/107.77 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.17/107.77 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 97.17/107.77 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 97.17/107.77 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.17/107.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (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)) ) 97.17/107.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), c_Int_Onat ) 97.17/107.77 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 97.17/107.77 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.17/107.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (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)) ) 97.17/107.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), c_Int_Onat ) 97.17/107.77 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.17/107.77 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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))) ) 97.17/107.77 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (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))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))))) ) 97.17/107.78 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.17/107.78 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 97.17/107.78 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.17/107.78 ) 97.17/107.78 (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)))) ) 97.17/107.78 ( tc_Nat_Onat ) 97.17/107.78 ( tc_Int_Oint ) 97.17/107.78 ( tc_Code__Numeral_Ocode__numeral ) 97.17/107.78 ( t_a ) 97.17/107.78 ( tc_Com_Opname ) 97.17/107.78 ) 97.17/107.78 (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))) ) 97.17/107.78 ( tc_Nat_Onat, tc_HOL_Obool ) 97.17/107.78 ( tc_HOL_Obool, tc_HOL_Obool ) 97.17/107.78 ( tc_Int_Oint, tc_HOL_Obool ) 97.17/107.78 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.17/107.78 ( t_a, tc_HOL_Obool ) 97.17/107.78 ( (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 ) 97.17/107.78 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.17/107.78 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.17/107.78 ) 97.17/107.78 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_u_2) V_l_2) (hAPP (c_Finite__Set_Ocard tc_Nat_Onat) (c_SetInterval_Oord__class_OgreaterThanAtMost tc_Nat_Onat V_l_2 V_u_2))) ) 97.17/107.78 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.17/107.78 ) 97.17/107.78 (instantiation (forall ((V_Pa_2 $$unsorted) (V_y_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) V_y_2) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (not (forall ((B_x $$unsorted)) (hBOOL (hAPP V_Pa_2 (hAPP c_Code__Numeral_Onat__of B_x))) )) (hBOOL (hAPP V_Pa_2 V_y_2))) ) 97.17/107.78 ( c_Nat_OSuc, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.78 ( c_Nat_OSuc, v_n ) 97.17/107.78 ( c_Nat_OSuc, (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.17/107.78 ( c_Nat_OSuc, (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.17/107.78 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.78 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.17/107.78 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.78 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.78 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.78 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.78 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.78 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.78 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.78 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.78 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.78 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.78 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.78 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.78 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.78 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.78 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.78 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.78 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.78 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.78 ( 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)))))) ) 97.17/107.78 ( 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))))) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.78 ( c_Int_Onat, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.78 ( c_Int_Onat, (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.17/107.78 ( c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.78 ( c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.78 ( c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.78 ( (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat), (hAPP c_Nat_OSuc v_n) ) 97.17/107.78 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.78 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.78 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.78 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.78 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.78 ( (c_Groups_Ominus__class_Ominus tc_Nat_Onat), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.17/107.78 ( (c_Finite__Set_Ocard t_a), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U) ) 97.17/107.78 ( (c_Finite__Set_Ocard t_a), v_G ) 97.17/107.78 ( v_mgt__call, v_pn ) 97.17/107.78 ( (c_Set_Oimage tc_Com_Opname t_a v_mgt__call), v_U ) 97.17/107.78 ( (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U))), (hAPP c_Nat_OSuc v_n) ) 97.17/107.78 ( (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 97.17/107.78 ( c_Nat__Numeral_Oneg, (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.17/107.78 ( c_Nat__Numeral_Oneg, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool), c_fequal ) 97.17/107.78 ( (c_member tc_Com_Opname), v_pn ) 97.17/107.78 ( (c_Nat_Osize__class_Osize tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool), (c_Orderings_Oord__class_Oless tc_Nat_Onat) ) 97.17/107.78 ( (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) ) 97.17/107.78 ( (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) ) 97.17/107.78 ( (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 ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (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) ) 97.17/107.78 ( (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) ) 97.17/107.78 ( (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) ) 97.17/107.78 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.78 ( (c_Finite__Set_Ofinite tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 97.17/107.78 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.78 ( (c_Set_Oinsert t_a), (hAPP v_mgt__call v_pn) ) 97.17/107.78 ( (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_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.17/107.78 ( (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_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (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))) ) 97.17/107.78 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.78 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.78 ( (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))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)) ) 97.17/107.78 ( (c_Set_Oinsert tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (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 ) 97.17/107.78 ( (hAPP (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) ) 97.17/107.78 ( (c_Finite__Set_Ofinite tc_Int_Oint), (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 97.17/107.78 ( (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)), v_G ) 97.17/107.78 ( (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G) ) 97.17/107.78 ( (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 97.17/107.78 ( (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) ) 97.17/107.78 ( (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))))) ) 97.17/107.78 ( (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)))) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.78 ( (c_member t_a), (hAPP v_mgt__call v_pn) ) 97.17/107.78 ( (hAPP (c_member t_a) (hAPP v_mgt__call v_pn)), v_G ) 97.17/107.78 ( (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) ) 97.17/107.78 ( (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) ) 97.17/107.78 ( (c_COMBK tc_HOL_Obool tc_Nat_Onat), c_fTrue ) 97.17/107.78 ( (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.78 ( (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.78 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.17/107.78 ( (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) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (c_Nat_Osize__class_Osize tc_HOL_Obool), c_fTrue ) 97.17/107.78 ( (c_Nat_Osize__class_Osize tc_HOL_Obool), c_fFalse ) 97.17/107.78 ( (c_Finite__Set_Ocard tc_Product__Type_Ounit), (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)) ) 97.17/107.78 ( (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)), v_G ) 97.17/107.78 ( (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G)), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U) ) 97.17/107.78 ( (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)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.17/107.78 ( (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)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.17/107.78 ( (c_Finite__Set_Ocard tc_HOL_Obool), (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (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 ) 97.17/107.78 ( (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat), (c_Groups_Oabs__class_Oabs tc_Int_Oint) ) 97.17/107.78 ( (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)) ) 97.17/107.78 ( (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) ) 97.17/107.78 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 97.17/107.78 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0))))))), (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))))) ) 97.17/107.78 ( (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))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))))), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))) ) 97.17/107.78 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0))))))), (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))))) ) 97.17/107.78 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), c_Int_Onat ) 97.17/107.78 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.78 ( (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))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))))), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))) ) 97.17/107.79 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.79 ) 97.17/107.79 (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))) ))) 97.17/107.79 ( v_pn, v_U, tc_Com_Opname ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2)) (= (= V_y_2 V_x_2) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)))) ) 97.17/107.79 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.17/107.79 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.17/107.79 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.17/107.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.79 ) 97.17/107.79 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (let ((_let_1 (hAPP _let_0 V_u))) (let ((_let_2 (hAPP _let_0 V_v))) (let ((_let_3 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) _let_1) _let_2))) (let ((_let_4 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) _let_1) _let_2)))) (forall ((V_v $$unsorted) (V_u $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (not (class_Int_Onumber T_b)) (and (or _let_4 (= _let_1 _let_3)) (or (not _let_4) (= _let_2 _let_3)))) )))))) 97.17/107.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.17/107.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.17/107.79 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.79 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.17/107.79 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.79 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.79 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_b) V_a))) (= V_a V_b) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_b) V_a))) ) 97.17/107.79 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.17/107.79 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.17/107.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((V_j_2 $$unsorted) (V_i_2 $$unsorted)) (= (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_j_2) V_i_2)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_j_2)) (= (c_List_Olist_ONil tc_Nat_Onat) (c_List_Oupt V_i_2 V_j_2))) ) 97.17/107.79 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_x))) ) 97.17/107.79 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.17/107.79 ) 97.17/107.79 (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)))) ) 97.17/107.79 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.17/107.79 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.17/107.79 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.17/107.79 ) 97.17/107.79 (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_Int_Onat (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_z)) (hAPP c_Nat_OSuc (hAPP c_Int_Onat V_z)))) ) 97.17/107.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.79 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.17/107.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.79 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.17/107.79 ) 97.17/107.79 (instantiation (let ((_let_0 (hAPP (c_Set_Oinsert T_b) V_x_2))) (let ((_let_1 (c_Big__Operators_Olinorder__class_OMax T_b (hAPP _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 _let_0 (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 $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or (not _let_4) (= V_x_2 _let_1)) (or _let_4 (= _let_1 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMax T_b _let_3)))))) )))))) 97.17/107.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.17/107.79 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.79 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.17/107.79 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.79 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((V_Pa_2 $$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))) ) 97.17/107.79 ( (c_member tc_Com_Opname), tc_Com_Opname, v_pn ) 97.17/107.79 ( (c_member t_a), t_a, (hAPP v_mgt__call v_pn) ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((V_i $$unsorted) (V_d $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_d) V_i)) (= (c_Lazy__Sequence_Oappend tc_Int_Oint (hAPP (c_Lazy__Sequence_Osingle tc_Int_Oint) V_i) (c_Lazy__Sequence_Osmall__lazy_H V_d (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_i) (c_Groups_Oone__class_Oone tc_Int_Oint)))) (c_Lazy__Sequence_Osmall__lazy_H V_d V_i))) ) 97.17/107.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.79 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.79 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((V_i $$unsorted) (V_d $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_d) V_i))) (= (c_Lazy__Sequence_Osmall__lazy_H V_d V_i) (c_Lazy__Sequence_Oempty tc_Int_Oint))) ) 97.17/107.79 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.79 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.79 ) 97.17/107.79 (instantiation (let ((_let_0 (tc_fun T_b T_c))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Enum_Oenum T_b)) (not (class_Orderings_Oorder T_c)) (= (and (hBOOL (hAPP (c_Enum_Oenum__class_Oenum__ex T_b) (hAPP (hAPP (c_COMBB tc_HOL_Obool tc_HOL_Obool T_b) c_fNot) (hAPP (hAPP (c_COMBS T_b T_c tc_HOL_Obool) (hAPP (hAPP (c_COMBB T_c (tc_fun T_c tc_HOL_Obool) T_b) c_fequal) V_f_2)) V_g_2)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_f_2) V_g_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_f_2) V_g_2)))) )) 97.17/107.79 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a, tc_HOL_Obool ) 97.17/107.79 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a, tc_HOL_Obool ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (class_Lattices_Osemilattice__sup T_b)) (= (c_Orderings_Oord__class_Omax T_b) (c_Lattices_Osemilattice__sup__class_Osup T_b))) ) 97.17/107.79 ( tc_HOL_Obool ) 97.17/107.79 ( tc_Int_Oint ) 97.17/107.79 ( tc_Code__Numeral_Ocode__numeral ) 97.17/107.79 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.17/107.79 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (= (hAPP c_Nat_OSuc V_y) (hAPP c_Nat_OSuc V_x))) (= V_y V_x)) ) 97.17/107.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), v_n ) 97.17/107.79 ( v_n, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.17/107.79 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), v_n ) 97.17/107.79 ) 97.17/107.79 (instantiation (let ((_let_0 (hAPP (c_Set_Oinsert T_b) V_a_2))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (hAPP _let_0 (c_Orderings_Obot__class_Obot _let_1))) V_A_2) (hAPP _let_0 V_A_2)) ))) 97.17/107.79 ( v_G, (hAPP v_mgt__call v_pn), t_a ) 97.17/107.79 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.79 ( (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) ) 97.17/107.79 ( (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) ) 97.17/107.79 ( (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)) ) 97.17/107.79 ) 97.17/107.79 (instantiation (let ((_let_0 (hAPP (c_Set_Oinsert T_b) V_x_2))) (let ((_let_1 (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP _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 _let_0 (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 $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or (not _let_4) (= V_x_2 _let_1)) (or _let_4 (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_x_2) (c_Big__Operators_Olattice__class_OInf__fin T_b _let_3)))))) )))))) 97.17/107.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.17/107.79 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.79 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.17/107.79 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.79 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.79 ) 97.17/107.79 (instantiation (let ((_let_0 (hAPP (c_Set_Oinsert T_b) V_a_2))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_1) V_C_2))) (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (V_C_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP _let_2 (hAPP (hAPP (c_COMBB _let_1 _let_1 T_c) _let_0) V_B_2)) (hAPP _let_0 (hAPP _let_2 V_B_2))) )))) 97.17/107.79 ( (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 ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Nat_Osize T_b)) (c_FunDef_Ois__measure T_b (c_Nat_Osize__class_Osize T_b))) ) 97.17/107.79 ( tc_Nat_Onat ) 97.17/107.79 ( tc_HOL_Obool ) 97.17/107.79 ( tc_Code__Evaluation_Oterm ) 97.17/107.79 ( tc_Code__Numeral_Ocode__numeral ) 97.17/107.79 ( tc_Com_Ocom ) 97.17/107.79 ( tc_Product__Type_Ounit ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Finite__Set_Ofinite T_1)) (not (class_Finite__Set_Ofinite T_2)) (class_Finite__Set_Ofinite (tc_prod T_2 T_1))) ) 97.17/107.79 ( tc_Nat_Onat, tc_Nat_Onat ) 97.17/107.79 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.79 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.17/107.79 ) 97.17/107.79 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Nat_Osemiring__1__class_ONats T_b))) (forall ((V_b_2 $$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_b_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_b_2)) _let_1))) ))) 97.17/107.79 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Orderings_Oord__class_Omin T_b)) V_a_2) V_A_2))) ) 97.17/107.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.17/107.79 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.17/107.79 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.17/107.79 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.79 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.17/107.79 ) 97.17/107.79 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_c) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2))) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)))) ) 97.17/107.79 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.17/107.79 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.17/107.79 ( v_mgt__call, t_a, v_U, tc_Com_Opname ) 97.17/107.79 ) 97.17/107.79 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (forall ((B_x $$unsorted)) (= B_x (hAPP V_f_2 (hAPP (c_Hilbert__Choice_Oinv__into T_c T_b _let_0 V_f_2) B_x))) ) (= (hAPP (c_Set_Oimage T_c T_b V_f_2) _let_0) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) )) 97.17/107.79 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.17/107.79 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.17/107.79 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.17/107.79 ( v_mgt__call, t_a, tc_Com_Opname ) 97.17/107.79 ) 97.17/107.79 (instantiation (let ((_let_0 (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (let ((_let_2 (hAPP _let_1 V_A_2))) (let ((_let_3 (hAPP _let_1 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or (not _let_0) (= _let_2 _let_3)) (or _let_0 (= _let_3 (hAPP c_Nat_OSuc _let_2))))) ))))) 97.17/107.79 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.17/107.79 ( v_pn, v_U, tc_Com_Opname ) 97.17/107.79 ( (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)) ) 97.17/107.80 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.17/107.80 ( (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_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) ) 97.17/107.80 ( (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_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) ) 97.17/107.80 ) 97.17/107.80 (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))) ) 97.17/107.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.80 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.80 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.17/107.80 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.80 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.80 ) 97.17/107.80 (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_Oupto V_i V_j) (c_List_Olist_ONil tc_Int_Oint))) ) 97.17/107.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.17/107.80 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.17/107.80 ) 97.17/107.80 (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 $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= _let_1 (hAPP (hAPP _let_0 V_x_2) _let_1))) ))) 97.34/107.80 ( v_pn, v_U, tc_Com_Opname ) 97.34/107.80 ) 97.34/107.80 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (forall ((V_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) _let_0) V_n))) (= V_n (hAPP c_Nat_OSuc (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_n) (hAPP c_Nat_OSuc _let_0))))) )) 97.34/107.80 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.34/107.80 ) 97.34/107.80 (instantiation (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) (c_Complete__Lattice_OSup__class_OSup T_b V_A_2)))) ) 97.34/107.80 ( v_U, v_pn, tc_Com_Opname ) 97.34/107.80 ) 97.34/107.80 (instantiation (forall ((V_i_2 $$unsorted) (V_j_2 $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_j_2) V_i_2)) (= (hAPP (hAPP (c_Set_Oinsert tc_Int_Oint) V_i_2) (c_SetInterval_Oord__class_OatLeastAtMost tc_Int_Oint (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_i_2) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_j_2)) (c_SetInterval_Oord__class_OatLeastAtMost tc_Int_Oint V_i_2 V_j_2))) ) 97.34/107.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.34/107.80 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.34/107.80 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.34/107.80 ) 97.34/107.80 (instantiation (forall ((V_i_2 $$unsorted) (V_j_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_j_2) V_i_2))) (= (c_SetInterval_Oord__class_OatLeastAtMost tc_Int_Oint V_i_2 V_j_2) (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)))) ) 97.34/107.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.34/107.80 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.34/107.80 ) 97.34/107.80 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Power_Opower T_b)) (= (c_Power_Opower_Opower T_b (c_Groups_Oone__class_Oone T_b) (c_Groups_Otimes__class_Otimes T_b)) (c_Power_Opower__class_Opower T_b))) ) 97.34/107.80 ( tc_Nat_Onat ) 97.34/107.80 ( tc_Int_Oint ) 97.34/107.80 ( tc_Code__Numeral_Ocode__numeral ) 97.34/107.80 ) 97.34/107.80 (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 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_b_2)) (hAPP _let_1 V_a_2))) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2)))) ))) 97.34/107.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.34/107.80 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.34/107.80 ) 97.34/107.80 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$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_B_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2))) )) 97.34/107.80 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.34/107.80 ) 97.34/107.80 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (c_Orderings_Obot__class_Obot T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (c_Orderings_Otop__class_Otop T_a)))) ) 97.34/107.80 ( tc_Nat_Onat ) 97.34/107.80 ( tc_HOL_Obool ) 97.34/107.80 ( tc_Int_Oint ) 97.34/107.80 ( (tc_fun tc_HOL_Obool tc_HOL_Obool) ) 97.34/107.80 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.34/107.80 ( (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 97.34/107.80 ( (tc_fun tc_Int_Oint tc_HOL_Obool) ) 97.34/107.80 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.34/107.80 ( (tc_fun tc_Product__Type_Ounit tc_HOL_Obool) ) 97.34/107.80 ) 97.34/107.80 (instantiation (let ((_let_0 (c_Transitive__Closure_Otrancl T_b V_r_2))) (forall ((V_r_2 $$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))) )) 97.34/107.80 ( (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) (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 ) 97.34/107.80 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.34/107.80 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.34/107.80 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.34/107.80 ) 97.34/107.80 (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)) (= (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2) _let_0) (and (= V_B_2 _let_0) (= V_A_2 _let_0))) )) 97.34/107.80 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.34/107.80 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.34/107.80 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.34/107.80 ) 97.34/107.80 (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))) (= (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)))) (c_Nitpick_Ocard_H T_b V_A_2))) ))) 97.34/107.80 ( v_U, tc_Com_Opname ) 97.34/107.80 ) 97.34/107.80 (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))) ) 97.34/107.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.34/107.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.34/107.80 ) 97.34/107.80 (instantiation (forall ((V_m $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m) V_m)) ) 97.34/107.80 ( (hAPP c_Nat_OSuc v_n) ) 97.34/107.80 ) 97.34/107.80 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool))) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_Oimage T_c T_b V_f_2) V_A_2))) ) 97.34/107.80 ( v_U, v_mgt__call, t_a, tc_Com_Opname ) 97.34/107.80 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.34/107.80 ) 97.34/107.80 (instantiation (let ((_let_0 (tc_prod T_b T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (tc_fun T_b _let_0))) (forall ((T_b $$unsorted)) (= (c_Relation_OId T_b) (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)))))) )))) 97.34/107.80 ( tc_Nat_Onat ) 97.34/107.80 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.34/107.80 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.34/107.80 ( (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)) ) 97.34/107.80 ) 97.34/107.80 (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 $$unsorted) (V_z $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_z))) (not (hBOOL (hAPP _let_0 V_z_H))) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP c_Int_Onat V_z)) (hAPP c_Int_Onat V_z_H)) (hAPP c_Int_Onat (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_z) V_z_H)))) )) 97.34/107.80 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.34/107.80 ) 97.34/107.80 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_l_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_l_2 V_u_2)) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_u_2)))) ) 97.34/107.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.34/107.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.34/107.80 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.34/107.80 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.34/107.80 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.34/107.80 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.34/107.80 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.34/107.80 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.34/107.80 ) 97.34/107.80 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$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))) )) 97.34/107.80 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.34/107.80 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (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)) ) 97.34/107.80 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.34/107.80 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.35/107.80 ) 97.35/107.80 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_x) V_y))) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_x))) (= V_y V_x)) )) 97.35/107.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.80 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.80 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.80 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.35/107.80 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.35/107.80 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.35/107.80 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.35/107.80 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.80 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.80 ) 97.35/107.80 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$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 (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP _let_1 V_A_2)) (hAPP _let_1 V_B_2)) (hAPP _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_2) V_A_2) V_B_2)))) )))) 97.35/107.80 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.80 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.81 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.81 ( (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 ) 97.35/107.81 ) 97.35/107.81 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_b) V_a))) (not (hBOOL (hAPP (hAPP _let_0 V_a) V_b)))) )) 97.35/107.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.81 ) 97.35/107.81 (instantiation (forall ((V_n $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Ozero__class_Ozero T_a)) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) V_n)))) ) 97.35/107.81 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.35/107.81 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.35/107.81 ) 97.35/107.81 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Oorder T_1)) (class_Orderings_Oorder (tc_fun T_2 T_1))) ) 97.35/107.81 ( tc_Nat_Onat, tc_HOL_Obool ) 97.35/107.81 ( tc_HOL_Obool, tc_HOL_Obool ) 97.35/107.81 ( tc_Int_Oint, tc_HOL_Obool ) 97.35/107.81 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.35/107.81 ( t_a, tc_HOL_Obool ) 97.35/107.81 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.35/107.81 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.35/107.81 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.35/107.81 ) 97.35/107.81 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) _let_1)))) (let ((_let_3 (= _let_1 _let_2))) (let ((_let_4 (c_Big__Operators_Olattice_OInf__fin T_b (c_Orderings_Oord__class_Omin T_b) V_A_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (and (or _let_3 (= (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 _let_2)) _let_4)) (or (not _let_3) (= V_x_2 _let_4))))) )))))) 97.35/107.81 ( v_pn, v_U, tc_Com_Opname ) 97.35/107.81 ) 97.35/107.81 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Nat_Onat))) (let ((_let_1 (hBOOL (hAPP (hAPP V_Pa_2 V_na_2) V_m_2)))) (let ((_let_2 (not _let_1))) (forall ((V_Pa_2 $$unsorted) (V_na_2 $$unsorted) (V_m_2 $$unsorted)) (or (and (hBOOL (hAPP (hAPP _let_0 V_m_2) V_na_2)) _let_2) (and (= V_na_2 V_m_2) _let_2) (and (hBOOL (hAPP (hAPP _let_0 V_na_2) V_m_2)) _let_2) _let_1) )))) 97.35/107.81 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.81 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.81 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.81 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.35/107.81 ( (c_Groups_Ominus__class_Ominus tc_Nat_Onat), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.35/107.81 ( (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 ) 97.35/107.81 ( (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) ) 97.35/107.81 ( (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) ) 97.35/107.81 ( (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) ) 97.35/107.81 ( (c_Set_Oinsert t_a), (hAPP v_mgt__call v_pn), v_G ) 97.35/107.81 ( (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_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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))))) ) 97.35/107.81 ( (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_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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))))) ) 97.35/107.81 ( (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))) ) 97.35/107.81 ( (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)) ) 97.35/107.81 ( (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) ) 97.35/107.81 ( (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) ) 97.35/107.81 ( (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))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 97.35/107.81 ( (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)) ) 97.35/107.81 ( (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) ) 97.35/107.81 ( (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U) ) 97.35/107.81 ( (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) ) 97.35/107.81 ( (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)) ) 97.35/107.81 ( (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)) ) 97.35/107.81 ( (c_member t_a), (hAPP v_mgt__call v_pn), v_G ) 97.35/107.81 ( (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)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))) ) 97.35/107.81 ( (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)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))) ) 97.35/107.81 ( (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 ) 97.35/107.81 ( (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) ) 97.35/107.81 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), c_Int_Onat, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.81 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), c_Int_Onat, (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.81 ) 97.35/107.81 (instantiation (let ((_let_0 (c_Relation_ODomain T_b T_b))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (hAPP _let_0 (c_Transitive__Closure_Otrancl T_b V_r_2)) (hAPP _let_0 V_r_2)) )) 97.35/107.81 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc))), tc_Nat_Onat ) 97.35/107.81 ) 97.35/107.81 (instantiation (forall ((V_k_2 $$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)))) ) 97.35/107.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.35/107.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.81 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.35/107.81 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.35/107.81 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.35/107.81 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.81 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.81 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.81 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.81 ) 97.35/107.81 (instantiation (forall ((V_B_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_B_2) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBS T_b tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_b) c_fdisj) (hAPP (hAPP (c_COMBC T_b T_b tc_HOL_Obool) c_fequal) V_a_2))) (hAPP (hAPP (c_COMBC T_b (tc_fun T_b tc_HOL_Obool) tc_HOL_Obool) (c_member T_b)) V_B_2)))) ) 97.35/107.81 ( v_G, (hAPP v_mgt__call v_pn), t_a ) 97.35/107.81 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.81 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.81 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.81 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.81 ) 97.35/107.81 (instantiation (forall ((V_b $$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))) ) 97.35/107.81 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.81 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.81 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.35/107.81 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.35/107.81 ) 97.35/107.81 (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 $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_1)))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP _let_0 V_A_2)) (c_Groups_Oone__class_Oone tc_Nat_Onat)))) ))) 97.35/107.81 ( v_pn, v_U, tc_Com_Opname ) 97.35/107.81 ) 97.35/107.81 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$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))) (hBOOL (hAPP (hAPP (c_member _let_0) V_A_2) (hAPP (c_Set_OPow T_b) V_B_2)))) )) 97.35/107.81 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.35/107.81 ) 97.35/107.81 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Ozero__class_Ozero T_a)) (c_Groups_Oone__class_Oone T_a)))) ) 97.35/107.81 ( tc_Nat_Onat ) 97.35/107.81 ( tc_Code__Numeral_Ocode__numeral ) 97.35/107.81 ( (tc_fun t_a tc_HOL_Obool) ) 97.35/107.81 ) 97.35/107.81 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_a) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (c_Groups_Oone__class_Oone T_a))))) ) 97.35/107.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.81 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.81 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.81 ) 97.35/107.81 (instantiation (let ((_let_0 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_d_2) V_i_2)))) (let ((_let_1 (c_Lazy__Sequence_Osmall__lazy_H V_d_2 V_i_2))) (forall ((V_i_2 $$unsorted) (V_d_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Lazy__Sequence_Osmall__lazy_H__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) V_d_2) V_i_2)))) (and (or _let_0 (= (c_Lazy__Sequence_Oappend tc_Int_Oint (hAPP (c_Lazy__Sequence_Osingle tc_Int_Oint) V_i_2) (c_Lazy__Sequence_Osmall__lazy_H V_d_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_i_2) (c_Groups_Oone__class_Oone tc_Int_Oint)))) _let_1)) (or (not _let_0) (= (c_Lazy__Sequence_Oempty tc_Int_Oint) _let_1)))) ))) 97.35/107.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.81 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.81 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.81 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.81 ) 97.35/107.81 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (and (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2)) (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2))) (= V_y_2 V_x_2))) )) 97.35/107.81 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.81 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.81 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.81 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.35/107.81 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.35/107.81 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.35/107.81 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.35/107.81 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.35/107.81 ( (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)))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.35/107.81 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.35/107.82 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.82 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.82 ) 97.35/107.82 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m) V_n)) (= (c_Divides_Odiv__class_Omod tc_Nat_Onat V_m V_n) (c_Divides_Odiv__class_Omod tc_Nat_Onat (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n) V_n))) ) 97.35/107.82 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.35/107.82 ) 97.35/107.82 (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))) ) 97.35/107.82 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.82 ( (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 ) 97.35/107.82 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 97.35/107.82 ( (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 ) 97.35/107.82 ) 97.35/107.82 (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_OgreaterThan T_b) V_x_2)) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) (hAPP _let_0 V_x_2)))) )) 97.35/107.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.82 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.82 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.82 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.82 ) 97.35/107.82 (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))) ) 97.35/107.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.82 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.82 ) 97.35/107.82 (instantiation (forall ((V_M_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_M_2))) (not (forall ((B_h $$unsorted)) (not (c_Fun_Obij__betw tc_Nat_Onat T_b B_h (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Finite__Set_Ocard T_b) V_M_2)) V_M_2)) ))) ) 97.35/107.82 ( v_U, tc_Com_Opname ) 97.35/107.82 ) 97.35/107.82 (instantiation (let ((_let_0 (c_Set_Oinsert t_a))) (let ((_let_1 (hAPP _let_0 (hAPP v_mgt__call V_pn_2)))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun t_a tc_HOL_Obool)))) (forall ((V_G_2 $$unsorted) (V_pn_2 $$unsorted)) (or (not (v_P (hAPP _let_1 V_G_2) (hAPP (hAPP _let_0 (v_mgt (c_Option_Othe tc_Com_Ocom (c_Com_Obody V_pn_2)))) _let_2))) (v_P V_G_2 (hAPP _let_1 _let_2))) )))) 97.35/107.82 ( v_G, v_pn ) 97.35/107.82 ) 97.35/107.82 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 _let_1) (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2))) (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)))) ))) 97.35/107.82 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.82 ) 97.35/107.82 (instantiation (let ((_let_0 (tc_fun T_b T_c))) (let ((_let_1 (c_Orderings_Oord__class_Oless__eq _let_0))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Orderings_Oord T_c)) (= (and (hBOOL (hAPP (hAPP _let_1 V_f_2) V_g_2)) (not (hBOOL (hAPP (hAPP _let_1 V_g_2) V_f_2)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_f_2) V_g_2)))) ))) 97.35/107.82 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a, tc_HOL_Obool ) 97.35/107.82 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a, tc_HOL_Obool ) 97.35/107.82 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a, tc_HOL_Obool ) 97.35/107.82 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a, tc_HOL_Obool ) 97.35/107.82 ) 97.35/107.82 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_1 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w))) (forall ((V_w $$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 (c_Product__Type_Osnd tc_Int_Oint tc_Int_Oint) (c_Divides_OposDivAlg _let_0 _let_1)) (c_Divides_Odiv__class_Omod tc_Int_Oint _let_0 _let_1))) ))) 97.35/107.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.82 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.82 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.82 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.82 ) 97.35/107.82 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Oone__class_Oone T_a)) (c_Groups_Ozero__class_Ozero T_a))))) ) 97.35/107.82 ( tc_Nat_Onat ) 97.35/107.82 ( tc_Int_Oint ) 97.35/107.82 ( tc_Code__Numeral_Ocode__numeral ) 97.35/107.82 ( (tc_fun t_a tc_HOL_Obool) ) 97.35/107.82 ) 97.35/107.82 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)))) ) 97.35/107.82 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.35/107.82 ) 97.35/107.82 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Groups_Ouminus T_1)) (class_Groups_Ouminus (tc_fun T_2 T_1))) ) 97.35/107.82 ( tc_Nat_Onat, tc_HOL_Obool ) 97.35/107.82 ( tc_HOL_Obool, tc_HOL_Obool ) 97.35/107.82 ( tc_Int_Oint, tc_HOL_Obool ) 97.35/107.82 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.35/107.82 ( t_a, tc_HOL_Obool ) 97.35/107.82 ( (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 ) 97.35/107.82 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.35/107.82 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.35/107.82 ) 97.35/107.82 (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)))) )) 97.35/107.82 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.82 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.82 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.82 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.82 ) 97.35/107.82 (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 _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_c) tc_HOL_Obool)) V_A_2) V_B_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP _let_0 V_A_2)) (hAPP _let_0 V_B_2))) )) 97.35/107.82 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _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) ) 97.35/107.82 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _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) ) 97.35/107.82 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.82 ) 97.35/107.82 (instantiation (let ((_let_0 (c_Set_Oinsert T_b))) (forall ((V_b_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_b_2) (c_Complete__Lattice_OSup__class_OSup T_b (hAPP (hAPP _let_0 V_a_2) (hAPP (hAPP _let_0 V_b_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))))) )) 97.35/107.82 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.35/107.82 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.35/107.82 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.35/107.82 ) 97.35/107.82 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (c_Finite__Set_Ocard (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_OPow T_b) V_A_2)) (hAPP (hAPP (c_Power_Opower__class_Opower tc_Nat_Onat) (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)))) ) 97.35/107.82 ( v_U, tc_Com_Opname ) 97.35/107.82 ) 97.35/107.82 (instantiation (let ((_let_0 (c_Set_Oimage T_c T_b V_f_2))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (= (c_Orderings_Otop__class_Otop _let_2) (hAPP _let_0 (c_Orderings_Otop__class_Otop _let_1)))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_1) (hAPP (c_Set_Ovimage T_c T_b V_f_2) V_B_2)) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_2) V_B_2) (hAPP _let_0 V_A_2)))) )))) 97.35/107.82 ( v_U, (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), v_mgt__call, t_a, tc_Com_Opname ) 97.35/107.82 ) 97.35/107.82 (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))) ) 97.35/107.82 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.82 ) 97.35/107.82 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (and (c_Relation_Orefl__on T_b V_A_2 V_r_2) (c_Relation_Osym T_b V_r_2) (c_Relation_Otrans T_b V_r_2))) ) 97.35/107.82 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.82 ) 97.35/107.82 (instantiation (forall ((V_b $$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)))) ) 97.35/107.82 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.35/107.82 ( (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 ) 97.35/107.82 ) 97.35/107.82 (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)) (= (c_Complete__Lattice_OInf__class_OInf _let_0 (hAPP (c_Set_Oimage T_c _let_0 V_B_2) V_A_2)) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) V_B_2)) )) 97.35/107.82 ( (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 ) 97.35/107.82 ) 97.35/107.82 (instantiation (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_d $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (hAPP (c_Fun_Ocomp T_c T_b T_d V_f_2) V_g_2) V_x_2) (hAPP V_f_2 (hAPP V_g_2 V_x_2))) ) 97.35/107.82 ( (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 ) 97.35/107.82 ) 97.35/107.82 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite (tc_prod T_b T_b)) V_r_2))) (= (c_Wellfounded_Owf T_b V_r_2) (c_Wellfounded_Oacyclic T_b V_r_2))) ) 97.35/107.82 ( (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) (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 ) 97.35/107.82 ( (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 ) 97.35/107.82 ( (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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 ) 97.35/107.82 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.82 ) 97.35/107.82 (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))) ) 97.35/107.82 ( tc_Nat_Onat, tc_HOL_Obool ) 97.35/107.82 ( tc_HOL_Obool, tc_HOL_Obool ) 97.35/107.82 ( tc_Int_Oint, tc_HOL_Obool ) 97.35/107.82 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.35/107.82 ( t_a, tc_HOL_Obool ) 97.35/107.82 ( (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 ) 97.35/107.82 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.35/107.82 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.35/107.82 ) 97.35/107.82 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m) V_n)) (= V_m (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n)))) ) 97.35/107.82 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.35/107.82 ) 97.35/107.82 (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))) )) 97.35/107.82 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _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) ) 97.35/107.82 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _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) ) 97.35/107.82 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.82 ) 97.35/107.82 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Oord T_1)) (class_Orderings_Oord (tc_fun T_2 T_1))) ) 97.35/107.82 ( tc_Nat_Onat, tc_HOL_Obool ) 97.35/107.82 ( tc_HOL_Obool, tc_HOL_Obool ) 97.35/107.82 ( tc_Int_Oint, tc_HOL_Obool ) 97.35/107.82 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.35/107.82 ( t_a, tc_HOL_Obool ) 97.35/107.82 ( (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 ) 97.35/107.82 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.35/107.82 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.35/107.82 ) 97.35/107.82 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_R_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) (hAPP (c_Relation_OImage T_b T_b V_R_2) V_A_2)))) (= V_A_2 (c_Orderings_Obot__class_Obot _let_0))) )) 97.35/107.83 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool))))), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.83 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_2 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_3 (hAPP _let_2 V_v_H_2))) (let ((_let_4 (hBOOL (hAPP c_Nat__Numeral_Oneg _let_3)))) (let ((_let_5 (hAPP _let_2 V_v_2))) (let ((_let_6 (hBOOL (hAPP c_Nat__Numeral_Oneg _let_5)))) (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (= (and (or _let_6 (and (or _let_4 (= V_v_H_2 V_v_2)) (or (not _let_4) (= _let_0 _let_5)))) (or (not _let_6) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_3) _let_0)))) (= (hAPP _let_1 V_v_H_2) (hAPP _let_1 V_v_2))) )))))))) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.83 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.83 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.83 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.83 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted)) (= _let_0 (c_List_Oremdups T_a _let_0)) )) 97.35/107.83 ( tc_Nat_Onat ) 97.35/107.83 ( tc_Int_Oint ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat))) (forall ((V_na_2 $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Set_Oimage tc_Nat_Onat tc_Nat_Onat c_Nat_OSuc) (hAPP _let_0 V_na_2))) (hAPP _let_0 (hAPP c_Nat_OSuc V_na_2))) )) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.83 ( v_n ) 97.35/107.83 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.35/107.83 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (tc_fun T_d tc_HOL_Obool))) (let ((_let_2 (tc_fun T_d (tc_fun T_b tc_HOL_Obool)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (T_d $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_c _let_2 _let_0) (hAPP (hAPP (c_COMBB _let_1 (tc_fun _let_2 _let_0) T_c) _let_0) V_B_2)) V_C_2)) (hAPP (hAPP _let_0 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_1) V_A_2) V_B_2)) V_C_2))) )))) 97.35/107.83 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.83 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.83 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.83 ) 97.35/107.83 (instantiation (forall ((V_n $$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)))) ) 97.35/107.83 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.35/107.83 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.35/107.83 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (hAPP _let_0 V_m)) (hAPP _let_0 V_n)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m) V_n))) )) 97.35/107.83 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_Nat_Osize__class_Osize tc_Nat_Onat))) (forall ((V_nat $$unsorted)) (= (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))) (hAPP _let_0 (hAPP c_Nat_OSuc V_nat))) )) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.83 ( v_n ) 97.35/107.83 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.35/107.83 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.35/107.83 ) 97.35/107.83 (instantiation (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_na_2)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m_2) V_na_2))) ) 97.35/107.83 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.35/107.83 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.35/107.83 ) 97.35/107.83 (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)))) )) 97.35/107.83 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP _let_0 V_B_2)) (hAPP _let_0 V_A_2)))) (= V_A_2 V_B_2)) )) 97.35/107.83 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) V_n))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (= _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) _let_0))) )) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.35/107.83 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 97.35/107.83 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.35/107.83 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.83 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v))))) (let ((_let_1 (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v)))) (forall ((V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (and (or (not _let_0) (= (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_v) _let_1)) (or _let_0 (= _let_1 (c_Groups_Ozero__class_Ozero T_a))))) ))) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.35/107.83 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.83 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.35/107.83 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.35/107.83 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.35/107.83 ) 97.35/107.83 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (= V_x (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (c_Groups_Osgn__class_Osgn T_a V_x)) (hAPP (c_Groups_Oabs__class_Oabs T_a) V_x)))) ) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (c_Fun_Oid _let_0) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c _let_0) (c_Product__Type_OPair T_b T_c))) )) 97.35/107.83 ( tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.83 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.83 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.35/107.83 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Oring__char__0 T_b)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) (c_Int_Oring__1__class_OInts T_b)))) (= (= V_a_2 _let_0) (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2)))) )) 97.35/107.83 ( v_pn, tc_Com_Opname ) 97.35/107.83 ( (hAPP v_mgt__call v_pn), t_a ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_c))) (forall ((V_A_2 $$unsorted) (T_c $$unsorted) (V_I_2 $$unsorted) (T_b $$unsorted)) (or (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP _let_0 (hAPP V_A_2 B_x)))) (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) V_I_2)))) ) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_b (tc_fun T_c tc_HOL_Obool)) V_I_2) V_A_2)))) )) 97.35/107.83 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v_H))) (forall ((V_v_H $$unsorted)) (or (hBOOL (hAPP c_Nat__Numeral_Oneg _let_0)) (= (hAPP c_Int_Onat (c_Divides_Odiv__class_Omod tc_Int_Oint (c_Groups_Oone__class_Oone tc_Int_Oint) _let_0)) (c_Divides_Odiv__class_Omod tc_Nat_Onat (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v_H)))) )) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.83 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.83 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.83 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) (forall ((V_v_H $$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)))) )) 97.35/107.83 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.83 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.83 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_Groups_Ominus__class_Ominus T_b))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oab__group__add T_b)) (not (= (hAPP (hAPP _let_0 V_a_2) V_b_2) (hAPP (hAPP _let_0 V_c_2) V_d_2))) (= (= V_b_2 V_a_2) (= V_d_2 V_c_2))) )) 97.35/107.83 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.35/107.83 ) 97.35/107.83 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_k) (c_Groups_Oone__class_Oone tc_Int_Oint)) (c_Int_Opred V_k)) ) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.83 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.83 ) 97.35/107.83 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__sup__class_Osup T_b)) V_x_2) V_A_2) (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) ) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.35/107.83 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.83 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.35/107.83 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.83 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.83 ) 97.35/107.83 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (c_Finite__Set_Ocard T_b) V_A_2) (hAPP (hAPP (hAPP (c_Finite__Set_Ofold__image tc_Nat_Onat T_b (c_Groups_Oplus__class_Oplus tc_Nat_Onat)) (hAPP (c_COMBK tc_Nat_Onat T_b) (c_Groups_Oone__class_Oone tc_Nat_Onat))) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_A_2))) ) 97.35/107.83 ( v_U, tc_Com_Opname ) 97.35/107.83 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.35/107.83 ( v_G, t_a ) 97.35/107.83 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 97.35/107.83 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 97.35/107.83 ) 97.35/107.83 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) V_A_2))) ) 97.35/107.83 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.35/107.83 ( v_G, t_a ) 97.35/107.83 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.35/107.83 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.35/107.83 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 97.35/107.83 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 97.35/107.83 ) 97.35/107.83 (instantiation (forall ((T_b $$unsorted) (T_c $$unsorted)) (= (c_Product__Type_Oapsnd T_c T_c T_b (c_Fun_Oid T_c)) (c_Fun_Oid (tc_prod T_b T_c))) ) 97.35/107.83 ( tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.83 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.83 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ogroup__add T_b)) (= (= V_b_2 (hAPP _let_0 V_a_2)) (= V_a_2 (hAPP _let_0 V_b_2)))) )) 97.35/107.83 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.83 ( (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (or (= V_y_2 V_x_2) (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2))) (not (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2))))) )) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.83 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.83 ) 97.35/107.83 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (c_Groups_Ozero__class_Ozero T_a)) V_a))) ) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.83 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.83 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 97.35/107.83 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (tc_fun T_b T_c))) (forall ((T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool))))) )) 97.35/107.83 ( tc_HOL_Obool, tc_Nat_Onat ) 97.35/107.83 ( tc_HOL_Obool, tc_HOL_Obool ) 97.35/107.83 ( tc_HOL_Obool, tc_Int_Oint ) 97.35/107.83 ( tc_HOL_Obool, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.83 ( tc_HOL_Obool, t_a ) 97.35/107.83 ( tc_HOL_Obool, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.83 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.83 ( tc_HOL_Obool, tc_Product__Type_Ounit ) 97.35/107.83 ) 97.35/107.83 (instantiation (forall ((V_nat_H_2 $$unsorted) (V_nat_2 $$unsorted)) (= (= (hAPP c_Nat_OSuc V_nat_2) (hAPP c_Nat_OSuc V_nat_H_2)) (= V_nat_H_2 V_nat_2)) ) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), v_n ) 97.35/107.83 ( v_n, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.83 ( v_n, (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_u_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_u_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_u_2) (c_Orderings_Obot__class_Obot _let_0))) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_u_2))) )) 97.35/107.83 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.83 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.83 ( (hAPP v_mgt__call v_pn), t_a ) 97.35/107.83 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.83 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (forall ((V_y $$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))) )) 97.35/107.83 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.35/107.83 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.35/107.83 ) 97.35/107.83 (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))) (= (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (c_Set_Oimage T_b T_b _let_0) V_S_2)) (hAPP _let_0 (c_Big__Operators_Olinorder__class_OMax T_b V_S_2)))) )) 97.35/107.83 ( v_U, tc_Com_Opname ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2))) )) 97.35/107.83 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_n))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) V_m))) (= (c_Divides_Odivmod__nat V_m V_n) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (hAPP c_Nat_OSuc (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Nat_Onat) _let_0) V_n))) (c_Divides_Odiv__class_Omod tc_Nat_Onat _let_0 V_n)))) )) 97.35/107.83 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.35/107.83 ) 97.35/107.83 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Odistrib__lattice T_1)) (class_Lattices_Odistrib__lattice (tc_fun T_2 T_1))) ) 97.35/107.83 ( tc_Nat_Onat, tc_HOL_Obool ) 97.35/107.83 ( tc_HOL_Obool, tc_HOL_Obool ) 97.35/107.83 ( tc_Int_Oint, tc_HOL_Obool ) 97.35/107.83 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.35/107.83 ( t_a, tc_HOL_Obool ) 97.35/107.83 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.35/107.83 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.35/107.83 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.35/107.83 ) 97.35/107.83 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (c_Finite__Set_Ofinite T_b))) (forall ((V_B_2 $$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))) (= (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_0) V_A_2) V_B_2)))) )))) 97.35/107.84 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.84 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.84 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.84 ) 97.35/107.84 (instantiation (let ((_let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a))) (let ((_let_1 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_a) (c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oabs__if T_a)) (and (or _let_1 (= V_a _let_0)) (or (not _let_1) (= _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a))))) ))) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.84 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.84 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.84 ) 97.35/107.84 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP (c_Finite__Set_Ofold1 T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b)) V_A_2)) V_a_2))) ) 97.35/107.84 ( v_pn, v_U, tc_Com_Opname ) 97.35/107.84 ) 97.35/107.84 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (forall ((V_B_2 $$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)))) )))) 97.35/107.84 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.84 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.84 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.84 ) 97.35/107.84 (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)))) )) 97.35/107.84 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.84 ( v_pn, tc_Com_Opname ) 97.35/107.84 ( (hAPP v_mgt__call v_pn), t_a ) 97.35/107.84 ) 97.35/107.84 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_y_2) V_x_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2))))) ) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.84 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.35/107.84 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.35/107.84 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.35/107.84 ) 97.35/107.84 (instantiation (let ((_let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v)))) (let ((_let_1 (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v))))) (forall ((V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (and (or _let_1 (= _let_0 (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_v))) (or (not _let_1) (= _let_0 (c_Groups_Ozero__class_Ozero T_a))))) ))) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.35/107.84 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.84 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.35/107.84 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.35/107.84 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.35/107.84 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.35/107.84 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.35/107.84 ) 97.35/107.84 (instantiation (let ((_let_0 (c_Set_Oimage T_c T_b V_f_2))) (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$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 _let_0 V_A_2))) (not (forall ((B_AA $$unsorted)) (or (not (= V_B_2 (hAPP _let_0 B_AA))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_c tc_HOL_Obool)) B_AA) V_A_2)))) ))) )) 97.35/107.84 ( v_U, v_mgt__call, tc_Com_Opname, v_G, t_a ) 97.35/107.84 ( v_U, v_mgt__call, tc_Com_Opname, (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a ) 97.35/107.84 ) 97.35/107.84 (instantiation (forall ((V_b $$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)))) ) 97.35/107.84 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.35/107.84 ( (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 ) 97.35/107.84 ) 97.35/107.84 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (forall ((V_w_2 $$unsorted)) (= (hAPP (hAPP (c_HOL_OLet tc_Nat_Onat tc_Nat_Onat) (hAPP _let_0 V_w_2)) (hAPP (hAPP (c_COMBS tc_Nat_Onat tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oplus__class_Oplus tc_Nat_Onat)) (c_COMBI tc_Nat_Onat))) (hAPP _let_0 (c_Int_OBit0 V_w_2))) )) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.84 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.84 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.84 ) 97.35/107.84 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) V_r_2) (c_Transitive__Closure_Ortrancl T_b V_r_2)) (c_Transitive__Closure_Otrancl T_b V_r_2)) ) 97.35/107.84 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc))), tc_Nat_Onat ) 97.35/107.84 ) 97.35/107.84 (instantiation (forall ((V_l_2 $$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)) ) 97.35/107.84 ( (c_List_Olist_ONil tc_Int_Oint) ) 97.35/107.84 ) 97.35/107.84 (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))) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_x) V_y) (c_Nat__Transfer_Otsub V_x V_y))) ) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.84 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.84 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.84 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.84 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.84 ) 97.35/107.84 (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))) ) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.84 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.84 ) 97.35/107.84 (instantiation (forall ((V_na_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_na_2)) (c_Nat_Osemiring__1__class_ONats T_b)))) ) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.35/107.84 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 97.35/107.84 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.35/107.84 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.84 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.84 ) 97.35/107.84 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_k_2 $$unsorted) (V_f_2 $$unsorted) (V_na_2 $$unsorted)) (or (not (forall ((B_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_i) V_na_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_na_2)))) (not (forall ((B_i $$unsorted)) (or (not (= V_k_2 (hAPP V_f_2 B_i))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) B_i) V_na_2)))) ))) )) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_OAbs__Integ, (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))) ) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.84 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.84 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.35/107.84 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_Int_OAbs__Integ, (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))) ) 97.35/107.84 ) 97.35/107.84 (instantiation (forall ((T_b $$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))) ) 97.35/107.84 ( tc_Nat_Onat ) 97.35/107.84 ( tc_HOL_Obool ) 97.35/107.84 ( tc_Int_Oint ) 97.35/107.84 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.84 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.35/107.84 ( t_a ) 97.35/107.84 ( (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 97.35/107.84 ( (tc_fun tc_Int_Oint tc_HOL_Obool) ) 97.35/107.84 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.84 ( (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)) ) 97.35/107.84 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.84 ( tc_Product__Type_Ounit ) 97.35/107.84 ) 97.35/107.84 (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) V_b) (hAPP (hAPP _let_0 V_a_H) V_b_H))) (and (= V_a_H V_a) (= V_b_H V_b))) )) 97.35/107.84 ( (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 ) 97.35/107.84 ( (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_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.84 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.35/107.84 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.35/107.85 ) 97.35/107.85 (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 $$unsorted)) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Ozero__class_Ozero T_a)) V_a))) (not (hBOOL (hAPP _let_0 V_b))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)))) )) 97.35/107.85 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.85 ) 97.35/107.85 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_r_2 $$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)))) )) 97.35/107.85 ( 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) ) 97.35/107.85 ) 97.35/107.85 (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 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (= V_A_2 (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP _let_0 (c_Orderings_Obot__class_Obot _let_1)))))) ))) 97.35/107.85 ( v_U, v_pn, tc_Com_Opname ) 97.35/107.85 ) 97.35/107.85 (instantiation (forall ((V_x_2 $$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_OMin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)))) ) 97.35/107.85 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.35/107.85 ) 97.35/107.85 (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)))) ) 97.35/107.85 ( v_U, tc_Com_Opname ) 97.35/107.85 ) 97.35/107.85 (instantiation (forall ((V_c_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= (hAPP (hAPP (c_Set_Oinsert T_c) V_c_2) (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool))) (hAPP (c_Set_Oimage T_b T_c (hAPP (c_COMBK T_c T_b) V_c_2)) V_A_2))) ) 97.35/107.85 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, v_U, v_pn, tc_Com_Opname ) 97.35/107.85 ) 97.35/107.85 (instantiation (let ((_let_0 (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2))) (forall ((V_x_2 $$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))) )) 97.35/107.85 ( v_pn, v_U, tc_Com_Opname ) 97.35/107.85 ) 97.35/107.85 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 V_A_2)) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 97.35/107.85 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.35/107.85 ) 97.35/107.85 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Obounded__lattice T_1)) (class_Lattices_Obounded__lattice (tc_fun T_2 T_1))) ) 97.35/107.85 ( tc_Nat_Onat, tc_HOL_Obool ) 97.35/107.85 ( tc_HOL_Obool, tc_HOL_Obool ) 97.35/107.85 ( tc_Int_Oint, tc_HOL_Obool ) 97.35/107.85 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.35/107.85 ( t_a, tc_HOL_Obool ) 97.35/107.85 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.35/107.85 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.35/107.85 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.35/107.85 ) 97.35/107.85 (instantiation (forall ((V_na_2 $$unsorted)) (= (hAPP (c_List_Oset tc_Nat_Onat) (c_List_Oupt (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP c_Nat_OSuc V_na_2))) (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_na_2)) ) 97.35/107.85 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.85 ( v_n ) 97.35/107.85 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.35/107.85 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.35/107.85 ) 97.35/107.85 (instantiation (forall ((V_w $$unsorted)) (= (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w) (hAPP (c_Int_Oring__1__class_Oof__int tc_Int_Oint) V_w)) ) 97.35/107.85 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.85 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.85 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.85 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.85 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.85 ) 97.35/107.85 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (not (forall ((B_n $$unsorted)) (not (= V_z_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_w_2) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) )) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_w_2) V_z_2))) ) 97.35/107.85 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.85 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.85 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.85 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.85 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.85 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.85 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.85 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.85 ) 97.35/107.85 (instantiation (forall ((V_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_n))) (= V_n (hAPP c_Nat_OSuc (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_n) (c_Groups_Oone__class_Oone tc_Nat_Onat))))) ) 97.35/107.85 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.35/107.85 ) 97.35/107.85 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP _let_0 V_v)) (hAPP _let_0 V_w)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_v) V_w)))) )) 97.35/107.85 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.35/107.85 ) 97.35/107.85 (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 $$unsorted)) (or (not (hBOOL (hAPP _let_0 B_A))) (not (hBOOL (hAPP (hAPP (c_member T_b) B_a) B_A))) (not (hBOOL (hAPP V_Pa_2 B_A))) (hBOOL (hAPP V_Pa_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus (tc_fun T_b tc_HOL_Obool)) B_A) (hAPP (hAPP (c_Set_Oinsert T_b) B_a) _let_1))))) )) (hBOOL (hAPP V_Pa_2 _let_1))) ))) 97.35/107.85 ( (c_Set_Oimage tc_Com_Opname t_a v_mgt__call), v_U, tc_Com_Opname ) 97.35/107.85 ) 97.35/107.85 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (c_Groups_Ominus__class_Ominus tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (= _let_0 (hAPP (hAPP _let_1 V_m) V_n))) (not (= _let_0 (hAPP (hAPP _let_1 V_n) V_m))) (= V_n V_m)) ))) 97.35/107.85 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.35/107.85 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.35/107.85 ) 97.35/107.85 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (c_List_Olinorder__class_Osorted T_a (c_List_Olist_ONil T_a))) ) 97.35/107.85 ( tc_Nat_Onat ) 97.35/107.85 ( tc_Int_Oint ) 97.35/107.85 ( tc_Code__Numeral_Ocode__numeral ) 97.35/107.85 ) 97.35/107.85 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (c_Orderings_Obot__class_Obot _let_2))) (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_3) (not (hBOOL (hAPP _let_0 V_B_2))) (= V_B_2 _let_3) (not (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_2) V_A_2) V_B_2) _let_3)) (= (c_Big__Operators_Olattice_OInf__fin T_b _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_2) V_A_2) V_B_2)) (hAPP (hAPP _let_1 (c_Big__Operators_Olattice_OInf__fin T_b _let_1 V_A_2)) (c_Big__Operators_Olattice_OInf__fin T_b _let_1 V_B_2)))) ))))) 97.35/107.85 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.85 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.85 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.85 ) 97.35/107.85 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Oorder T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_x))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_z) V_y))) (hBOOL (hAPP (hAPP _let_0 V_z) V_x))) )) 97.35/107.85 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.85 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.85 ) 97.35/107.85 (instantiation (forall ((V_x_2 $$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)))) ) 97.35/107.85 ( v_pn, v_U, tc_Com_Opname ) 97.35/107.85 ) 97.35/107.85 (instantiation (forall ((V_k $$unsorted)) (= V_k (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_k)) ) 97.35/107.85 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.85 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.85 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.85 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.85 ) 97.35/107.85 (instantiation (forall ((V_l_2 $$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)))) ) 97.35/107.85 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.85 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.85 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.85 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.85 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.85 ) 97.35/107.85 (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 $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) (hAPP _let_1 V_k_2)) (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) V_k_2) (c_Orderings_Obot__class_Obot _let_0))) (hAPP _let_1 (hAPP c_Nat_OSuc V_k_2))) ))) 97.35/107.85 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.85 ( v_n ) 97.35/107.85 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.35/107.85 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.35/107.85 ) 97.35/107.85 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_x) V_y)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (hAPP _let_0 V_x)) (hAPP _let_0 V_y))) )) 97.35/107.85 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.35/107.85 ) 97.35/107.85 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (c_Finite__Set_Ofinite T_b))) (forall ((V_B_2 $$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) (= (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)) (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)))) )))) 97.35/107.85 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.85 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.85 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.85 ) 97.35/107.85 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_l_2) V_u_2))) (= (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_l_2) V_u_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP (hAPP (c_Set_Oinsert T_b) V_l_2) (c_Orderings_Obot__class_Obot _let_0))) (c_SetInterval_Oord__class_OgreaterThanLessThan T_b V_l_2 V_u_2)))) )) 97.35/107.85 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.85 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.85 ) 97.35/107.85 (instantiation (forall ((V_a_2 $$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_Omax T_b)) V_a_2) V_A_2) (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)))) ) 97.35/107.85 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.35/107.85 ( (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)) ) 97.35/107.85 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.35/107.85 ( (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) ) 97.35/107.85 ( (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) ) 97.35/107.85 ) 97.35/107.85 (instantiation (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oab__semigroup__mult T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2)) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_a_2) V_A_2) (hAPP (c_Finite__Set_Ofold1 T_b _let_0) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)))) )) 97.35/107.86 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.35/107.86 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.86 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.35/107.86 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.86 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.86 ) 97.35/107.86 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Orderings_Otop__class_Otop T_b) (c_Complete__Lattice_OSup__class_OSup T_b (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))))) ) 97.35/107.86 ( tc_Nat_Onat ) 97.35/107.86 ( tc_HOL_Obool ) 97.35/107.86 ( tc_Int_Oint ) 97.35/107.86 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.86 ( t_a ) 97.35/107.86 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.86 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.86 ( tc_Product__Type_Ounit ) 97.35/107.86 ) 97.35/107.86 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (c_Orderings_Oord__class_Oless__eq 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_0 (c_Groups_Ozero__class_Ozero T_a)) B_z))) (not (hBOOL (hAPP (hAPP _let_0 B_z) (c_Groups_Oone__class_Oone T_a)))) (hBOOL (hAPP (hAPP _let_1 (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) B_z) V_x)) V_y))) )) (hBOOL (hAPP (hAPP _let_1 V_x) V_y))) ))) 97.35/107.86 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.35/107.86 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.35/107.86 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.86 ) 97.35/107.86 (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_Lazy__Sequence_Osmall__lazy_H__rel))) (let ((_let_2 (hAPP V_Pa_2 B_d))) (forall ((V_Pa_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP _let_1 (hAPP (hAPP _let_0 V_a0_2) V_a1_2)))) (not (forall ((B_d $$unsorted) (B_i $$unsorted)) (or (not (hBOOL (hAPP _let_1 (hAPP (hAPP _let_0 B_d) B_i)))) (and (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) B_d) B_i))) (not (hBOOL (hAPP _let_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) B_i) (c_Groups_Oone__class_Oone tc_Int_Oint)))))) (hBOOL (hAPP _let_2 B_i))) )) (hBOOL (hAPP (hAPP V_Pa_2 V_a0_2) V_a1_2))) )))) 97.35/107.86 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.86 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.86 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.86 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.86 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.86 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.35/107.86 ( (c_Groups_Ominus__class_Ominus tc_Nat_Onat), (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.35/107.86 ( (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) ) 97.35/107.86 ( (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)) ) 97.35/107.86 ( (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)) ) 97.35/107.86 ( (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)) ) 97.35/107.86 ( (c_Set_Oinsert t_a), v_G, (hAPP v_mgt__call v_pn) ) 97.35/107.86 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.35/107.86 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.35/107.86 ( (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)) ) 97.35/107.86 ( (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)) ) 97.35/107.86 ( (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) ) 97.35/107.86 ( (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) ) 97.35/107.86 ( (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)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)) ) 97.35/107.86 ( (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) ) 97.35/107.86 ( (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 ) 97.35/107.86 ( (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G) ) 97.35/107.86 ( (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) ) 97.35/107.86 ( (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)) ) 97.35/107.86 ( (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)) ) 97.35/107.86 ( (c_member t_a), v_G, (hAPP v_mgt__call v_pn) ) 97.35/107.86 ( (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)), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.35/107.86 ( (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)), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.35/107.86 ( (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)) ) 97.35/107.86 ( (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)) ) 97.35/107.86 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 97.35/107.86 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_Int_Onat ) 97.35/107.86 ) 97.35/107.86 (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 $$unsorted)) (= (hAPP _let_1 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) V_B_2)) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) (hAPP (hAPP (c_COMBB _let_0 _let_0 T_c) _let_1) V_B_2))) ))) 97.35/107.86 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.86 ) 97.35/107.86 (instantiation (forall ((T_b $$unsorted)) (= (hAPP (c_Relation_OField T_b) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) ) 97.35/107.86 ( tc_Nat_Onat ) 97.35/107.86 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.86 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.35/107.86 ) 97.35/107.86 (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)))) ))) 97.35/107.86 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.86 ) 97.35/107.86 (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)))) )) 97.35/107.86 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.86 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.86 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.86 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.86 ) 97.35/107.86 (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_Groups_Oab__semigroup__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) (not (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2))) (= (hAPP _let_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_b) (hAPP _let_2 V_A_2)) (hAPP _let_2 V_B_2)))) ))))) 97.35/107.86 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.86 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.86 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.86 ) 97.35/107.86 (instantiation (forall ((V_A_2 $$unsorted)) (= (hAPP (c_Finite__Set_Ocard tc_Nat_Onat) V_A_2) (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))) ) 97.35/107.86 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 97.35/107.86 ) 97.35/107.86 (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 (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)) (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))) )) 97.35/107.86 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _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) ) 97.35/107.86 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _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) ) 97.35/107.86 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.87 ) 97.35/107.87 (instantiation (let ((_let_0 (c_Set_OPow T_b))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_a_2))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (hAPP _let_0 V_A_2))) (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun _let_2 tc_HOL_Obool)) _let_3) (hAPP (c_Set_Oimage _let_2 _let_2 _let_1) _let_3)) (hAPP _let_0 (hAPP _let_1 V_A_2))) ))))) 97.35/107.87 ( v_G, (hAPP v_mgt__call v_pn), t_a ) 97.35/107.87 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.87 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.87 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.87 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.87 ) 97.35/107.87 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oab__group__add T_b)) (= (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_b_2) (c_Groups_Ozero__class_Ozero T_b)) (= V_b_2 V_a_2))) ) 97.35/107.87 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.35/107.87 ( (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 ) 97.35/107.87 ) 97.35/107.87 (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 $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_1))))) (hAPP _let_0 V_A_2)))) ))) 97.35/107.87 ( v_pn, v_U, tc_Com_Opname ) 97.35/107.87 ) 97.35/107.87 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (forall ((V_B_2 $$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) (= (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMax T_b V_B_2)) (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2)))) )))) 97.35/107.87 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.87 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.87 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.87 ) 97.35/107.87 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (= V_a_2 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_a_2) (c_Big__Operators_Olattice_OSup__fin T_b (c_Orderings_Oord__class_Omax T_b) V_A_2)))) ) 97.35/107.87 ( v_pn, v_U, tc_Com_Opname ) 97.35/107.87 ) 97.35/107.87 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (forall ((T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) _let_0))) )) 97.35/107.87 ( tc_Nat_Onat ) 97.35/107.87 ( tc_Code__Numeral_Ocode__numeral ) 97.35/107.87 ) 97.35/107.87 (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_OatMost T_b) V_k_2)) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_k_2))) ) 97.35/107.87 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.87 ) 97.35/107.87 (instantiation (forall ((V_na_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_na_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_na_2)))) ) 97.35/107.87 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.35/107.87 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.35/107.87 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 97.35/107.87 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.35/107.87 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.87 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.87 ) 97.35/107.87 (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)))) ) 97.35/107.87 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (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)) ) 97.35/107.87 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.35/107.87 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.35/107.87 ) 97.35/107.87 (instantiation (let ((_let_0 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_k) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (let ((_let_1 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (let ((_let_2 (hAPP (c_Int_Oring__1__class_Oof__int T_a) V_k))) (forall ((V_k $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (and (or (not _let_0) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (hAPP _let_1 (hAPP c_Int_Onat (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_k)))) _let_2)) (or _let_0 (= _let_2 (hAPP _let_1 (hAPP c_Int_Onat V_k)))))) )))) 97.35/107.87 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.87 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.35/107.87 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.87 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.35/107.87 ) 97.35/107.87 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b _let_0 (c_Set_Oinsert T_b)) V_B_2) V_A_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2))) )) 97.35/107.87 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.87 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.87 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.87 ) 97.35/107.87 (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 (not (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2)))) ) 97.35/107.87 ( v_U, tc_Com_Opname ) 97.35/107.87 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.35/107.87 ( v_G, t_a ) 97.35/107.87 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.35/107.87 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.35/107.87 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 97.35/107.87 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 97.35/107.87 ) 97.35/107.87 (instantiation (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_b_2) V_a_2))) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_a_2 V_b_2))) ) 97.35/107.87 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.87 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.87 ) 97.35/107.87 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_v) V_w)) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (hAPP _let_0 V_v)) (hAPP _let_0 V_w)))) )) 97.35/107.87 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.35/107.87 ) 97.35/107.87 (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))) )))) 97.35/107.87 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.87 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.87 ) 97.35/107.87 (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)))) )))) 97.35/107.87 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.87 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.87 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.87 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.87 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.87 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.87 ) 97.35/107.87 (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 $$unsorted)) (= (hAPP _let_1 _let_2) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) (hAPP _let_1 V_k_2)) (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) _let_2) (c_Orderings_Obot__class_Obot _let_0)))) )))) 97.35/107.87 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.87 ( v_n ) 97.35/107.87 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.35/107.87 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.35/107.87 ) 97.35/107.87 (instantiation (forall ((V_n $$unsorted)) (= (hAPP c_Nat_OSuc V_n) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) (c_Groups_Oone__class_Oone tc_Nat_Onat))) ) 97.35/107.87 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.87 ( v_n ) 97.35/107.87 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.35/107.87 ) 97.35/107.87 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (= V_a_2 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_a_2) (c_Big__Operators_Olattice_OInf__fin T_b (c_Orderings_Oord__class_Omin T_b) V_A_2)))) ) 97.35/107.87 ( v_pn, v_U, tc_Com_Opname ) 97.35/107.87 ) 97.35/107.87 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_a_2 $$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)))) )) 97.35/107.87 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.35/107.87 ( (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)) ) 97.35/107.87 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.35/107.87 ( (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) ) 97.35/107.87 ( (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) ) 97.35/107.87 ) 97.35/107.87 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (= (c_Groups_Oone__class_Oone T_a) (hAPP (c_Int_Oring__1__class_Oof__int T_a) (c_Groups_Oone__class_Oone tc_Int_Oint)))) ) 97.35/107.87 ( tc_Nat_Onat ) 97.35/107.87 ( tc_Int_Oint ) 97.35/107.87 ( tc_Code__Numeral_Ocode__numeral ) 97.35/107.87 ) 97.35/107.87 (instantiation (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_na_2))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_na_2) (hAPP c_Nat_OSuc V_m_2))) (= V_na_2 V_m_2))) ) 97.35/107.87 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.35/107.87 ) 97.35/107.87 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_Osucc (c_Int_OBit0 V_k)) (c_Int_OBit1 V_k)) ) 97.35/107.87 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.87 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.87 ) 97.35/107.87 (instantiation (forall ((V_k_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_k_2) (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) (hAPP c_Nat_OSuc V_k_2))) ) 97.35/107.87 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.87 ( v_n ) 97.35/107.87 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.35/107.87 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.35/107.87 ) 97.35/107.87 (instantiation (let ((_let_0 (c_List_Olinorder__class_Osorted__list__of__set T_b V_A_2))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (c_List_Olinorder__class_Osorted T_b _let_0) (hBOOL (hAPP (c_List_Odistinct T_b) _let_0)) (= V_A_2 (hAPP (c_List_Oset T_b) _let_0)))) )) 97.35/107.87 ( v_U, tc_Com_Opname ) 97.35/107.87 ) 97.35/107.87 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_x_2 $$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)))) )) 97.35/107.88 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.35/107.88 ) 97.35/107.88 (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) (= (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)) (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)))) ))))) 97.35/107.88 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.88 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.88 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.88 ) 97.35/107.88 (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)) ) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.88 ) 97.35/107.88 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) V_b))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) V_b))) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a)) V_b))) )) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.88 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.88 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.88 ) 97.35/107.88 (instantiation (let ((_let_0 (c_member (tc_prod T_b T_b)))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (let ((_let_2 (hAPP _let_1 V_a_2))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Otrans T_b V_r_2)) (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_b_2)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_b_2) V_c_2)) V_r_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) V_r_2))) )))) 97.35/107.88 ( (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_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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 ) 97.35/107.88 ) 97.35/107.88 (instantiation (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (forall ((V_m_2 $$unsorted)) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2) (hAPP c_Int_OAbs__Integ (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_m_2) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))))) )) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.35/107.88 ) 97.35/107.88 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Enum_Oenum T_2)) (not (class_Enum_Oenum T_1)) (class_Enum_Oenum (tc_prod T_2 T_1))) ) 97.35/107.88 ( tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.88 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.88 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.35/107.88 ) 97.35/107.88 (instantiation (let ((_let_0 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_w_2)))) (forall ((V_w_2 $$unsorted) (V_m_2 $$unsorted)) (= (= V_m_2 (hAPP c_Int_Onat V_w_2)) (and (or _let_0 (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_m_2)) (or (not _let_0) (= V_w_2 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2))))) )) 97.35/107.88 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (hAPP c_Int_Onat (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.88 ) 97.35/107.88 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_a_2 V_a_2))) ) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.88 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.88 ( (hAPP v_mgt__call v_pn), t_a ) 97.35/107.88 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.88 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.88 ) 97.35/107.88 (instantiation (forall ((V_y $$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))) ) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.88 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.88 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.35/107.88 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.35/107.88 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.88 ) 97.35/107.88 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Olattice (tc_fun T_2 T_1))) ) 97.35/107.88 ( tc_Nat_Onat, tc_HOL_Obool ) 97.35/107.88 ( tc_HOL_Obool, tc_HOL_Obool ) 97.35/107.88 ( tc_Int_Oint, tc_HOL_Obool ) 97.35/107.88 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.35/107.88 ( t_a, tc_HOL_Obool ) 97.35/107.88 ( (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 ) 97.35/107.88 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.35/107.88 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.35/107.88 ) 97.35/107.88 (instantiation (forall ((V_k $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) V_k) (c_Groups_Osgn__class_Osgn T_a V_k)) (hAPP (c_Groups_Oabs__class_Oabs T_a) V_k))) ) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.88 ) 97.35/107.88 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 V_A_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.35/107.88 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.88 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.35/107.88 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.88 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.88 ) 97.35/107.88 (instantiation (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Int_Oint tc_HOL_Obool))) (forall ((V_d_2 $$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))))) ))) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.88 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.88 ) 97.35/107.88 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (forall ((V_m $$unsorted)) (= (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) V_m) (c_Divides_Odivmod__nat V_m _let_0)) )) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.88 ) 97.35/107.88 (instantiation (forall ((V_Pa_2 $$unsorted) (T_c $$unsorted) (T_b $$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)) V_Pa_2)) (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)))) ) 97.35/107.88 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.88 ( (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 ) 97.35/107.88 ) 97.35/107.88 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Rings_Oring__1 T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (c_Groups_Ozero__class_Ozero T_b)) (c_Int_Oring__1__class_OInts T_b)))) ) 97.35/107.88 ( tc_Nat_Onat ) 97.35/107.88 ( tc_Int_Oint ) 97.35/107.88 ( tc_Code__Numeral_Ocode__numeral ) 97.35/107.88 ( t_a ) 97.35/107.88 ( tc_Com_Opname ) 97.35/107.88 ) 97.35/107.88 (instantiation (forall ((V_n $$unsorted) (V_i $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP c_Int_Onat V_i)) V_n) (c_Int_Onat__aux V_i V_n)) ) 97.35/107.88 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.35/107.88 ) 97.35/107.88 (instantiation (forall ((V_na_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Oring__1 T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_b) V_na_2)) (c_Int_Oring__1__class_OInts T_b)))) ) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.35/107.88 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 97.35/107.88 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.88 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.88 ) 97.35/107.88 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_r_2 $$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))) )) 97.35/107.88 ( 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) ) 97.35/107.88 ) 97.35/107.88 (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))) ) 97.35/107.88 ( v_U, tc_Com_Opname ) 97.35/107.88 ) 97.35/107.88 (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)))) ) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.88 ) 97.35/107.88 (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)))) ) 97.35/107.88 ( v_U, v_mgt__call, tc_Com_Opname, t_a ) 97.35/107.88 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.88 ( (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 ) 97.35/107.88 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 97.35/107.88 ( (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 ) 97.35/107.88 ) 97.35/107.88 (instantiation (forall ((V_j $$unsorted) (V_i $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_j) V_i) (hAPP (c_Nat_Osize__class_Osize (tc_List_Olist tc_Nat_Onat)) (c_List_Oupt V_i V_j))) ) 97.35/107.88 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.35/107.88 ) 97.35/107.88 (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)) ))) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.88 ( (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) ) 97.35/107.88 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.35/107.88 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.35/107.88 ) 97.35/107.88 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (forall ((V_w_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (class_Int_Oring__char__0 T_b)) (= (c_Int_Oiszero T_b (hAPP _let_0 V_w_2)) (c_Int_Oiszero T_b (hAPP _let_0 (c_Int_OBit0 V_w_2))))) )) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.88 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.35/107.88 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.35/107.88 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.88 ) 97.35/107.88 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_b_2)) (c_Groups_Ozero__class_Ozero T_b))) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2)))) )) 97.35/107.89 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.35/107.89 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 97.35/107.89 ) 97.35/107.89 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) V_m))) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n)) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) (hAPP _let_0 V_m)) (hAPP _let_0 V_n)))) )) 97.35/107.89 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.35/107.89 ) 97.35/107.89 (instantiation (forall ((V_f_2 $$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))) ) 97.35/107.89 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.89 ( v_mgt__call, t_a, tc_Com_Opname ) 97.35/107.89 ) 97.35/107.89 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OgreaterThan T_b))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP _let_0 V_l_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (c_SetInterval_Oord__class_OgreaterThanAtMost T_b V_l_2 V_u_2)) (hAPP _let_0 V_u_2)))) )) 97.35/107.89 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.89 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.89 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.89 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.35/107.89 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.35/107.89 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.89 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.89 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.89 ) 97.35/107.89 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Big__Operators_Olinorder__class_OMin T_b V_A_2))) (forall ((V_B_2 $$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_B_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= _let_1 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) (c_Big__Operators_Olinorder__class_OMin T_b V_B_2)) _let_1))) ))) 97.35/107.89 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.35/107.89 ) 97.35/107.89 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_l_2) V_u_2))) (= (c_SetInterval_Oord__class_OgreaterThanAtMost T_b V_l_2 V_u_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (c_SetInterval_Oord__class_OgreaterThanLessThan T_b V_l_2 V_u_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_u_2) (c_Orderings_Obot__class_Obot _let_0))))) )) 97.35/107.89 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.89 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.89 ) 97.35/107.89 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (forall ((V_b $$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))) ))) 97.35/107.89 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.89 ) 97.35/107.89 (instantiation (let ((_let_0 (tc_List_Olist T_b))) (forall ((T_b $$unsorted)) (= (c_List_Olists T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hAPP (hAPP (c_Set_Oinsert _let_0) (c_List_Olist_ONil T_b)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) )) 97.35/107.89 ( tc_Nat_Onat ) 97.35/107.89 ( tc_Int_Oint ) 97.35/107.89 ) 97.35/107.89 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_b))) (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (hAPP _let_0 V_m_2)) (hAPP _let_0 V_na_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) V_na_2)))) )) 97.35/107.89 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.35/107.89 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.35/107.89 ) 97.35/107.89 (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 $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or _let_0 (= _let_3 _let_4)) (or (not _let_0) (= _let_3 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) _let_4) (c_Groups_Oone__class_Oone tc_Nat_Onat)))))) )))))) 97.35/107.89 ( v_pn, v_U, tc_Com_Opname ) 97.35/107.89 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.35/107.89 ) 97.35/107.89 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_b_2 $$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_b_2)) V_a_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_a_2)) V_b_2)))) ))) 97.35/107.89 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.89 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.89 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.35/107.89 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.89 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.89 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.89 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.89 ) 97.35/107.89 (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 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) _let_1)) (hBOOL (hAPP (hAPP _let_0 _let_1) V_a_2)))) ))) 97.35/107.89 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.89 ) 97.35/107.89 (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 $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= _let_0 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) _let_0))) )) 97.35/107.89 ( v_pn, v_U, tc_Com_Opname ) 97.35/107.89 ) 97.35/107.89 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) V_b))) (not (hBOOL (hAPP (hAPP _let_0 V_b) V_a)))) )) 97.35/107.89 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.35/107.89 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.89 ) 97.35/107.89 (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))) ) 97.35/107.89 ( (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) (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 ) 97.35/107.89 ( (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 ) 97.35/107.89 ( (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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 ) 97.35/107.89 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.89 ) 97.35/107.89 (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))) )))) 97.35/107.89 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.89 ) 97.35/107.89 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Ocomm__ring__1 T_a)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_x) V_y) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_x) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_y)))) ) 97.35/107.89 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.35/107.89 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 97.35/107.89 ) 97.35/107.89 (instantiation (forall ((V_y $$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)))) ) 97.35/107.89 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.35/107.89 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.35/107.89 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.35/107.89 ) 97.35/107.89 (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))) )) 97.35/107.89 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.35/107.89 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.89 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.89 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.89 ) 97.35/107.89 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)))) ) 97.35/107.89 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.35/107.89 ) 97.35/107.89 (instantiation (forall ((V_v $$unsorted)) (or (not (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v)))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v))) ) 97.35/107.89 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.89 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.89 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.35/107.89 ) 97.35/107.89 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (forall ((V_Pa_2 $$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)))) )) 97.35/107.89 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.89 ( (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 ) 97.35/107.89 ) 97.35/107.89 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) ) 97.35/107.89 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.35/107.89 ) 97.35/107.89 (instantiation (forall ((V_u_2 $$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))) ) 97.35/107.89 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.89 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.89 ) 97.35/107.89 (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)))) ))) 97.35/107.89 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.89 ) 97.35/107.89 (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))) )) 97.35/107.89 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.35/107.89 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.35/107.89 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.35/107.89 ) 97.35/107.89 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_OBit1 (c_Int_Opred V_k)) (c_Int_Opred (c_Int_OBit0 V_k))) ) 97.35/107.89 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.89 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.90 ) 97.35/107.90 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Osemilattice__inf 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_Lattices_Osemilattice__inf__class_Oinf T_b) V_x_2) V_y_2)))) ) 97.35/107.90 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.90 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.90 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.35/107.90 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.90 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.35/107.90 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.35/107.90 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.35/107.90 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.90 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.35/107.90 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.90 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.35/107.90 ) 97.35/107.90 (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)))) ))))) 97.35/107.90 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.90 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.90 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.90 ) 97.35/107.90 (instantiation (let ((_let_0 (tc_fun T_c tc_HOL_Obool))) (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (c_Orderings_Otop__class_Otop (tc_fun (tc_prod T_b T_c) tc_HOL_Obool)) (hAPP (hAPP (c_Product__Type_OSigma T_b T_c) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))) (hAPP (c_COMBK _let_0 T_b) (c_Orderings_Otop__class_Otop _let_0)))) )) 97.35/107.90 ( tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.90 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.90 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.35/107.90 ) 97.35/107.90 (instantiation (forall ((V_N_2 $$unsorted)) (= (not (forall ((B_m $$unsorted)) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_x) V_N_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) B_x) B_m))) )) )) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) V_N_2))) ) 97.35/107.90 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 97.35/107.90 ) 97.35/107.90 (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_Omax 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_OSup__fin T_b _let_2 V_A_2)) V_A_2))) ))))) 97.35/107.90 ( v_U, tc_Com_Opname ) 97.35/107.90 ) 97.35/107.90 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_OBit0 V_k) (c_Int_Opred (c_Int_OBit1 V_k))) ) 97.35/107.90 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.35/107.90 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.35/107.90 ) 97.35/107.90 (instantiation (forall ((V_u_2 $$unsorted)) (= (hAPP c_Nat_OSuc V_u_2) (hAPP (c_Finite__Set_Ocard tc_Nat_Onat) (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_u_2))) ) 97.35/107.90 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.35/107.90 ( v_n ) 97.35/107.90 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.35/107.90 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.35/107.90 ) 97.35/107.90 (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)))) ) 97.35/107.90 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.35/107.90 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.35/107.90 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.35/107.90 ) 97.35/107.90 (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 $$unsorted)) (= (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c T_d) (hAPP (hAPP (c_COMBB T_e _let_1 T_b) V_f_2) V_g_2)) (hAPP (hAPP (c_COMBS _let_0 T_c T_d) (hAPP (hAPP (c_COMBB T_e _let_1 _let_0) V_f_2) (hAPP (hAPP (c_COMBB T_b T_e _let_0) V_g_2) (c_Product__Type_Ofst T_b T_c)))) (c_Product__Type_Osnd T_b T_c))) ))) 97.35/107.90 ( c_Nat_OSuc, (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal), tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.90 ) 97.35/107.90 (instantiation (let ((_let_0 (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$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_B_2 (c_Orderings_Obot__class_Obot _let_1)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_1) V_B_2) V_A_2))) (= _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) (c_Big__Operators_Olattice__class_OInf__fin T_b V_B_2)) _let_0))) ))) 97.35/107.90 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.35/107.90 ) 97.35/107.90 (instantiation (forall ((T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (c_Relation_ORange T_c T_b) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_c T_b) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) ) 97.35/107.90 ( tc_Nat_Onat, tc_Nat_Onat ) 97.35/107.90 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.90 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.35/107.90 ) 97.35/107.90 (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)))))) ) 97.35/107.90 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.35/107.90 ( (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)) ) 97.35/107.90 ( (hAPP v_mgt__call v_pn), t_a ) 97.35/107.90 ( (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) ) 97.35/107.90 ( (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) ) 97.35/107.90 ) 97.35/107.90 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$unsorted)) (not (= (c_Orderings_Otop__class_Otop _let_0) (c_Orderings_Obot__class_Obot _let_0))) )) 97.35/107.90 ( tc_Nat_Onat ) 97.35/107.90 ( tc_HOL_Obool ) 97.35/107.90 ( tc_Int_Oint ) 97.35/107.90 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.90 ( t_a ) 97.35/107.90 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.35/107.90 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.90 ( tc_Product__Type_Ounit ) 97.35/107.90 ) 97.35/107.90 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_s_2 $$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))) )) 97.35/107.90 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.35/107.90 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.35/107.90 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.90 ) 97.35/107.90 (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))))) )) 97.35/107.90 ( tc_HOL_Obool, tc_Nat_Onat ) 97.35/107.90 ( tc_HOL_Obool, tc_HOL_Obool ) 97.35/107.90 ( tc_HOL_Obool, tc_Int_Oint ) 97.35/107.90 ( tc_HOL_Obool, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.35/107.90 ( tc_HOL_Obool, t_a ) 97.35/107.90 ( 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)) ) 97.35/107.90 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.35/107.90 ( tc_HOL_Obool, tc_Product__Type_Ounit ) 97.35/107.90 ) 97.35/107.90 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_f_2 $$unsorted)) (or (not (hBOOL (hAPP V_f_2 (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_a_2) V_b_2)))) (hBOOL (hAPP (hAPP (c_Product__Type_Ocurry T_b T_c tc_HOL_Obool V_f_2) V_a_2) V_b_2))) ) 97.53/107.90 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat, (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 97.53/107.90 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat, (c_Set_Oinsert (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 97.53/107.90 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Set_Oinsert (tc_prod _let_0 _let_0))) ) 97.53/107.90 ) 97.53/107.90 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Product__Type_Ocurry T_b T_c tc_HOL_Obool V_f_2) V_a_2) V_b_2))) (hBOOL (hAPP V_f_2 (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_a_2) V_b_2)))) ) 97.53/107.90 ( (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 ) 97.53/107.90 ( (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 ) 97.53/107.90 ( (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) ) 97.53/107.90 ) 97.53/107.90 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (c_Finite__Set_Ofun__left__comm T_b (tc_List_Olist T_b) (c_List_Olinorder__class_Oinsort__key T_b T_b (c_COMBI T_b)))) ) 97.53/107.90 ( tc_Nat_Onat ) 97.53/107.90 ( tc_Int_Oint ) 97.53/107.90 ( tc_Code__Numeral_Ocode__numeral ) 97.53/107.90 ) 97.53/107.90 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 97.53/107.90 ( v_pn, tc_Com_Opname ) 97.53/107.90 ( (hAPP v_mgt__call v_pn), t_a ) 97.53/107.90 ) 97.53/107.90 (instantiation (forall ((T_b $$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))) ) 97.53/107.90 ( tc_Nat_Onat ) 97.53/107.90 ( tc_HOL_Obool ) 97.53/107.90 ( tc_Int_Oint ) 97.53/107.90 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.90 ( t_a ) 97.53/107.90 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.90 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.90 ( tc_Product__Type_Ounit ) 97.53/107.90 ) 97.53/107.90 (instantiation (forall ((V_nat $$unsorted)) (= (c_Nat_Onat_Onat__size (hAPP c_Nat_OSuc V_nat)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Nat_Onat_Onat__size V_nat)) (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) ) 97.53/107.90 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.53/107.90 ( v_n ) 97.53/107.90 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.53/107.90 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.53/107.90 ) 97.53/107.90 (instantiation (forall ((V_f_2 $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= V_f_2 (c_Product__Type_Ocurry T_b T_c T_d (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_c T_d) V_f_2))) ) 97.53/107.90 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_HOL_Obool, tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.90 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_HOL_Obool, tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.90 ) 97.53/107.90 (instantiation (forall ((T_b $$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))) ) 97.53/107.90 ( tc_Nat_Onat ) 97.53/107.90 ( tc_Int_Oint ) 97.53/107.90 ( tc_Code__Numeral_Ocode__numeral ) 97.53/107.90 ( (tc_fun t_a tc_HOL_Obool) ) 97.53/107.90 ) 97.53/107.90 (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)))) )) 97.53/107.90 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.90 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.90 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.90 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.90 ) 97.53/107.90 (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_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))) (= V_A_2 _let_1) (not (hBOOL (hAPP _let_3 V_B_2))) (= V_B_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)) (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)))) ))))) 97.53/107.91 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.91 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.91 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.91 ) 97.53/107.91 (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_Olattice_OInf__fin T_b (c_Orderings_Oord__class_Omin T_b) (hAPP _let_1 V_A_2)))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or _let_4 (= (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 _let_3)) _let_5)) (or (not _let_4) (= V_x_2 _let_5))))) ))))))) 97.53/107.91 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.91 ( (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)) ) 97.53/107.91 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.53/107.91 ( (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) ) 97.53/107.91 ( (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) ) 97.53/107.91 ) 97.53/107.91 (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)) ) 97.53/107.91 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.53/107.91 ( v_G, t_a ) 97.53/107.91 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 97.53/107.91 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 97.53/107.91 ) 97.53/107.91 (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)))) ))) 97.53/107.91 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.91 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.91 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.53/107.91 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.91 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.91 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.91 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.91 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.91 ) 97.53/107.91 (instantiation (forall ((V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) V_n) (hAPP c_Nat_OSuc V_n)) ) 97.53/107.91 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.53/107.91 ( v_n ) 97.53/107.91 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.53/107.91 ) 97.53/107.91 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Finite__Set_Ofinite T_1)) (not (class_Finite__Set_Ofinite T_2)) (class_Finite__Set_Ofinite (tc_fun T_2 T_1))) ) 97.53/107.91 ( tc_HOL_Obool, tc_Nat_Onat ) 97.53/107.91 ( tc_HOL_Obool, tc_HOL_Obool ) 97.53/107.91 ( tc_HOL_Obool, tc_Int_Oint ) 97.53/107.91 ( tc_HOL_Obool, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.91 ( tc_HOL_Obool, t_a ) 97.53/107.91 ( tc_HOL_Obool, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.91 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.91 ( tc_HOL_Obool, tc_Product__Type_Ounit ) 97.53/107.91 ) 97.53/107.91 (instantiation (forall ((V_Pa_2 $$unsorted) (T_b $$unsorted)) (= (forall ((B_x $$unsorted)) (not (hBOOL (hAPP V_Pa_2 B_x))) ) (= (hAPP (c_Set_OCollect T_b) V_Pa_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 97.53/107.91 ( (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) ) 97.53/107.91 ( (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) ) 97.53/107.91 ) 97.53/107.91 (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 $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_x_2)) (hAPP _let_1 V_y_2))))) ))) 97.53/107.91 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.91 ) 97.53/107.91 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus (tc_fun T_b tc_HOL_Obool)))) (forall ((V_B_2 $$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)))) )) 97.53/107.91 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.91 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.91 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.91 ) 97.53/107.91 (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)))))) ) 97.53/107.91 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.91 ( (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)) ) 97.53/107.91 ( (hAPP v_mgt__call v_pn), t_a ) 97.53/107.91 ( (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) ) 97.53/107.91 ( (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) ) 97.53/107.91 ) 97.53/107.91 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Oplus__class_Oplus T_b))) (let ((_let_2 (c_Groups_Ozero__class_Ozero 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 (hAPP (hAPP _let_1 (hAPP (hAPP _let_1 (c_Groups_Oone__class_Oone T_b)) V_a_2)) V_a_2)) _let_2)) (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_2)))) )))) 97.53/107.91 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.91 ( v_pn, tc_Com_Opname ) 97.53/107.91 ( (hAPP v_mgt__call v_pn), t_a ) 97.53/107.91 ) 97.53/107.91 (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 $$unsorted)) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) _let_1))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_b) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_1))) ))) 97.53/107.91 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.91 ) 97.53/107.91 (instantiation (forall ((T_b $$unsorted)) (= (hAPP (c_List_Oset T_b) (c_List_Olist_ONil T_b)) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) ) 97.53/107.91 ( tc_Nat_Onat ) 97.53/107.91 ( tc_HOL_Obool ) 97.53/107.91 ( tc_Int_Oint ) 97.53/107.91 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.91 ( t_a ) 97.53/107.91 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.91 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.91 ( tc_Product__Type_Ounit ) 97.53/107.91 ) 97.53/107.91 (instantiation (forall ((V_v $$unsorted)) (= (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v) (hAPP c_Int_Onat (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v))) ) 97.53/107.91 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.91 ) 97.53/107.91 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_0) V_a))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_a) V_b))) (= _let_0 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_a) V_b))) )) 97.53/107.91 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.91 ) 97.53/107.91 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c _let_0))) (let ((_let_2 (tc_fun T_c tc_HOL_Obool))) (let ((_let_3 (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_d $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (hAPP _let_3 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d _let_2) V_A_2) V_B_2)) V_C_2) (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_d _let_1 _let_0) (hAPP (hAPP (c_COMBB _let_2 (tc_fun _let_1 _let_0) T_d) _let_3) V_B_2)) V_C_2))) ))))) 97.53/107.91 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.91 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.91 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.91 ) 97.53/107.91 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2)) (= V_y_2 V_x_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)))) ) 97.53/107.91 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.53/107.91 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.91 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.53/107.91 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.91 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.91 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.91 ) 97.53/107.91 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2))) (hBOOL (hAPP _let_0 V_A_2))) )) 97.53/107.91 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.53/107.91 ) 97.53/107.91 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Osemilattice__sup (tc_fun T_2 T_1))) ) 97.53/107.91 ( tc_Nat_Onat, tc_HOL_Obool ) 97.53/107.91 ( tc_HOL_Obool, tc_HOL_Obool ) 97.53/107.91 ( tc_Int_Oint, tc_HOL_Obool ) 97.53/107.91 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.53/107.91 ( t_a, tc_HOL_Obool ) 97.53/107.91 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.53/107.91 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.53/107.91 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.53/107.91 ) 97.53/107.91 (instantiation (forall ((T_b $$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))))) ) 97.53/107.91 ( tc_Nat_Onat ) 97.53/107.91 ( tc_HOL_Obool ) 97.53/107.91 ( tc_Int_Oint ) 97.53/107.91 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.91 ( t_a ) 97.53/107.91 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.91 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.91 ( tc_Product__Type_Ounit ) 97.53/107.91 ) 97.53/107.91 (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 tc_Int_Oint) V_a) V_b))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_b) _let_0)))) (= (c_Divides_OposDivAlg V_a V_b) (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) _let_0) V_a))) )) 97.53/107.91 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.91 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.91 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.91 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.91 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.91 ) 97.53/107.91 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_Fun_Oinj__on T_b T_c V_f_2 _let_0) (= (hAPP (c_Fun_Ocomp T_c T_b T_b (c_Hilbert__Choice_Oinv__into T_b T_c _let_0 V_f_2)) V_f_2) (c_Fun_Oid T_b))) )) 97.53/107.91 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.53/107.91 ) 97.53/107.91 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP _let_1 V_A_2)) (hAPP _let_1 V_B_2)) (hAPP _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) V_B_2)))) ))) 97.53/107.91 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.53/107.91 ) 97.53/107.91 (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))))) ) 97.53/107.91 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.53/107.91 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 97.53/107.91 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.53/107.91 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.91 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.91 ) 97.53/107.91 (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))) (= (= V_z_H_2 V_z_2) (= (hAPP c_Int_Onat V_z_2) (hAPP c_Int_Onat V_z_H_2)))) )) 97.53/107.91 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.53/107.91 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.91 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.91 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.91 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.91 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.91 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.91 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.53/107.91 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.91 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.91 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.53/107.91 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.92 ) 97.53/107.92 (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))) ) 97.53/107.92 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ) 97.53/107.92 (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)))) )) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.53/107.92 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.53/107.92 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.53/107.92 ) 97.53/107.92 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$unsorted)) (= (c_Orderings_Otop__class_Otop _let_0) (hAPP (c_Groups_Ouminus__class_Ouminus _let_0) (c_Orderings_Obot__class_Obot _let_0))) )) 97.53/107.92 ( tc_Nat_Onat ) 97.53/107.92 ( tc_HOL_Obool ) 97.53/107.92 ( tc_Int_Oint ) 97.53/107.92 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.92 ( t_a ) 97.53/107.92 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.92 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.92 ( tc_Product__Type_Ounit ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_k_2) V_i_2)) (hBOOL (hAPP (hAPP (c_member T_b) V_i_2) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_k_2))))) ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.92 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.92 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.92 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.53/107.92 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.53/107.92 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.53/107.92 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.92 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (= V_y_2 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)))) ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.53/107.92 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.92 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.53/107.92 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.92 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.92 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Complete__Lattice_OInf__class_OInf T_b V_A_2) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b)) (c_Orderings_Otop__class_Otop T_b)) V_A_2))) ) 97.53/107.92 ( v_U, tc_Com_Opname ) 97.53/107.92 ) 97.53/107.92 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_1 (c_Groups_Oone__class_Oone T_a))) (forall ((V_m $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Ocomm__semiring__1 T_a)) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (hAPP (hAPP _let_0 _let_1) _let_1)) V_m) (hAPP (hAPP _let_0 V_m) V_m))) ))) 97.53/107.92 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w_2) V_z_2)) (not (forall ((B_n $$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))))) ))) ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.92 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.92 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.92 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.92 ) 97.53/107.92 (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))) ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.53/107.92 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.92 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.53/107.92 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.92 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.53/107.92 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.53/107.92 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.53/107.92 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.53/107.92 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_R2_2 $$unsorted) (T_c $$unsorted) (V_R1_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Otrans T_b V_R1_2)) (not (c_Relation_Otrans T_c V_R2_2)) (c_Relation_Otrans (tc_prod T_b T_c) (c_Wellfounded_Olex__prod T_b T_c V_R1_2 V_R2_2))) ) 97.53/107.92 ( (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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, (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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 ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2)) (c_Fun_Obij__betw T_b T_c V_f_2 V_A_2 (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2))) ) 97.53/107.92 ( v_U, v_mgt__call, t_a, tc_Com_Opname ) 97.53/107.92 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.92 ( (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 ) 97.53/107.92 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.53/107.92 ( (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 ) 97.53/107.92 ) 97.53/107.92 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v))) (forall ((V_v $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) _let_0))) (= _let_0 (hAPP c_Nat_OSuc (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) _let_0) (c_Groups_Oone__class_Oone tc_Nat_Onat))))) )) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.92 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.92 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.53/107.92 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.53/107.92 ) 97.53/107.92 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Opreorder T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2)) (and (not (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2))) (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2))))) )) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.92 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.53/107.92 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.92 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.53/107.92 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.92 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.53/107.92 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.53/107.92 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.53/107.92 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.53/107.92 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (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_Groups_Ozero__class_Ozero tc_Int_Oint))))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ) 97.53/107.92 (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)))) )))) 97.53/107.92 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.92 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.92 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_1)) (class_Lattices_Oboolean__algebra (tc_fun T_2 T_1))) ) 97.53/107.92 ( tc_Nat_Onat, tc_HOL_Obool ) 97.53/107.92 ( tc_HOL_Obool, tc_HOL_Obool ) 97.53/107.92 ( tc_Int_Oint, tc_HOL_Obool ) 97.53/107.92 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.53/107.92 ( t_a, tc_HOL_Obool ) 97.53/107.92 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.53/107.92 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.53/107.92 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)) V_a))) (= (c_Groups_Oone__class_Oone T_a) (c_Groups_Osgn__class_Osgn T_a V_a))) ) 97.53/107.92 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ) 97.53/107.92 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_1 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_v $$unsorted)) (or (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v))) (= (hAPP c_Nat_OSuc (hAPP (hAPP _let_1 (hAPP _let_0 V_v)) V_n)) (hAPP (hAPP _let_1 (hAPP _let_0 (c_Int_Osucc V_v))) V_n))) ))) 97.53/107.92 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.92 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_l_2)) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_l_2 V_u_2)) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_u_2))) ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.92 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.92 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.92 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.92 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ) 97.53/107.92 (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 $$unsorted) (V_b_2 $$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_b_2) (c_Orderings_Obot__class_Obot _let_1)))) (hAPP _let_0 V_r_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_b_2)) V_r_2))) )))) 97.53/107.92 ( (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 ) 97.53/107.92 ( (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 ) 97.53/107.92 ( (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) ) 97.53/107.92 ) 97.53/107.92 (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_b tc_HOL_Obool)))) (let ((_let_2 (c_Orderings_Otop__class_Otop (tc_fun T_d tc_HOL_Obool)))) (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (= (hAPP (c_Set_Oimage T_c T_b V_f_2) _let_0) _let_1)) (not (= _let_2 (hAPP (c_Set_Oimage T_b T_d V_g_2) _let_1))) (= _let_2 (hAPP (c_Set_Oimage T_c T_d (hAPP (c_Fun_Ocomp T_b T_d T_c V_g_2) V_f_2)) _let_0))) )))) 97.53/107.92 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, c_Code__Numeral_Onat__of, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral ) 97.53/107.92 ( c_Int_Onat, tc_Nat_Onat, (c_Groups_Oabs__class_Oabs tc_Int_Oint), tc_Int_Oint, tc_Int_Oint ) 97.53/107.92 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral, c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.53/107.92 ) 97.53/107.92 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_b $$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)))) )) 97.53/107.92 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.92 ) 97.53/107.92 (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))) ) 97.53/107.92 ( tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.92 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.92 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_na_2 $$unsorted)) (= (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Nat_OSuc V_na_2)) (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_na_2)) ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.53/107.92 ( v_n ) 97.53/107.92 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.53/107.92 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_na_2 $$unsorted)) (= (c_SetInterval_Oord__class_OatLeastAtMost tc_Nat_Onat (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_na_2) (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_na_2)) ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Divides_Osemiring__div T_a)) (= (c_Divides_Odiv__class_Omod T_a V_a V_b) (c_Divides_Odiv__class_Omod T_a (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_b))) ) 97.53/107.92 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.92 ) 97.53/107.92 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (let ((_let_1 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (hAPP _let_0 V_w))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP _let_1 (hAPP (hAPP _let_1 (c_Groups_Oone__class_Oone T_a)) _let_2)) _let_2) (hAPP _let_0 (c_Int_OBit1 V_w)))) )))) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.92 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.53/107.92 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.92 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.53/107.92 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_r_2 $$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))))) ) 97.53/107.92 ( 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) ) 97.53/107.92 ) 97.53/107.92 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)) (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))))) ) 97.53/107.92 ( v_U, tc_Com_Opname ) 97.53/107.92 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.53/107.92 ( v_G, t_a ) 97.53/107.92 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.92 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.53/107.92 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 97.53/107.92 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 97.53/107.92 ) 97.53/107.92 (instantiation (let ((_let_0 (c_Groups_Ominus__class_Ominus T_b))) (let ((_let_1 (c_Orderings_Oord__class_Oless__eq T_b))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (not (= (hAPP (hAPP _let_0 V_a_2) V_b_2) (hAPP (hAPP _let_0 V_c_2) V_d_2))) (= (hBOOL (hAPP (hAPP _let_1 V_c_2) V_d_2)) (hBOOL (hAPP (hAPP _let_1 V_a_2) V_b_2)))) ))) 97.53/107.92 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.53/107.93 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 97.53/107.93 ) 97.53/107.93 (instantiation (forall ((V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (not (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2))) ) 97.53/107.93 ( v_G, (hAPP v_mgt__call v_pn), t_a ) 97.53/107.93 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.93 ( (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) ) 97.53/107.93 ( (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) ) 97.53/107.93 ( (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)) ) 97.53/107.93 ) 97.53/107.93 (instantiation (forall ((V_l $$unsorted)) (or (not (c_List_Onat__list V_l)) (= V_l (c_List_Oembed__list (c_List_Oreturn__list V_l)))) ) 97.53/107.93 ( (c_List_Olist_ONil tc_Int_Oint) ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_b) V_a_2)) V_b_2)) (and (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) V_b_2)) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2))))) )) 97.53/107.93 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_y_2) V_x_2))) (= (= V_x_2 V_y_2) (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2)))) )) 97.53/107.93 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.93 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.93 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.93 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.93 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.53/107.93 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.53/107.93 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (tc_fun t_a tc_HOL_Obool) ) 97.53/107.93 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((T_b $$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)))) )) 97.53/107.93 ( tc_HOL_Obool ) 97.53/107.93 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.93 ( t_a ) 97.53/107.93 ( tc_Com_Opname ) 97.53/107.93 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.93 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.93 ( tc_Product__Type_Ounit ) 97.53/107.93 ) 97.53/107.93 (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 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) _let_1))) (= (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) _let_0) _let_1) (hAPP (c_Product__Type_Ofst tc_Int_Oint tc_Int_Oint) (c_Divides_OposDivAlg _let_0 _let_1)))) ))) 97.53/107.93 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.93 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.93 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.53/107.93 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.53/107.93 ) 97.53/107.93 (instantiation (forall ((V_a_2 $$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)))) ) 97.53/107.93 ( v_pn, v_U, tc_Com_Opname ) 97.53/107.93 ) 97.53/107.93 (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_Lattices_Osemilattice__sup__class_Osup 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_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__class_OSup__fin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2))) (c_Big__Operators_Olattice__class_OSup__fin T_b _let_2)) (hAPP (hAPP _let_3 (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OSup__fin T_b V_B_2)))) ))))) 97.53/107.93 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.93 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.93 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_b_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_b_2))) (hBOOL (hAPP (hAPP _let_0 V_b_2) (hAPP _let_1 V_a_2))))) ))) 97.53/107.93 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.93 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ) 97.53/107.93 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) V_m))) (= V_m (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n)) V_n))) ) 97.53/107.93 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_A_2))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) 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))) ))) 97.53/107.93 ( (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_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.93 ( (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_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.93 ) 97.53/107.93 (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 $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) _let_1) (hAPP _let_0 V_k_2)) (hAPP _let_0 _let_1)) ))) 97.53/107.93 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.53/107.93 ( v_n ) 97.53/107.93 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.53/107.93 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)) (hBOOL (hAPP (hAPP _let_0 _let_1) (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2))))) ))) 97.53/107.93 ( (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.93 ( v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.93 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.53/107.93 ) 97.53/107.93 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (= V_A_2 (hAPP (c_Set_Ovimage T_b T_c V_f_2) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) ) 97.53/107.93 ( v_U, v_mgt__call, t_a, tc_Com_Opname ) 97.53/107.93 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.93 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.53/107.93 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.53/107.93 ) 97.53/107.93 (instantiation (forall ((T_b $$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)) ) 97.53/107.93 ( tc_Nat_Onat ) 97.53/107.93 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.93 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (let ((_let_2 (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat))) (let ((_let_3 (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel))) (let ((_let_4 (c_Set_Oinsert _let_0))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP c_Int_OAbs__Integ (hAPP _let_3 (hAPP (hAPP _let_4 (hAPP (hAPP _let_2 V_x_2) V_y_2)) _let_1)))) (hAPP c_Int_OAbs__Integ (hAPP _let_3 (hAPP (hAPP _let_4 (hAPP (hAPP _let_2 V_y_2) V_x_2)) _let_1)))) )))))) 97.53/107.93 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.53/107.93 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.53/107.93 ) 97.53/107.93 (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))) )) 97.53/107.93 ( (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 ) 97.53/107.93 ( (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 ) 97.53/107.93 ( (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 ) 97.53/107.93 ) 97.53/107.93 (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 $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert T_b) (hAPP V_f_2 V_a_2)) (hAPP _let_0 V_B_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_c) V_a_2) V_B_2))) )) 97.53/107.93 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (c_Groups_Ominus__class_Ominus tc_Nat_Onat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) V_m))) (= (hAPP c_Nat_OSuc (hAPP (hAPP _let_0 V_m) V_n)) (hAPP (hAPP _let_0 (hAPP c_Nat_OSuc V_m)) V_n))) )) 97.53/107.93 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone T_a))) (forall ((T_a $$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)))) )) 97.53/107.93 ( tc_Nat_Onat ) 97.53/107.93 ( tc_Int_Oint ) 97.53/107.93 ( tc_Code__Numeral_Ocode__numeral ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Nat_Onat))) (forall ((V_i $$unsorted) (V_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_n))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_n) (hAPP c_Nat_OSuc V_i))) V_n))) )) 97.53/107.93 ( v_n, (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_2 (c_Big__Operators_Olattice_OInf__fin T_b _let_1 V_A_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_B_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= _let_2 (hAPP (hAPP _let_1 (c_Big__Operators_Olattice_OInf__fin T_b _let_1 V_B_2)) _let_2))) )))) 97.53/107.93 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (c_Groups_Oone__class_Oone T_a))) (forall ((V_b $$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))) )))) 97.53/107.93 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_B_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) (c_Big__Operators_Olattice__class_OSup__fin T_b V_B_2)) _let_1))) ))) 97.53/107.93 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.53/107.93 ) 97.53/107.93 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_z))) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (hAPP c_Int_Onat V_z)) (hAPP (c_Int_Oring__1__class_Oof__int T_a) V_z))) ) 97.53/107.93 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.53/107.93 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.93 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.53/107.93 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.93 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (tc_fun T_c tc_HOL_Obool))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (hAPP (c_Finite__Set_Ofold__image _let_0 T_b (c_Lattices_Osemilattice__sup__class_Osup _let_0)) (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (hAPP (hAPP (c_COMBB T_c (tc_fun _let_0 _let_0) T_b) (c_Set_Oinsert T_c)) V_f_2)) _let_0)) _let_0) V_A_2) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) )) 97.53/107.93 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.93 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.53/107.93 ( v_mgt__call, t_a, v_U, tc_Com_Opname ) 97.53/107.93 ) 97.53/107.93 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero T_a))) ) 97.53/107.93 ( tc_Nat_Onat ) 97.53/107.93 ) 97.53/107.93 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (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_OINFI T_c (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2) _let_0) (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_c) B_x) V_A_2))) (= _let_0 (hAPP V_B_2 B_x))) )) )) 97.53/107.93 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.93 ) 97.53/107.93 (instantiation (forall ((V_x $$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)))) ) 97.53/107.94 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.94 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.94 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.94 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.94 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.94 ) 97.53/107.94 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_Osucc (c_Int_OBit1 V_k)) (c_Int_OBit0 (c_Int_Osucc V_k))) ) 97.53/107.94 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.94 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.94 ) 97.53/107.94 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Nat_OSuc V_m)) V_n))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m) V_n))) ) 97.53/107.94 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), v_n ) 97.53/107.94 ) 97.53/107.94 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Complete__Lattice_OSup__class_OSup T_b V_A_2) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2))) ) 97.53/107.94 ( v_U, tc_Com_Opname ) 97.53/107.94 ) 97.53/107.94 (instantiation (let ((_let_0 (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (hAPP c_Nat_OSuc (hAPP _let_0 V_n)) (hAPP _let_0 (hAPP c_Nat_OSuc V_n))) )) 97.53/107.94 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.53/107.94 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.53/107.94 ) 97.53/107.94 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_a_2 $$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)))) )) 97.53/107.94 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.94 ( (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)) ) 97.53/107.94 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.53/107.94 ( (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) ) 97.53/107.94 ( (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) ) 97.53/107.94 ) 97.53/107.94 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_x_2) V_A_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 97.53/107.94 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.94 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.94 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.53/107.94 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.94 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.94 ) 97.53/107.94 (instantiation (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (= (and (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_na_2)) (not (= V_na_2 V_m_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) V_na_2))) ) 97.53/107.94 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.53/107.94 ) 97.53/107.94 (instantiation (forall ((V_v $$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)))) ) 97.53/107.94 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.94 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.53/107.94 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.53/107.94 ) 97.53/107.94 (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))) ) 97.53/107.94 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.94 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.94 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.94 ) 97.53/107.94 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) V_x_2))) ) 97.53/107.94 ( v_pn, v_U, tc_Com_Opname ) 97.53/107.94 ) 97.53/107.94 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (c_Divides_Odiv__class_Odiv tc_Nat_Onat))) (let ((_let_2 (hAPP (hAPP _let_1 V_m) V_n))) (let ((_let_3 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) _let_0) V_n))) (and (or (not _let_3) (= _let_0 _let_2)) (or _let_3 (= _let_2 (hAPP c_Nat_OSuc (hAPP (hAPP _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n)) V_n)))))) ))))) 97.53/107.94 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.53/107.94 ) 97.53/107.94 (instantiation (forall ((V_k_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (c_Groups_Ouminus__class_Ouminus (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_k_2)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_k_2))) ) 97.53/107.94 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.94 ) 97.53/107.94 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (c_member T_b))) (forall ((V_f_2 $$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 (not (hBOOL (hAPP (hAPP _let_1 B_x) V_A_2))) (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))))))) ))) ))) 97.53/107.94 ( c_Nat_OSuc, tc_Nat_Onat, (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.94 ( (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 ) 97.53/107.94 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.53/107.94 ) 97.53/107.94 (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 $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_R_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) V_R_2) V_S_2)) V_R_2))) (c_FunDef_Oreduction__pair T_b (hAPP (hAPP (c_Product__Type_OPair _let_0 _let_0) V_R_2) V_S_2))) )) 97.53/107.94 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.94 ) 97.53/107.94 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot _let_1))) (forall ((V_B_2 $$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)))) )))) 97.53/107.94 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.94 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.94 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.94 ) 97.53/107.94 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (c_Orderings_Obot__class_Obot T_a)) (c_Orderings_Otop__class_Otop T_a))) ) 97.53/107.94 ( tc_Nat_Onat ) 97.53/107.94 ( tc_HOL_Obool ) 97.53/107.94 ( tc_Int_Oint ) 97.53/107.94 ( (tc_fun tc_HOL_Obool tc_HOL_Obool) ) 97.53/107.94 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.53/107.94 ( (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 97.53/107.94 ( (tc_fun tc_Int_Oint tc_HOL_Obool) ) 97.53/107.94 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.53/107.94 ( (tc_fun tc_Product__Type_Ounit tc_HOL_Obool) ) 97.53/107.94 ) 97.53/107.94 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olattice_OSup__fin T_b _let_0 V_A_2) (hAPP (c_Finite__Set_Ofold1 T_b _let_0) V_A_2))) )) 97.53/107.94 ( v_U, tc_Com_Opname ) 97.53/107.94 ) 97.53/107.94 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (let ((_let_2 (c_Finite__Set_Ofinite T_b))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP _let_2 V_A_2))) (not (hBOOL (hAPP _let_2 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_0) 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_0) 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)))) )))) 97.53/107.94 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.94 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.94 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.94 ( (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 ) 97.53/107.94 ) 97.53/107.94 (instantiation (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_w_2))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP c_Int_Onat V_w_2)) (hAPP c_Int_Onat V_z_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_w_2) V_z_2)))) ) 97.53/107.94 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.94 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.94 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.94 ) 97.53/107.94 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Enum_Oenum T_2)) (not (class_Enum_Oenum T_1)) (class_Enum_Oenum (tc_fun T_2 T_1))) ) 97.53/107.94 ( tc_HOL_Obool, tc_Nat_Onat ) 97.53/107.94 ( tc_HOL_Obool, tc_HOL_Obool ) 97.53/107.94 ( tc_HOL_Obool, tc_Int_Oint ) 97.53/107.94 ( tc_HOL_Obool, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.94 ( tc_HOL_Obool, t_a ) 97.53/107.94 ( tc_HOL_Obool, (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.94 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.94 ( tc_HOL_Obool, tc_Product__Type_Ounit ) 97.53/107.94 ) 97.53/107.94 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (forall ((V_A_2 $$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))) )) 97.53/107.94 ( v_U, tc_Com_Opname ) 97.53/107.94 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.53/107.94 ( v_G, t_a ) 97.53/107.94 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 97.53/107.94 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 97.53/107.94 ) 97.53/107.94 (instantiation (let ((_let_0 (c_Groups_Oabs__class_Oabs T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) V_b))) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP _let_0 V_a)) (hAPP _let_0 V_b))))) )) 97.53/107.94 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.53/107.94 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 97.53/107.94 ) 97.53/107.94 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 V_A_2) V_B_2))) (not (hBOOL (hAPP (hAPP _let_0 V_B_2) V_A_2))) (= V_B_2 V_A_2)) )) 97.53/107.94 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.53/107.94 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.53/107.94 ) 97.53/107.94 (instantiation (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_b_2) V_a_2))) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_a_2) V_b_2))) ) 97.53/107.94 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.94 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.94 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.94 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.94 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.94 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.94 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.94 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.94 ) 97.53/107.94 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_w $$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) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_w))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) (hAPP _let_0 V_v)) (hAPP _let_0 V_w)))) )) 97.53/107.94 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.53/107.94 ) 97.53/107.94 (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_c $$unsorted) (T_b $$unsorted)) (= (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2) _let_0) (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_c) B_x) V_A_2))) (= _let_0 (hAPP V_B_2 B_x))) )) )) 97.53/107.94 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.94 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.94 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.95 ) 97.53/107.95 (instantiation (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (forall ((V_a_2 $$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 (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))) )) 97.53/107.95 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.95 ( (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)) ) 97.53/107.95 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.53/107.95 ( (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) ) 97.53/107.95 ( (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) ) 97.53/107.95 ) 97.53/107.95 (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_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)))) ) 97.53/107.95 ( v_U, v_mgt__call, t_a, tc_Com_Opname ) 97.53/107.95 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.95 ( (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 ) 97.53/107.95 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.53/107.95 ( (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 ) 97.53/107.95 ) 97.53/107.95 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Orderings_Oord__class_Omax T_b)) V_x_2) V_A_2))) ) 97.53/107.95 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.95 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.95 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.53/107.95 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.95 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.95 ) 97.53/107.95 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (= _let_1 (hAPP (c_Set_Oimage T_c T_b V_f_2) _let_0))) (c_Fun_Oinj__on T_b T_c (c_Hilbert__Choice_Oinv__into T_c T_b _let_0 V_f_2) _let_1)) ))) 97.53/107.95 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.95 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.53/107.95 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.53/107.95 ( v_mgt__call, t_a, tc_Com_Opname ) 97.53/107.95 ) 97.53/107.95 (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 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (= (= (hAPP (hAPP _let_0 V_a_2) (hAPP (hAPP _let_0 V_b_2) _let_1)) (hAPP (hAPP _let_0 V_c_2) (hAPP (hAPP _let_0 V_d_2) _let_1))) (or (and (= V_d_2 V_a_2) (= V_c_2 V_b_2)) (and (= V_c_2 V_a_2) (= V_d_2 V_b_2)))) ))) 97.53/107.95 ( (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 ) 97.53/107.95 ( (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)) ) 97.53/107.95 ( (hAPP v_mgt__call v_pn), (hAPP v_mgt__call v_pn), (hAPP v_mgt__call v_pn), (hAPP v_mgt__call v_pn), t_a ) 97.53/107.95 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.95 ( (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)), (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) ) 97.53/107.95 ( (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)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.95 ) 97.53/107.95 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (= (hAPP (c_Finite__Set_Ocard T_c) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)) (hAPP (c_Finite__Set_Ocard T_b) V_A_2))) (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2)) ) 97.53/107.95 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.95 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.53/107.95 ( v_mgt__call, t_a, v_U, tc_Com_Opname ) 97.53/107.95 ) 97.53/107.95 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (c_Finite__Set_Ofold1 T_b (c_Orderings_Oord__class_Omin T_b)) V_A_2) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2))) ) 97.53/107.95 ( v_U, tc_Com_Opname ) 97.53/107.95 ) 97.53/107.95 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (c_Orderings_Obot__class_Obot T_a) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x)) V_x))) ) 97.53/107.95 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.95 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.95 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.95 ) 97.53/107.95 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Int_Oring__1__class_OInts T_b))) (forall ((V_b_2 $$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_b_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_b_2)) _let_1))) ))) 97.53/107.95 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.95 ) 97.53/107.95 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__sup__class_Osup T_b)) V_a_2) V_A_2))) ) 97.53/107.95 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.95 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.95 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.53/107.95 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.95 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.95 ) 97.53/107.95 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x)) (c_Orderings_Otop__class_Otop T_a))) ) 97.53/107.95 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.95 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.95 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.53/107.95 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.95 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.95 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.95 ) 97.53/107.95 (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 $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (not (class_Int_Onumber__ring T_a)) (and (or (not _let_1) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) _let_0) _let_2)) (or _let_1 (= _let_0 _let_2)))) )))) 97.53/107.95 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.53/107.95 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.95 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.53/107.95 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.95 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.53/107.95 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.95 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.53/107.95 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.53/107.95 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.53/107.95 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.53/107.95 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.53/107.95 ) 97.53/107.95 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OlessThan T_b))) (forall ((V_u_2 $$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 (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)) (hAPP _let_0 V_u_2))) )) 97.53/107.95 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.95 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.95 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.95 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.95 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.95 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.95 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.95 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.95 ) 97.53/107.95 (instantiation (forall ((V_x $$unsorted)) (= V_x (c_Int_Osucc (c_Int_Opred V_x))) ) 97.53/107.95 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.95 ) 97.53/107.95 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_x_2))) (not (hBOOL (hAPP _let_0 V_y_2))) (= (= V_y_2 V_x_2) (= (hAPP c_Int_Onat V_y_2) (hAPP c_Int_Onat V_x_2)))) )) 97.53/107.95 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.53/107.95 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.95 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.95 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.95 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.95 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.95 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.95 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.53/107.95 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.95 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.95 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.53/107.95 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.95 ) 97.53/107.95 (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)))) ) 97.53/107.95 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.95 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.53/107.95 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.53/107.95 ) 97.53/107.95 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (forall ((V_w_2 $$unsorted)) (or (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w_2))) (= (hAPP _let_0 (c_Int_OBit1 V_w_2)) (hAPP (hAPP (c_HOL_OLet tc_Nat_Onat tc_Nat_Onat) (hAPP _let_0 V_w_2)) (hAPP (hAPP (c_COMBB tc_Nat_Onat tc_Nat_Onat tc_Nat_Onat) c_Nat_OSuc) (hAPP (hAPP (c_COMBS tc_Nat_Onat tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oplus__class_Oplus tc_Nat_Onat)) (c_COMBI tc_Nat_Onat)))))) )) 97.53/107.95 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.95 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.95 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.53/107.95 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.53/107.95 ) 97.53/107.95 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) _let_1)))) (let ((_let_3 (= _let_1 _let_2))) (let ((_let_4 (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2))) (forall ((V_x_2 $$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))) (and (or _let_3 (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_x_2) (c_Big__Operators_Olattice__class_OInf__fin T_b _let_2)) _let_4)) (or (not _let_3) (= V_x_2 _let_4)))) )))))) 97.53/107.95 ( v_pn, v_U, tc_Com_Opname ) 97.53/107.95 ) 97.53/107.95 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Rings_Osemiring__1 T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (c_Groups_Ozero__class_Ozero T_b)) (c_Nat_Osemiring__1__class_ONats T_b)))) ) 97.53/107.95 ( tc_Nat_Onat ) 97.53/107.95 ( tc_Int_Oint ) 97.53/107.95 ( tc_Code__Numeral_Ocode__numeral ) 97.53/107.95 ( t_a ) 97.53/107.95 ( tc_Com_Opname ) 97.53/107.95 ) 97.53/107.95 (instantiation (forall ((T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_OCollect T_b) (hAPP (c_COMBK tc_HOL_Obool T_b) c_fFalse))) ) 97.53/107.95 ( tc_Nat_Onat ) 97.53/107.95 ( tc_HOL_Obool ) 97.53/107.95 ( tc_Int_Oint ) 97.53/107.95 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.95 ( t_a ) 97.53/107.95 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.95 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.95 ( tc_Product__Type_Ounit ) 97.53/107.95 ) 97.53/107.95 (instantiation (forall ((V_pn_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Com_Opname) V_pn_2) v_U))) (v_wt (c_Option_Othe tc_Com_Ocom (c_Com_Obody V_pn_2)))) ) 97.53/107.95 ( v_pn ) 97.53/107.95 ) 97.53/107.95 (instantiation (forall ((V_z $$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))) ) 97.53/107.95 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.53/107.95 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.53/107.95 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.95 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.95 ) 97.53/107.95 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 V_m) V_n))) (not (hBOOL (hAPP (hAPP _let_0 V_n) V_m))) (= V_n V_m)) )) 97.53/107.95 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.53/107.95 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.53/107.95 ) 97.53/107.95 (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__sup__class_Osup 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_OSup__fin T_b V_A_2)) V_A_2))) )))) 97.53/107.95 ( v_U, tc_Com_Opname ) 97.53/107.95 ) 97.53/107.95 (instantiation (forall ((V_f_2 $$unsorted) (V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_c tc_HOL_Obool)) V_B_2) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) V_B_2))) ) 97.53/107.95 ( v_mgt__call, v_G, t_a, v_U, tc_Com_Opname ) 97.53/107.95 ) 97.53/107.95 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Nat_Onat))) (let ((_let_1 (c_Finite__Set_Ofinite T_b))) (let ((_let_2 (c_Finite__Set_Ocard T_b))) (let ((_let_3 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP _let_1 V_A_2))) (not (hBOOL (hAPP _let_1 V_B_2))) (= (hAPP (hAPP _let_0 (hAPP _let_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_3) V_A_2) V_B_2))) (hAPP _let_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_3) V_A_2) V_B_2))) (hAPP (hAPP _let_0 (hAPP _let_2 V_A_2)) (hAPP _let_2 V_B_2)))) ))))) 97.53/107.96 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.96 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.96 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.96 ) 97.53/107.96 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m) V_n))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m) (hAPP c_Nat_OSuc V_n)))) ) 97.53/107.96 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.53/107.96 ) 97.53/107.96 (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))) ) 97.53/107.96 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.53/107.96 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.96 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.96 ) 97.53/107.96 (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 $$unsorted)) (= (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_z_2) (hAPP c_Int_OAbs__Integ (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR _let_0 _let_1) (hAPP c_Int_ORep__Integ V_z_2)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat _let_1) (hAPP (hAPP (c_COMBB _let_2 _let_2 tc_Nat_Onat) (hAPP (c_COMBB _let_1 _let_1 tc_Nat_Onat) (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel))) (hAPP (hAPP (c_COMBC tc_Nat_Onat _let_1 _let_2) (hAPP (hAPP (c_COMBB _let_4 (tc_fun _let_1 _let_2) tc_Nat_Onat) (c_COMBC tc_Nat_Onat _let_1 _let_1)) (hAPP (hAPP (c_COMBB (tc_fun tc_Nat_Onat _let_0) _let_4 tc_Nat_Onat) (hAPP (c_COMBB _let_0 _let_3 tc_Nat_Onat) (c_Set_Oinsert _let_0))) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat _let_0) (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat))))) (c_Orderings_Obot__class_Obot _let_1))))))) )))))) 97.53/107.96 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.96 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.53/107.96 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.96 ) 97.53/107.96 (instantiation (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Orderings_Oorder T_c)) (not (class_Enum_Oenum T_b)) (= (hBOOL (hAPP (c_Enum_Oenum__class_Oenum__all T_b) (hAPP (hAPP (c_COMBS T_b T_c tc_HOL_Obool) (hAPP (hAPP (c_COMBB T_c (tc_fun T_c tc_HOL_Obool) T_b) (c_Orderings_Oord__class_Oless__eq T_c)) V_f_2)) V_g_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b T_c)) V_f_2) V_g_2)))) ) 97.53/107.96 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a, tc_HOL_Obool ) 97.53/107.96 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a, tc_HOL_Obool ) 97.53/107.96 ) 97.53/107.96 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) _let_1)))) (let ((_let_3 (c_Big__Operators_Olinorder__class_OMin T_b V_A_2))) (let ((_let_4 (= _let_1 _let_2))) (forall ((V_x_2 $$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)))) )))))) 97.53/107.96 ( v_pn, v_U, tc_Com_Opname ) 97.53/107.96 ) 97.53/107.96 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone T_a))) (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (= _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) _let_0))) )) 97.53/107.96 ( tc_Nat_Onat ) 97.53/107.96 ( tc_Int_Oint ) 97.53/107.96 ( tc_Code__Numeral_Ocode__numeral ) 97.53/107.96 ) 97.53/107.96 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (forall ((V_k $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (c_Groups_Oone__class_Oone T_a)) (hAPP _let_0 V_k)) (hAPP _let_0 (c_Int_Osucc V_k)))) )) 97.53/107.96 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.53/107.96 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.96 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.53/107.96 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.53/107.96 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.96 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.53/107.96 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.53/107.96 ) 97.53/107.96 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 V_z) V_w))) (not (hBOOL (hAPP (hAPP _let_0 V_w) V_z))) (= V_w V_z)) )) 97.53/107.96 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.96 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.96 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.96 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.96 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.96 ) 97.53/107.96 (instantiation (forall ((V_R_2 $$unsorted) (T_b $$unsorted)) (= (c_Transitive__Closure_Ortrancl T_b (c_Transitive__Closure_Otrancl T_b V_R_2)) (c_Transitive__Closure_Ortrancl T_b V_R_2)) ) 97.53/107.96 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc))), tc_Nat_Onat ) 97.53/107.96 ) 97.53/107.96 (instantiation (forall ((T_b $$unsorted)) (= (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Relation_ORange T_b T_b) (c_Relation_OId T_b))) ) 97.53/107.96 ( tc_Nat_Onat ) 97.53/107.96 ( tc_HOL_Obool ) 97.53/107.96 ( tc_Int_Oint ) 97.53/107.96 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.96 ( t_a ) 97.53/107.96 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.96 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.96 ( tc_Product__Type_Ounit ) 97.53/107.96 ) 97.53/107.96 (instantiation (forall ((V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) V_B_2))) (= (not (forall ((B_f $$unsorted)) (not (c_Fun_Obij__betw T_b T_c B_f V_A_2 V_B_2)) )) (= (hAPP (c_Finite__Set_Ocard T_b) V_A_2) (hAPP (c_Finite__Set_Ocard T_c) V_B_2)))) ) 97.53/107.96 ( v_U, tc_Com_Opname, v_U, tc_Com_Opname ) 97.53/107.96 ) 97.53/107.96 (instantiation (forall ((V_x $$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))) ) 97.53/107.96 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.96 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.96 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.96 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.96 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.96 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (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)) ) 97.53/107.96 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.96 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.96 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.96 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.96 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.96 ) 97.53/107.96 (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))) )) 97.53/107.96 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.96 ( (c_Int_Opred (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 ) 97.53/107.96 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.96 ) 97.53/107.96 (instantiation (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (T_e $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_d $$unsorted)) (or (not (= (hAPP (c_Fun_Ocomp T_d T_c T_b V_a_2) V_b_2) (hAPP (c_Fun_Ocomp T_e T_c T_b V_c_2) V_d_2))) (forall ((B_v $$unsorted)) (= (hAPP V_a_2 (hAPP V_b_2 B_v)) (hAPP V_c_2 (hAPP V_d_2 B_v))) )) ) 97.53/107.96 ( c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), tc_Nat_Onat, c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 97.53/107.96 ( c_Code__Numeral_Onat__of, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, c_Code__Numeral_Onat__of, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Code__Numeral_Ocode__numeral, tc_Int_Oint, tc_Nat_Onat ) 97.53/107.96 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), c_Int_Onat, tc_Int_Oint, (c_Groups_Oabs__class_Oabs tc_Int_Oint), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint ) 97.53/107.96 ) 97.53/107.96 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 _let_1) V_a_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) _let_1)))) ))) 97.53/107.96 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.96 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.96 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.53/107.96 ) 97.53/107.96 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_r_2)) (c_Wellfounded_Oacyclic T_b V_r_2)) ) 97.53/107.96 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc))), tc_Nat_Onat ) 97.53/107.96 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 97.53/107.96 ( (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))), tc_Nat_Onat ) 97.53/107.96 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))))) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.96 ) 97.53/107.96 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 _let_0)) (= _let_0 (hAPP (c_Set_Oimage T_c T_b (c_Hilbert__Choice_Oinv__into T_b T_c _let_0 V_f_2)) (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool))))) )) 97.53/107.96 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.53/107.96 ) 97.53/107.96 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Opreorder T_1)) (class_Orderings_Opreorder (tc_fun T_2 T_1))) ) 97.53/107.96 ( tc_Nat_Onat, tc_HOL_Obool ) 97.53/107.96 ( tc_HOL_Obool, tc_HOL_Obool ) 97.53/107.96 ( tc_Int_Oint, tc_HOL_Obool ) 97.53/107.96 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.53/107.96 ( t_a, tc_HOL_Obool ) 97.53/107.96 ( (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 ) 97.53/107.96 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.53/107.96 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.53/107.96 ) 97.53/107.96 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP _let_1 V_A_2)) (hAPP _let_1 V_B_2)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_A_2) V_B_2))) ))) 97.53/107.96 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.53/107.96 ) 97.53/107.96 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (forall ((V_k $$unsorted)) (= (c_Int_OBit1 (c_Int_Opred (hAPP _let_0 V_k))) (hAPP _let_0 (c_Int_OBit1 V_k))) )) 97.53/107.96 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.53/107.96 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.96 ) 97.53/107.96 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_A_2) V_B_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP _let_0 V_A_2)) (hAPP _let_0 V_B_2)))) )) 97.53/107.96 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.53/107.96 ) 97.53/107.96 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hAPP (c_Set_Oimage T_b T_b _let_0) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_x_2)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) (hAPP _let_0 V_x_2)))) )) 97.53/107.96 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.96 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.96 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.96 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.96 ) 97.53/107.96 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP (hAPP (c_Set_Oinsert T_b) V_l_2) (c_Orderings_Obot__class_Obot _let_0))) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_l_2)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_l_2))) )) 97.53/107.96 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.96 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.96 ( (hAPP v_mgt__call v_pn), t_a ) 97.53/107.96 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.97 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.97 ) 97.53/107.97 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$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)) )) 97.53/107.97 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.97 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.97 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.97 ) 97.53/107.97 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_b_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_b_2)) (c_Groups_Ozero__class_Ozero T_b))) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2)))) )) 97.53/107.97 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.53/107.97 ( (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 ) 97.53/107.97 ) 97.53/107.97 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) V_n)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP _let_0 V_m)) (hAPP _let_0 V_n)))) )) 97.53/107.97 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 97.53/107.97 ) 97.53/107.97 (instantiation (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_fun tc_Nat_Onat tc_HOL_Obool))) (let ((_let_2 (c_Rings_Odvd__class_Odvd tc_Nat_Onat))) (let ((_let_3 (tc_fun tc_Nat_Onat _let_0))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (not (c_Orderings_Oorder_Ostrict__mono tc_Nat_Onat T_b (hAPP (hAPP (c_COMBS tc_Nat_Onat _let_1 _let_1) (hAPP (hAPP (c_COMBB _let_3 (tc_fun _let_1 _let_1) tc_Nat_Onat) (c_COMBS tc_Nat_Onat tc_HOL_Obool tc_HOL_Obool)) (hAPP (hAPP (c_COMBB _let_1 _let_3 tc_Nat_Onat) (hAPP (c_COMBB tc_HOL_Obool _let_0 tc_Nat_Onat) c_fconj)) _let_2))) (hAPP (hAPP (c_COMBB _let_1 _let_1 tc_Nat_Onat) (hAPP (c_COMBB tc_HOL_Obool tc_HOL_Obool tc_Nat_Onat) c_fNot)) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) _let_2))) V_f_2)) (not (hBOOL (hAPP (hAPP _let_2 V_x_2) V_y_2))) (hBOOL (hAPP (hAPP _let_2 V_y_2) V_x_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (hAPP V_f_2 V_x_2)) (hAPP V_f_2 V_y_2)))) ))))) 97.53/107.97 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (c_Relation_OImage _let_1 _let_1 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)) (c_Orderings_Obot__class_Obot (tc_fun _let_1 tc_HOL_Obool)))))), c_Int_OAbs__Integ, tc_Int_Oint ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((V_na_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) V_na_2) (hAPP (c_List_Oset tc_Nat_Onat) (c_List_Oupt (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_na_2))) ) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2)) (and (not (= V_y_2 V_x_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2))))) ) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.53/107.97 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.97 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.53/107.97 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.97 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m) V_n))) (= V_n V_m) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m) V_n))) ) 97.53/107.97 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.53/107.97 ) 97.53/107.97 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_A_2) V_B_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) )) 97.53/107.97 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((V_G_2 $$unsorted) (V_ts_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) V_ts_2) V_G_2))) (v_P V_G_2 V_ts_2)) ) 97.53/107.97 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G ) 97.53/107.97 ) 97.53/107.97 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Nat_Onat))) (let ((_let_1 (c_Divides_Odiv__class_Odiv tc_Nat_Onat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_n))) (hBOOL (hAPP (hAPP _let_0 V_m) V_n)) (= (hAPP c_Nat_OSuc (hAPP (hAPP _let_1 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n)) V_n)) (hAPP (hAPP _let_1 V_m) V_n))) ))) 97.53/107.97 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((V_v $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Int_Onumber__class_Onumber__of T_a) V_v) (hAPP (c_Int_Oring__1__class_Oof__int T_a) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v)))) ) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.53/107.97 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.97 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.53/107.97 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.97 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.53/107.97 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.53/107.97 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.53/107.97 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.53/107.97 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.53/107.97 ) 97.53/107.97 (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_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)) (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))))) ))) 97.53/107.97 ( (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) ) 97.53/107.97 ( (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) ) 97.53/107.97 ) 97.53/107.97 (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)))) ) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.97 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.97 ) 97.53/107.97 (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))) )) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Oone__class_Oone T_a))) ) 97.53/107.97 ( tc_Nat_Onat ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((V_z $$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)) ) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.97 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.53/107.97 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.97 ) 97.53/107.97 (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)) (= (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))) (= _let_0 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_m_2))) )) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.97 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.53/107.97 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.97 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.97 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.53/107.97 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.97 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.97 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.53/107.97 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.53/107.97 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.97 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.53/107.97 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.53/107.97 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.97 ) 97.53/107.97 (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))) )) 97.53/107.97 ( (c_Int_Opred (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 ) 97.53/107.97 ) 97.53/107.97 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 (c_Orderings_Otop__class_Otop _let_0))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_c tc_HOL_Obool)) V_B_2) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) (hAPP (c_Set_Ovimage T_b T_c V_f_2) V_B_2)) V_A_2))) )) 97.53/107.97 ( v_U, v_G, v_mgt__call, t_a, tc_Com_Opname ) 97.53/107.97 ) 97.53/107.97 (instantiation (let ((_let_0 (c_member (tc_prod T_b T_b)))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (let ((_let_2 (hAPP _let_1 V_a_2))) (let ((_let_3 (c_Transitive__Closure_Otrancl T_b V_r_2))) (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_b_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_b_2) V_c_2)) V_r_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))) ))))) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (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) (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_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.97 ) 97.53/107.97 (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 (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)))) )) 97.53/107.97 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.97 ) 97.53/107.97 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_l_2) V_u_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_u_2) (c_Orderings_Obot__class_Obot _let_0))) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_l_2 V_u_2))) )) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.97 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.97 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.97 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.97 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ) 97.53/107.97 (instantiation (let ((_let_0 (c_Set_Oimage T_c T_b V_f_2))) (forall ((V_B_H_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_B_H_2) (hAPP _let_0 V_A_2)))) (= V_B_H_2 (hAPP _let_0 (hAPP (c_Set_Oimage T_b T_c (c_Hilbert__Choice_Oinv__into T_c T_b V_A_2 V_f_2)) V_B_H_2)))) )) 97.53/107.97 ( v_G, v_U, v_mgt__call, t_a, tc_Com_Opname ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) (c_Groups_Ozero__class_Ozero T_a))) ) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.97 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.97 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.97 ) 97.53/107.97 (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 $$unsorted)) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP _let_0 V_a))) (not (hBOOL (hAPP _let_0 V_b))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)))) )) 97.53/107.97 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b V_r_2)) (c_Wellfounded_Owf (tc_fun T_b tc_HOL_Obool) (c_Wellfounded_Omin__ext T_b V_r_2))) ) 97.53/107.97 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))))) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.97 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0)))), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((V_m $$unsorted)) (= V_m (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.53/107.97 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.53/107.97 ) 97.53/107.97 (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 $$unsorted)) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b _let_1) V_A_2) (hAPP (hAPP (c_COMBC T_b _let_1 _let_1) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_1 _let_1) T_b) (c_Set_Oinsert _let_0)) (hAPP (hAPP (c_COMBB _let_0 _let_0 T_b) (c_Relation_OImage T_b T_b V_r_2)) (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (c_Set_Oinsert T_b)) (c_Orderings_Obot__class_Obot _let_0))))) (c_Orderings_Obot__class_Obot _let_1))) (hAPP (hAPP (c_Equiv__Relations_Oquotient T_b) V_A_2) V_r_2)) ))) 97.53/107.97 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_k) V_k) (c_Int_OBit0 V_k)) ) 97.53/107.97 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.97 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.97 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.97 ) 97.53/107.97 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (forall ((V_k $$unsorted)) (= (hAPP _let_0 (c_Int_OBit0 V_k)) (c_Int_OBit0 (hAPP _let_0 V_k))) )) 97.53/107.97 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.53/107.97 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (= (hAPP (c_Finite__Set_Ocard T_b) V_A_2) (hAPP (c_Finite__Set_Ocard T_c) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2))) (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2))) ) 97.53/107.97 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.97 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.53/107.97 ( v_mgt__call, t_a, v_U, tc_Com_Opname ) 97.53/107.97 ) 97.53/107.97 (instantiation (forall ((V_b $$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))) ) 97.53/107.97 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.53/107.97 ( (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 ) 97.53/107.97 ) 97.53/107.97 (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))))) )) 97.53/107.98 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.98 ( (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.53/107.98 ( v_G, (tc_fun t_a tc_HOL_Obool) ) 97.53/107.98 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.53/107.98 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.98 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.53/107.98 ) 97.53/107.98 (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))) )) 97.53/107.98 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.98 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.98 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.53/107.98 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (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)) ) 97.53/107.98 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.98 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.98 ) 97.53/107.98 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olattice_OInf__fin T_b _let_0 V_A_2) (hAPP (c_Finite__Set_Ofold1 T_b _let_0) V_A_2))) )) 97.53/107.98 ( v_U, tc_Com_Opname ) 97.53/107.98 ) 97.53/107.98 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_d tc_HOL_Obool)))) (forall ((V_g_2 $$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)) )) 97.53/107.98 ( c_Int_Onat, tc_Int_Oint, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 97.53/107.98 ( 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 ) 97.53/107.98 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), tc_Int_Oint, c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.53/107.98 ) 97.53/107.98 (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)))) ) 97.53/107.98 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (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)) ) 97.53/107.98 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.98 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.98 ) 97.53/107.98 (instantiation (forall ((V_A_2 $$unsorted) (V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (c_Set_Oimage T_c T_b V_f_2) (hAPP (c_Set_Oimage T_d T_c V_g_2) V_A_2)) (hAPP (c_Set_Oimage T_d T_b (hAPP (hAPP (c_COMBB T_c T_b T_d) V_f_2) V_g_2)) V_A_2)) ) 97.53/107.98 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.53/107.98 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.53/107.98 ) 97.53/107.98 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Finite__Set_Ofinite T_b)) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) ) 97.53/107.98 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.98 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.53/107.98 ) 97.53/107.98 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (= V_x_2 (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 97.53/107.98 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.98 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.98 ( (hAPP v_mgt__call v_pn), t_a ) 97.53/107.98 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.98 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.98 ) 97.53/107.98 (instantiation (forall ((T_b $$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)))) ) 97.53/107.98 ( tc_Nat_Onat ) 97.53/107.98 ( tc_Code__Numeral_Ocode__numeral ) 97.53/107.98 ) 97.53/107.98 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (c_Orderings_Oord__class_Omax T_b))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_2) V_A_2) V_B_2))) (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))) (= _let_3 (c_Orderings_Obot__class_Obot _let_2)) (= (hAPP (hAPP _let_1 (c_Big__Operators_Olattice_OSup__fin T_b _let_1 V_A_2)) (c_Big__Operators_Olattice_OSup__fin T_b _let_1 V_B_2)) (hAPP (hAPP _let_1 (c_Big__Operators_Olattice_OSup__fin T_b _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_2) V_A_2) V_B_2))) (c_Big__Operators_Olattice_OSup__fin T_b _let_1 _let_3)))) ))))) 97.53/107.98 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.98 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.98 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.98 ) 97.53/107.98 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (c_Set_OCollect T_b) (hAPP c_fequal V_a_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 97.53/107.98 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.98 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.98 ( (hAPP v_mgt__call v_pn), t_a ) 97.53/107.98 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.98 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.98 ) 97.53/107.98 (instantiation (forall ((V_h_2 $$unsorted) (T_c $$unsorted) (V_F_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_F_2))) (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (hAPP (c_Set_Oimage T_b T_c V_h_2) V_F_2)))) ) 97.53/107.98 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.98 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.53/107.98 ( v_mgt__call, t_a, v_U, tc_Com_Opname ) 97.53/107.98 ) 97.53/107.98 (instantiation (let ((_let_0 (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (let ((_let_2 (tc_fun T_c (tc_fun T_b tc_HOL_Obool)))) (forall ((V_C_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_d $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_d _let_0) V_A_2) (hAPP (hAPP (c_COMBC T_d _let_2 _let_0) (hAPP (hAPP (c_COMBB _let_1 (tc_fun _let_2 _let_0) T_d) _let_0) V_B_2)) V_C_2)) (hAPP (hAPP _let_0 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_d _let_1) V_A_2) V_B_2)) V_C_2))) )))) 97.53/107.98 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat ) 97.53/107.98 ) 97.53/107.98 (instantiation (forall ((V_m_2 $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) V_m_2) (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool))) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat V_m_2) (hAPP c_Nat_OSuc V_m_2))) ) 97.53/107.98 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.53/107.98 ( v_n ) 97.53/107.98 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.53/107.98 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.53/107.98 ) 97.53/107.98 (instantiation (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (not (class_Divides_Osemiring__div T_a)) (= (c_Divides_Odiv__class_Omod T_a (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_b) V_a) V_b) (c_Divides_Odiv__class_Omod T_a V_a V_b))) ) 97.53/107.98 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.98 ) 97.53/107.98 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$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) (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_B_2) V_A_2)))) )) 97.53/107.98 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.53/107.98 ) 97.53/107.98 (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 (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y) (c_Orderings_Otop__class_Otop T_a))) (= V_y (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x))) ) 97.53/107.98 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.98 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.53/107.98 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.53/107.98 ) 97.53/107.98 (instantiation (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_prod T_b T_b))) (let ((_let_2 (c_Product__Type_OPair T_b T_b))) (let ((_let_3 (tc_fun _let_1 tc_HOL_Obool))) (let ((_let_4 (tc_fun T_b tc_HOL_Obool))) (let ((_let_5 (c_COMBC T_b _let_3 tc_HOL_Obool))) (let ((_let_6 (hAPP (c_COMBB _let_1 (tc_fun _let_3 tc_HOL_Obool) T_b) (c_member _let_1)))) (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 $$unsorted)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_3) (c_Transitive__Closure_Otrancl T_b V_r_2)) (hAPP (c_Set_OCollect _let_1) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_b tc_HOL_Obool) (hAPP (hAPP (c_COMBC T_b _let_4 _let_4) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_4 _let_4) T_b) (c_COMBB tc_HOL_Obool tc_HOL_Obool T_b)) (hAPP (hAPP (c_COMBB tc_HOL_Obool _let_0 T_b) c_fconj) (hAPP (hAPP _let_5 (hAPP _let_6 (hAPP (hAPP (c_COMBC T_b T_b _let_1) _let_2) V_y_2))) _let_7)))) (hAPP (hAPP _let_5 (hAPP _let_6 (hAPP _let_2 V_x_2))) _let_7))))) (c_Transitive__Closure_Otrancl T_b (hAPP (hAPP (c_Set_Oinsert _let_1) (hAPP (hAPP _let_2 V_y_2) V_x_2)) V_r_2))) ))))))))) 97.53/107.99 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.99 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.99 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.53/107.99 ) 97.53/107.99 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_x) V_y)) (c_Nat__Transfer_Otsub (hAPP _let_0 V_x) (hAPP _let_0 V_y))) )) 97.53/107.99 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.53/107.99 ) 97.53/107.99 (instantiation (forall ((V_l $$unsorted) (V_k $$unsorted)) (not (= (c_Int_OBit0 V_l) (c_Int_OBit1 V_k))) ) 97.53/107.99 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.53/107.99 ) 97.53/107.99 (instantiation (let ((_let_0 (c_member T_b))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (forall ((B_Q $$unsorted)) (or (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP _let_0 B_x) B_Q))) ) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 B_x) B_Q))) (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) B_y) B_x)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 B_y) B_Q)))) ))) ))) ) (c_Wellfounded_Owf T_b V_r_2)) )) 97.53/107.99 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc))), tc_Nat_Onat ) 97.53/107.99 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 97.53/107.99 ( (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))), tc_Nat_Onat ) 97.53/107.99 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))))) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.99 ) 97.53/107.99 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2))) (let ((_let_3 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_B_2 $$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_Olinorder__class_OMin T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMin T_b V_B_2)) (hAPP (hAPP _let_3 (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2))) (c_Big__Operators_Olinorder__class_OMin T_b _let_2)))) ))))) 97.53/107.99 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.99 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/107.99 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.53/107.99 ) 97.53/107.99 (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))))) )))) 97.53/107.99 ( (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 ) 97.53/107.99 ) 97.53/107.99 (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 (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 _let_0 V_w_2) V_z_2)))) )) 97.53/107.99 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.53/107.99 ) 97.53/107.99 (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_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (= (hAPP (hAPP _let_0 V_a_2) _let_1) (hAPP (hAPP _let_0 V_b_2) _let_1))) (= V_b_2 V_a_2)) ))) 97.53/107.99 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.99 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.99 ) 97.53/107.99 (instantiation (forall ((V_A_2 $$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)))) ) 97.53/107.99 ( v_G, (hAPP v_mgt__call v_pn), t_a ) 97.53/107.99 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.99 ( (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) ) 97.53/107.99 ( (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) ) 97.53/107.99 ( (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)) ) 97.53/107.99 ) 97.53/107.99 (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)))) )) 97.53/107.99 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.53/107.99 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.53/107.99 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.53/107.99 ) 97.53/107.99 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (c_Orderings_Oord__class_Omax T_b) (c_Orderings_Oord_Omin T_b (hAPP (c_COMBC T_b T_b tc_HOL_Obool) (c_Orderings_Oord__class_Oless__eq T_b))))) ) 97.53/107.99 ( tc_Nat_Onat ) 97.53/107.99 ( tc_Int_Oint ) 97.53/107.99 ( tc_Code__Numeral_Ocode__numeral ) 97.53/107.99 ( (tc_fun t_a tc_HOL_Obool) ) 97.53/107.99 ) 97.53/107.99 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (let ((_let_1 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_m_2 $$unsorted) (V_na_2 $$unsorted)) (= (= (hAPP _let_1 V_m_2) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP _let_1 V_na_2))) (and (= _let_0 V_na_2) (= _let_0 V_m_2))) ))) 97.53/107.99 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.53/107.99 ) 97.53/107.99 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_n) V_m)) V_m) (hAPP (hAPP (c_Orderings_Oord__class_Omax tc_Nat_Onat) V_n) V_m)) ) 97.53/107.99 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.53/107.99 ) 97.53/107.99 (instantiation (forall ((V_A_2 $$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))))) ) 97.53/107.99 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 97.53/107.99 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 97.53/107.99 ) 97.53/107.99 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)))) (forall ((T_b $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted)) (= (= V_B_2 V_A_2) (and (hBOOL (hAPP (hAPP _let_0 V_B_2) V_A_2)) (hBOOL (hAPP (hAPP _let_0 V_A_2) V_B_2)))) )) 97.53/107.99 ( t_a, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G ) 97.53/107.99 ( t_a, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G) ) 97.53/107.99 ( t_a, v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U) ) 97.53/107.99 ( t_a, (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U) ) 97.53/107.99 ) 97.53/107.99 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (forall ((T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool))))) (hBOOL (hAPP (c_Finite__Set_Ofinite _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))))) )) 97.53/107.99 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.99 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.53/107.99 ) 97.53/107.99 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun (tc_prod T_b T_b) tc_HOL_Obool))) (let ((_let_3 (c_Equiv__Relations_Oquotient T_b))) (forall ((V_r_2 $$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_1 (hAPP (hAPP (c_COMBC T_b _let_2 _let_1) (hAPP (hAPP (c_COMBB _let_0 (tc_fun _let_2 _let_1) T_b) _let_3) (hAPP (hAPP (c_COMBC T_b _let_0 _let_0) (c_Set_Oinsert T_b)) (c_Orderings_Obot__class_Obot _let_0)))) V_r_2) V_A_2)) (= (hAPP (c_Finite__Set_Ocard T_b) V_A_2) (hAPP (c_Finite__Set_Ocard _let_0) (hAPP (hAPP _let_3 V_A_2) V_r_2)))) ))))) 97.53/107.99 ( 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) ) 97.53/107.99 ) 97.53/107.99 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 V_A_2)) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 97.53/107.99 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.53/107.99 ) 97.53/107.99 (instantiation (let ((_let_0 (c_member (tc_prod T_b T_b)))) (let ((_let_1 (c_Product__Type_OPair T_b T_b))) (let ((_let_2 (hAPP _let_1 B_x))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (forall ((B_x $$unsorted) (B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 B_y)) V_r_2))) (forall ((B_z $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_y) B_z)) V_r_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 B_z)) V_r_2))) )) ) (c_Relation_Otrans T_b V_r_2)) )))) 97.53/107.99 ( (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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 ) 97.53/107.99 ) 97.53/107.99 (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))) ) 97.53/107.99 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.53/107.99 ( v_G, t_a ) 97.53/107.99 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/107.99 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.53/107.99 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 97.53/107.99 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 97.53/107.99 ) 97.53/107.99 (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)) ) 97.53/107.99 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.53/107.99 ) 97.53/107.99 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m) V_n))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (hAPP _let_0 V_m)) (hAPP _let_0 V_n)))) )) 97.53/107.99 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.53/107.99 ) 97.53/107.99 (instantiation (forall ((V_i_2 $$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)))))) ) 97.53/107.99 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat_OSuc ) 97.53/107.99 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.53/107.99 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 97.53/107.99 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.99 ( (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)) ) 97.53/107.99 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), c_Nat_OSuc ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Set_Oinsert tc_Nat_Onat) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (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)) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (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)) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), c_Nat_OSuc ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.53/107.99 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.53/107.99 ) 97.53/107.99 (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)))))) ) 97.53/107.99 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.53/107.99 ( (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)) ) 97.53/107.99 ( (hAPP v_mgt__call v_pn), t_a ) 97.53/107.99 ( (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) ) 97.53/108.00 ( (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) ) 97.53/108.00 ) 97.53/108.00 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b)) V_a_2) V_A_2) (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) V_A_2)))) ) 97.53/108.00 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.53/108.00 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.53/108.00 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.53/108.00 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.00 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Groups_Ozero__class_Ozero T_b)))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP _let_0 V_a_2)) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2))))) )) 97.69/108.00 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.00 ) 97.69/108.00 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Lattices_Osemilattice__sup__class_Osup T_b)) (c_Orderings_Obot__class_Obot T_b)) V_A_2) (c_Complete__Lattice_OSup__class_OSup T_b V_A_2))) ) 97.69/108.00 ( v_U, tc_Com_Opname ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (c_Finite__Set_Ofold1 T_b (c_Groups_Otimes__class_Otimes T_b)))) (forall ((V_x_2 $$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)))) )) 97.69/108.00 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.69/108.00 ) 97.69/108.00 (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))) )) 97.69/108.00 ( v_pn, v_U, tc_Com_Opname ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (c_SetInterval_Oord__class_OatLeastAtMost T_b V_l_2 V_u_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (hAPP (hAPP (c_Set_Oinsert T_b) V_l_2) (c_Orderings_Obot__class_Obot _let_0))) (c_SetInterval_Oord__class_OgreaterThanAtMost T_b V_l_2 V_u_2)))) )) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.00 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.00 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.00 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.00 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.00 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.00 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.00 ) 97.69/108.00 (instantiation (forall ((V_v_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_d $$unsorted)) (or (not (= (hAPP (c_Fun_Ocomp T_d T_c T_b V_a_2) V_b_2) (hAPP (c_Fun_Ocomp T_c T_c T_b (c_Fun_Oid T_c)) V_c_2))) (= (hAPP V_c_2 V_v_2) (hAPP V_a_2 (hAPP V_b_2 V_v_2)))) ) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless 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 ) 97.69/108.00 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 97.69/108.00 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Equiv__Relations_Oquotient (tc_prod tc_Nat_Onat tc_Nat_Onat)), (c_Groups_Oabs__class_Oabs tc_Int_Oint), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat))) (forall ((V_k_2 $$unsorted)) (= (hAPP _let_0 (hAPP c_Nat_OSuc V_k_2)) (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) V_k_2) (hAPP _let_0 V_k_2))) )) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.69/108.00 ( v_n ) 97.69/108.00 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.69/108.00 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((V_x_2 $$unsorted) (V_Pa_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 _let_0)) (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_c) B_y) (hAPP (c_Set_Oimage T_b T_c V_f_2) _let_0)))) (hBOOL (hAPP V_Pa_2 (hAPP (c_Hilbert__Choice_Oinv__into T_b T_c _let_0 V_f_2) B_y)))) )) (hBOOL (hAPP V_Pa_2 V_x_2))) )) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.69/108.00 ) 97.69/108.00 (instantiation (forall ((T_1 $$unsorted) (T_2 $$unsorted)) (or (not (class_Lazy__Sequence_Osmall__lazy T_2)) (not (class_Lazy__Sequence_Osmall__lazy T_1)) (class_Lazy__Sequence_Osmall__lazy (tc_prod T_2 T_1))) ) 97.69/108.00 ( tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.00 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.00 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (c_Groups_Ominus__class_Ominus T_a))) (forall ((V_b $$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))) )) 97.69/108.00 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.00 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.69/108.00 ( (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 ) 97.69/108.00 ( (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 ) 97.69/108.00 ) 97.69/108.00 (instantiation (forall ((T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) (c_Relation_OId__on T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 97.69/108.00 ( tc_Nat_Onat ) 97.69/108.00 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.00 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_z))) (hBOOL (hAPP (hAPP _let_0 V_x) V_z))) )) 97.69/108.00 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.00 ) 97.69/108.00 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ocomm__monoid__add T_a)) (= V_a (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) ) 97.69/108.00 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Finite__Set_Ocard T_b))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) _let_0))) (not (= (hAPP _let_1 V_A_2) (hAPP _let_1 _let_0))) (= V_A_2 _let_0)) ))) 97.69/108.00 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.69/108.00 ( v_G, t_a ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot T_b))) (forall ((V_y_2 $$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_y_2 _let_0) (= V_x_2 _let_0)))) )) 97.69/108.00 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.00 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.00 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (or (and (not (hBOOL (hAPP (hAPP _let_1 _let_0) V_z_2))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) V_w_2)))) (= (hBOOL (hAPP (hAPP _let_1 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))))) ))) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.00 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.00 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.00 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (c_Relation_OImage T_c T_b V_r_2))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (tc_fun T_c tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_1) V_B_2) (hAPP (hAPP (c_COMBB _let_2 _let_1 T_c) _let_0) (hAPP (hAPP (c_COMBC T_c _let_2 _let_2) (c_Set_Oinsert T_c)) (c_Orderings_Obot__class_Obot _let_2)))) (hAPP _let_0 V_B_2)) )))) 97.69/108.00 ( (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) ) 97.69/108.00 ( (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) ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (c_Groups_Otimes__class_Otimes T_b))) (let ((_let_1 (c_Groups_Oplus__class_Oplus T_b))) (let ((_let_2 (c_Groups_Oone__class_Oone T_b))) (let ((_let_3 (c_Nat_Osemiring__1__class_Oof__nat T_b))) (let ((_let_4 (hAPP _let_3 V_na_2))) (forall ((V_na_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Ocomm__semiring__1 T_b)) (= (hAPP (hAPP _let_0 _let_4) (hAPP (hAPP _let_1 _let_4) _let_2)) (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 _let_2) _let_2)) (hAPP (hAPP (c_Big__Operators_Ocomm__monoid__add__class_Osetsum tc_Nat_Onat T_b) _let_3) (c_SetInterval_Oord__class_OatLeastAtMost tc_Nat_Onat (c_Groups_Oone__class_Oone tc_Nat_Onat) V_na_2))))) )))))) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.69/108.00 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 97.69/108.00 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.69/108.00 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.69/108.00 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.69/108.00 ) 97.69/108.00 (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 $$unsorted)) (= (c_Wellfounded_Ofinite__psubset T_b) (hAPP (c_Set_OCollect (tc_prod _let_1 _let_1)) (hAPP (c_Product__Type_Oprod_Oprod__case _let_1 _let_1 tc_HOL_Obool) (hAPP (hAPP (c_COMBC _let_1 _let_2 _let_2) (hAPP (hAPP (c_COMBB _let_3 (tc_fun _let_2 _let_2) _let_1) (c_COMBS _let_1 tc_HOL_Obool tc_HOL_Obool)) (hAPP (hAPP (c_COMBB _let_2 _let_3 _let_1) (hAPP (c_COMBB tc_HOL_Obool _let_0 _let_1) c_fconj)) (c_Orderings_Oord__class_Oless _let_1)))) (c_Finite__Set_Ofinite T_b))))) ))))) 97.69/108.00 ( tc_Nat_Onat ) 97.69/108.00 ( tc_Int_Oint ) 97.69/108.00 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.00 ( tc_Com_Opname ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (forall ((V_m_2 $$unsorted) (V_na_2 $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) V_na_2)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_na_2) (= (hAPP (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat _let_0) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat _let_0) tc_Nat_Onat) (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat)) c_Nat_OSuc)) (c_Divides_Odivmod__nat (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m_2) V_na_2) V_na_2)) (c_Divides_Odivmod__nat V_m_2 V_na_2))) )) 97.69/108.00 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.69/108.00 ) 97.69/108.00 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_N_2 $$unsorted) (V_M_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_M_2) V_N_2))) (= V_M_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Big__Operators_Olinorder__class_OMax T_b V_M_2)) (c_Big__Operators_Olinorder__class_OMax T_b V_N_2)))) )) 97.69/108.00 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.69/108.00 ) 97.69/108.00 (instantiation (forall ((V_i $$unsorted) (V_j $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_j) V_i))) (= (c_List_Olist_ONil tc_Int_Oint) (c_List_Oupto V_i V_j))) ) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.69/108.00 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.00 ) 97.69/108.00 (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_OSup__fin T_b (c_Orderings_Oord__class_Omax T_b) V_A_2))) (let ((_let_4 (= _let_1 _let_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (and (or _let_4 (= (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 _let_2)) _let_3)) (or (not _let_4) (= V_x_2 _let_3))))) )))))) 97.69/108.00 ( v_pn, v_U, tc_Com_Opname ) 97.69/108.00 ) 97.69/108.00 (instantiation (forall ((V_B_2 $$unsorted) (T_c $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_c) V_B_2))) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) V_A_2)) (hAPP (c_Finite__Set_Ocard T_c) V_B_2)) (hAPP (c_Finite__Set_Ocard (tc_sum T_b T_c)) (c_Sum__Type_OPlus T_b T_c V_A_2 V_B_2)))) ) 97.69/108.00 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit, (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), tc_Product__Type_Ounit ) 97.69/108.00 ) 97.69/108.00 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_a) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_b) V_a))) (= V_a (c_Divides_Odiv__class_Omod tc_Int_Oint V_a V_b))) ) 97.69/108.00 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.00 ) 97.69/108.00 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_OwfP T_b V_r_2)) (c_Wellfounded_Oacyclic T_b (hAPP (c_Set_OCollect (tc_prod T_b T_b)) (hAPP (c_Product__Type_Oprod_Oprod__case T_b T_b tc_HOL_Obool) V_r_2)))) ) 97.69/108.00 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.00 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat ) 97.69/108.00 ) 97.69/108.00 (instantiation (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (hBOOL (hAPP (hAPP (c_member T_b) V_i_2) (hAPP (c_SetInterval_Oord__class_OlessThan T_b) V_k_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_i_2) V_k_2)))) ) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.00 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.00 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.00 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.00 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.00 ) 97.69/108.00 (instantiation (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_i_2) V_j_2))) (= (= V_k_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_j_2) V_i_2)) (= V_j_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_k_2) V_i_2)))) ) 97.69/108.00 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.69/108.00 ) 97.69/108.00 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Otop T_1)) (class_Orderings_Otop (tc_fun T_2 T_1))) ) 97.69/108.00 ( tc_Nat_Onat, tc_HOL_Obool ) 97.69/108.00 ( tc_HOL_Obool, tc_HOL_Obool ) 97.69/108.00 ( tc_Int_Oint, tc_HOL_Obool ) 97.69/108.00 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.69/108.00 ( t_a, tc_HOL_Obool ) 97.69/108.00 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.69/108.01 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.69/108.01 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.69/108.01 ) 97.69/108.01 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (let ((_let_2 (tc_fun T_c _let_0))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_c _let_0) V_A_2) V_B_2) (c_Complete__Lattice_OInf__class_OInf _let_0 (hAPP (c_Set_OCollect _let_0) (hAPP (hAPP (c_COMBB _let_1 tc_HOL_Obool _let_0) (c_HOL_OEx T_c)) (hAPP (hAPP (c_COMBB _let_1 _let_1 _let_0) (hAPP (c_COMBS T_c tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_c) c_fconj) (hAPP (hAPP (c_COMBC T_c _let_1 tc_HOL_Obool) (c_member T_c)) V_A_2)))) (hAPP (hAPP (c_COMBC _let_0 _let_2 _let_1) (hAPP (hAPP (c_COMBB (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_2 _let_1) _let_0) (c_COMBB _let_0 tc_HOL_Obool T_c)) c_fequal)) V_B_2)))))) )))) 97.69/108.01 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.01 ) 97.69/108.01 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= V_x_2 (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 97.69/108.01 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.01 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.01 ( (hAPP v_mgt__call v_pn), t_a ) 97.69/108.01 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.01 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.01 ) 97.69/108.01 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 _let_0)) (= V_A_2 (hAPP (c_Set_Oimage T_c T_b (c_Hilbert__Choice_Oinv__into T_b T_c _let_0 V_f_2)) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) )) 97.69/108.01 ( v_U, v_mgt__call, t_a, tc_Com_Opname ) 97.69/108.01 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.01 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.69/108.01 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.69/108.01 ) 97.69/108.01 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_a_2))) (= (and (hBOOL (hAPP (hAPP _let_0 V_b_2) V_a_2)) (hBOOL (hAPP _let_1 V_b_2))) (hBOOL (hAPP _let_1 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_a_2) V_b_2))))) ))) 97.69/108.01 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.01 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.69/108.01 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.69/108.01 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.69/108.01 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.01 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.01 ) 97.69/108.01 (instantiation (let ((_let_0 (tc_fun tc_HOL_Obool tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (forall ((V_y_2 $$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)) ))) 97.69/108.01 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.01 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.01 ( (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) ) 97.69/108.01 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.69/108.01 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.69/108.01 ) 97.69/108.01 (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)))) ) 97.69/108.01 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.69/108.01 ) 97.69/108.01 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b (c_Orderings_Oord__class_Omin T_b)) V_x_2) V_A_2) (c_Big__Operators_Olinorder__class_OMin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) ) 97.69/108.01 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.69/108.01 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.01 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.69/108.01 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.01 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.01 ) 97.69/108.01 (instantiation (forall ((V_y $$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)))) ) 97.69/108.01 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.69/108.01 ( (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 ) 97.69/108.01 ) 97.69/108.01 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Groups_Omonoid__add T_b)) (= (c_List_Ofoldl T_b T_b (c_Groups_Oplus__class_Oplus T_b) (c_Groups_Ozero__class_Ozero T_b)) (c_List_Omonoid__add__class_Olistsum T_b))) ) 97.69/108.01 ( tc_Nat_Onat ) 97.69/108.01 ( tc_Int_Oint ) 97.69/108.01 ( tc_Code__Numeral_Ocode__numeral ) 97.69/108.01 ) 97.69/108.01 (instantiation (let ((_let_0 (c_Product__Type_OPair T_b T_c))) (forall ((V_b_H_2 $$unsorted) (V_a_H_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (and (= V_a_H_2 V_a_2) (= V_b_H_2 V_b_2)) (= (hAPP (hAPP _let_0 V_a_H_2) V_b_H_2) (hAPP (hAPP _let_0 V_a_2) V_b_2))) )) 97.69/108.01 ( (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 ) 97.69/108.01 ( (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 ) 97.69/108.01 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.69/108.01 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.69/108.01 ) 97.69/108.01 (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 $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 B_y) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) B_y))) )) (not (hBOOL (hAPP (hAPP _let_0 V_x_2) V_A_2))) (= V_x_2 (c_Big__Operators_Olinorder__class_OMin T_b V_A_2))) )) 97.69/108.01 ( v_pn, v_U, tc_Com_Opname ) 97.69/108.01 ) 97.69/108.01 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Relation_ODomain T_b T_c) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_c) tc_HOL_Obool)))) ) 97.69/108.01 ( tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.01 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.01 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.01 ) 97.69/108.01 (instantiation (let ((_let_0 (c_List_Odistinct T_b))) (let ((_let_1 (c_List_Oset T_b))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (forall ((B_x $$unsorted)) (or (not (c_List_Olinorder__class_Osorted T_b B_x)) (not (hBOOL (hAPP _let_0 B_x))) (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP _let_0 B_y))) (not (c_List_Olinorder__class_Osorted T_b B_y)) (not (= V_A_2 (hAPP _let_1 B_y))) (= B_x B_y)) )) (not (= V_A_2 (hAPP _let_1 B_x)))) ))) ))) 97.69/108.01 ( v_U, tc_Com_Opname ) 97.69/108.01 ) 97.69/108.01 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$unsorted)) (= (hAPP (c_Groups_Ouminus__class_Ouminus _let_0) (c_Orderings_Otop__class_Otop _let_0)) (c_Orderings_Obot__class_Obot _let_0)) )) 97.69/108.01 ( tc_Nat_Onat ) 97.69/108.01 ( tc_HOL_Obool ) 97.69/108.01 ( tc_Int_Oint ) 97.69/108.01 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.01 ( t_a ) 97.69/108.01 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.01 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.69/108.01 ( tc_Product__Type_Ounit ) 97.69/108.01 ) 97.69/108.01 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_u_2) (hAPP c_Nat_OSuc V_l_2)) (hAPP (c_Finite__Set_Ocard tc_Nat_Onat) (c_SetInterval_Oord__class_OgreaterThanLessThan tc_Nat_Onat V_l_2 V_u_2))) ) 97.69/108.01 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), v_n ) 97.69/108.01 ) 97.69/108.01 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_b)) (= (and (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) V_b_2)) (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_b) V_a_2)) V_b_2)))) )) 97.69/108.01 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.01 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.69/108.01 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.01 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.01 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.01 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.69/108.01 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.01 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.01 ) 97.69/108.01 (instantiation (forall ((T_b $$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))) ) 97.69/108.01 ( tc_Nat_Onat ) 97.69/108.01 ( tc_Int_Oint ) 97.69/108.01 ( tc_Code__Numeral_Ocode__numeral ) 97.69/108.01 ) 97.69/108.01 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (class_Lattices_Osemilattice__inf T_b)) (= (c_Orderings_Oord__class_Omin T_b) (c_Lattices_Osemilattice__inf__class_Oinf T_b))) ) 97.69/108.01 ( tc_HOL_Obool ) 97.69/108.01 ( tc_Int_Oint ) 97.69/108.01 ( tc_Code__Numeral_Ocode__numeral ) 97.69/108.01 ) 97.69/108.01 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Groups_Omonoid__add T_a)) (= (hAPP (c_List_Omonoid__add__class_Olistsum T_a) (c_List_Olist_ONil T_a)) (c_Groups_Ozero__class_Ozero T_a))) ) 97.69/108.01 ( tc_Nat_Onat ) 97.69/108.01 ( tc_Int_Oint ) 97.69/108.01 ( tc_Code__Numeral_Ocode__numeral ) 97.69/108.01 ) 97.69/108.01 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (c_Finite__Set_Ofun__left__comm__idem T_b T_b (c_Orderings_Oord__class_Omax T_b))) ) 97.69/108.02 ( tc_Nat_Onat ) 97.69/108.02 ( tc_Int_Oint ) 97.69/108.02 ( tc_Code__Numeral_Ocode__numeral ) 97.69/108.02 ) 97.69/108.02 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_member T_b))) (let ((_let_2 (c_Set_Oinsert T_b))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 _let_0) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (hBOOL (hAPP (hAPP _let_1 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) B_x) B_y)) (hAPP (hAPP _let_2 B_x) (hAPP (hAPP _let_2 B_y) _let_0)))) )) (hBOOL (hAPP (hAPP _let_1 (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) V_A_2))) )))) 97.69/108.02 ( v_U, tc_Com_Opname ) 97.69/108.02 ) 97.69/108.02 (instantiation (forall ((V_b $$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))) ) 97.69/108.02 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.02 ) 97.69/108.02 (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))) ))))) 97.69/108.02 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (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, tc_Nat_Onat ) 97.69/108.02 ) 97.69/108.02 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP _let_0 V_A_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2))))) )) 97.69/108.02 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.69/108.02 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.02 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.69/108.02 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.02 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.02 ) 97.69/108.02 (instantiation (forall ((V_M_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_M_2))) (not (forall ((B_h $$unsorted)) (not (c_Fun_Obij__betw T_b tc_Nat_Onat B_h V_M_2 (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) (hAPP (c_Finite__Set_Ocard T_b) V_M_2)))) ))) ) 97.69/108.02 ( v_U, tc_Com_Opname ) 97.69/108.02 ) 97.69/108.02 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Big__Operators_Olinorder__class_OMax T_b V_A_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_B_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) V_A_2))) (= _let_1 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) (c_Big__Operators_Olinorder__class_OMax T_b V_B_2)) _let_1))) ))) 97.69/108.02 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.69/108.02 ) 97.69/108.02 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint))) (forall ((V_m $$unsorted)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) (hAPP _let_0 V_m)) (hAPP _let_0 (hAPP c_Nat_OSuc V_m))) )) 97.69/108.02 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.69/108.02 ( v_n ) 97.69/108.02 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.69/108.02 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.69/108.02 ) 97.69/108.02 (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)))) ) 97.69/108.02 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.02 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.02 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.02 ) 97.69/108.02 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (= V_x_2 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2)))) ) 97.69/108.02 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.02 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.02 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.69/108.02 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.02 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.02 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.69/108.02 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.02 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.02 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.02 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.02 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.02 ) 97.69/108.02 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) (hAPP _let_0 V_x)) (hAPP _let_0 V_y)) (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) V_y)))) )) 97.69/108.02 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.02 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.02 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.69/108.02 ) 97.69/108.02 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Otrans T_b V_r_2)) (c_Relation_Otrans T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (c_Relation_OId T_b)))) ) 97.69/108.02 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.02 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.02 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.02 ) 97.69/108.02 (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))))) )) 97.69/108.02 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.02 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.02 ) 97.69/108.02 (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_b T_c V_f_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Obij__betw T_b T_c V_f_2 (c_Orderings_Otop__class_Otop _let_0) (c_Orderings_Otop__class_Otop _let_1))) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_d _let_1) V_A_2) (hAPP (hAPP (c_COMBB _let_0 _let_1 T_d) _let_2) V_B_2)) (hAPP _let_2 (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OINFI T_d _let_0) V_A_2) V_B_2)))) )))) 97.69/108.02 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.69/108.02 ) 97.69/108.02 (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))) ) 97.69/108.02 ( v_U, tc_Com_Opname ) 97.69/108.02 ) 97.69/108.02 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2))) (not (hBOOL (hAPP (hAPP _let_0 V_c_2) V_d_2))) (= (and (= V_c_2 V_a_2) (= V_d_2 V_b_2)) (= (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_c_2) V_d_2) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_a_2) V_b_2)))) )) 97.69/108.02 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.02 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.02 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.02 ) 97.69/108.02 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hBOOL (hAPP (hAPP (c_member T_b) (c_Big__Operators_Olinorder__class_OMin T_b V_A_2)) V_A_2))) ) 97.69/108.02 ( v_U, tc_Com_Opname ) 97.69/108.02 ) 97.69/108.02 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_0)))) (forall ((V_r_2 $$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)) ))) 97.69/108.02 ( 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) ) 97.69/108.02 ( 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) ) 97.69/108.02 ) 97.69/108.02 (instantiation (let ((_let_0 (tc_fun tc_Int_Oint tc_HOL_Obool))) (forall ((V_d_2 $$unsorted)) (= (hAPP (c_Set_OCollect (tc_prod tc_Int_Oint tc_Int_Oint)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Int_Oint tc_Int_Oint tc_HOL_Obool) (hAPP (hAPP (c_COMBB _let_0 _let_0 tc_Int_Oint) (hAPP (c_COMBS tc_Int_Oint tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) tc_Int_Oint) c_fconj) (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_d_2)))) (c_Orderings_Oord__class_Oless tc_Int_Oint)))) (c_Int_Oint__ge__less__than2 V_d_2)) )) 97.69/108.02 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.02 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.69/108.02 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.02 ) 97.69/108.02 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (= (c_Fun_Oid T_b) (hAPP (c_Fun_Ocomp T_c T_b T_b V_f_2) (c_Hilbert__Choice_Oinv__into T_c T_b _let_0 V_f_2))) (= (hAPP (c_Set_Oimage T_c T_b V_f_2) _let_0) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) )) 97.69/108.02 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.02 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.69/108.02 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.69/108.02 ( v_mgt__call, t_a, tc_Com_Opname ) 97.69/108.02 ) 97.69/108.02 (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))) ) 97.69/108.02 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.02 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0)))), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.02 ) 97.69/108.02 (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)))) ) 97.69/108.02 ( v_U, tc_Com_Opname ) 97.69/108.02 ) 97.69/108.02 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (forall ((V_G_2 $$unsorted) (V_F_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_F_2))) (not (hBOOL (hAPP _let_0 V_G_2))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) V_F_2) V_G_2)))) )) 97.69/108.02 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.02 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.02 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.69/108.03 ) 97.69/108.03 (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))) )) 97.69/108.03 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.03 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.03 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.69/108.03 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (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)) ) 97.69/108.03 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.03 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.03 ) 97.69/108.03 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ogroup__add T_b)) (= (= V_b_2 V_a_2) (= (c_Groups_Ozero__class_Ozero T_b) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_b_2)))) ) 97.69/108.03 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.69/108.03 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 97.69/108.03 ) 97.69/108.03 (instantiation (forall ((V_x $$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))) ) 97.69/108.03 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.03 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.03 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.03 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.03 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.03 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.03 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.03 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.03 ) 97.69/108.03 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_N_2 $$unsorted) (V_M_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_M_2) V_N_2))) (= V_M_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_N_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Big__Operators_Olinorder__class_OMin T_b V_N_2)) (c_Big__Operators_Olinorder__class_OMin T_b V_M_2)))) )) 97.69/108.03 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.69/108.03 ) 97.69/108.03 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_x_2))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP c_Nat_OSuc (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)))) )))) 97.69/108.03 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.69/108.03 ( (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)) ) 97.69/108.03 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.69/108.03 ( (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) ) 97.69/108.03 ( (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) ) 97.69/108.03 ) 97.69/108.03 (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_B_2) V_A_2) (hAPP (hAPP _let_0 V_A_2) V_B_2)) )) 97.69/108.03 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.03 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.03 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.69/108.03 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (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)) ) 97.69/108.03 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.03 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.03 ) 97.69/108.03 (instantiation (forall ((T_c $$unsorted) (V_b_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (not (hBOOL (hAPP (hAPP V_B_2 V_a_2) V_b_2))) (hBOOL (hAPP (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_b (tc_fun T_c tc_HOL_Obool)) V_A_2) V_B_2) V_b_2))) ) 97.69/108.03 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), v_U, (c_member tc_Com_Opname), v_U, v_pn, tc_Com_Opname ) 97.69/108.03 ) 97.69/108.03 (instantiation (let ((_let_0 (tc_prod T_b T_c))) (forall ((V_Pa_2 $$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)))) )) 97.69/108.03 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.03 ( (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 ) 97.69/108.03 ) 97.69/108.03 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_b))) (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_na_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP _let_0 V_m_2)) (hAPP _let_0 V_na_2))))) )) 97.69/108.03 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.69/108.03 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 97.69/108.03 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.69/108.03 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.69/108.03 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.69/108.03 ) 97.69/108.03 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_1)) (class_Complete__Lattice_Ocomplete__lattice (tc_fun T_2 T_1))) ) 97.69/108.03 ( tc_Nat_Onat, tc_HOL_Obool ) 97.69/108.03 ( tc_HOL_Obool, tc_HOL_Obool ) 97.69/108.03 ( tc_Int_Oint, tc_HOL_Obool ) 97.69/108.03 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.69/108.03 ( t_a, tc_HOL_Obool ) 97.69/108.03 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.69/108.03 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.69/108.03 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.69/108.03 ) 97.69/108.03 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (forall ((V_x_2 $$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)) (= (c_Big__Operators_Olattice_OSup__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Finite__Set_Ofold T_b T_b _let_0) V_x_2) V_A_2))) )) 97.69/108.03 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.69/108.03 ( (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)) ) 97.69/108.03 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.69/108.03 ( (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) ) 97.69/108.03 ( (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) ) 97.69/108.03 ) 97.69/108.03 (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))) ) 97.69/108.03 ( v_U, v_mgt__call, tc_Com_Opname, t_a ) 97.69/108.03 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.03 ( (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 ) 97.69/108.03 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 97.69/108.03 ( (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 ) 97.69/108.03 ) 97.69/108.03 (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 $$unsorted)) (or (not (class_Lattices_Oab__semigroup__idem__mult T_b)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_b) V_x_2) (hAPP _let_0 V_A_2)) (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 97.69/108.03 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.69/108.03 ) 97.69/108.03 (instantiation (let ((_let_0 (c_Relation_OImage T_b T_b V_r_2))) (let ((_let_1 (c_Set_Oinsert T_b))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (forall ((V_a_2 $$unsorted) (V_b_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_b_2) _let_2))) (hAPP _let_0 (hAPP (hAPP _let_1 V_a_2) _let_2))))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_b_2) V_A_2))) (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_b_2)) V_r_2))) )))) 97.69/108.03 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.03 ) 97.69/108.03 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a) (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a))) ) 97.69/108.03 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.69/108.03 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.03 ) 97.69/108.03 (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 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= _let_0 (hAPP (hAPP (c_Set_Oinsert T_c) (hAPP V_f_2 V_x_2)) _let_0))) )) 97.69/108.03 ( c_Int_Onat, tc_Nat_Onat, (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.69/108.04 ) 97.69/108.04 (instantiation (let ((_let_0 (c_member T_b))) (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 B_x) V_A_2))) (forall ((B_xa $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 B_xa) V_A_2))) (not (= (hAPP V_f_2 B_x) (hAPP V_f_2 B_xa))) (= B_x B_xa)) )) ) (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2)) )) 97.69/108.04 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_A_2 $$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)) ) 97.69/108.04 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.69/108.04 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.04 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2) (c_Complete__Lattice_OInf__class_OInf T_b V_A_2))) ) 97.69/108.04 ( v_U, tc_Com_Opname ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_k $$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)) ) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.04 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.69/108.04 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.04 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.04 ) 97.69/108.04 (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 $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_1) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot _let_1))))) (hAPP _let_0 V_A_2))) ))) 97.69/108.04 ( v_pn, v_U, tc_Com_Opname ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_a_2) V_b_2))) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (c_SetInterval_Oord__class_OatLeastAtMost T_b V_a_2 V_b_2)))) ) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.69/108.04 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.04 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.69/108.04 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.04 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.04 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ) 97.69/108.04 (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 $$unsorted)) (= (hAPP (c_Set_Oimage T_c T_b (hAPP (hAPP (c_COMBB T_d T_b T_c) V_f_2) V_g_2)) _let_0) (hAPP (c_Set_Oimage T_d T_b V_f_2) (hAPP (c_Set_Oimage T_c T_d V_g_2) _let_0))) )) 97.69/108.04 ( c_Nat_OSuc, (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal), tc_Nat_Onat, (tc_fun tc_Nat_Onat tc_HOL_Obool), tc_Nat_Onat ) 97.69/108.04 ) 97.69/108.04 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_a) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 V_b) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_1))) ))) 97.69/108.04 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.04 ) 97.69/108.04 (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 (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))) (hAPP (c_Set_Oimage T_c T_b V_f_2) V_A_2)) )) 97.69/108.04 ( v_U, v_mgt__call, t_a, tc_Com_Opname ) 97.69/108.04 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.04 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.69/108.04 ( (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 ) 97.69/108.04 ) 97.69/108.04 (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))))) )) 97.69/108.04 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Ogroup__add T_a)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_a) V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_b)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b))) ) 97.69/108.04 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) (c_Groups_Ozero__class_Ozero T_a)) V_a))) (= V_a (hAPP (c_Groups_Oabs__class_Oabs T_a) V_a))) ) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.69/108.04 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.69/108.04 ) 97.69/108.04 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (forall ((T_a $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (= _let_0 (hAPP (c_Groups_Oabs__class_Oabs T_a) _let_0))) )) 97.69/108.04 ( tc_Nat_Onat ) 97.69/108.04 ( tc_Int_Oint ) 97.69/108.04 ( tc_Code__Numeral_Ocode__numeral ) 97.69/108.04 ) 97.69/108.04 (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)) ) 97.69/108.04 ( (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) (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 ) 97.69/108.04 ) 97.69/108.04 (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 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2))) (hBOOL (hAPP _let_0 V_a_2)))) )) 97.69/108.04 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.04 ) 97.69/108.04 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Obij__betw T_b T_c V_f_2 _let_0 _let_1)) (= (hAPP (c_Set_Oimage T_b T_c V_f_2) _let_0) _let_1)) ))) 97.69/108.04 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.04 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.69/108.04 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.69/108.04 ( v_mgt__call, t_a, tc_Com_Opname ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_A_2 $$unsorted)) (or (not (c_Nat__Transfer_Onat__set V_A_2)) (= (hAPP (c_Finite__Set_Ocard tc_Nat_Onat) (hAPP (c_Set_Oimage tc_Int_Oint tc_Nat_Onat c_Int_Onat) V_A_2)) (hAPP (c_Finite__Set_Ocard tc_Int_Oint) V_A_2))) ) 97.69/108.04 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Osym T_b V_r_2)) (not (c_Relation_Otrans T_b V_r_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) (hAPP (c_Relation_Oconverse T_b T_b) V_r_2)) V_r_2)) V_r_2))) ) 97.69/108.04 ( (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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 ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (= V_r_2 (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) (hAPP (c_Relation_Oconverse T_b T_b) V_r_2)) V_r_2))) ) 97.69/108.04 ( c_Int_Ointrel, (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_A_2 $$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)))) ) 97.69/108.04 ( v_G, (hAPP v_mgt__call v_pn), t_a ) 97.69/108.04 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.04 ( (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) ) 97.69/108.04 ( (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) ) 97.69/108.04 ( (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)) ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Lattices_Osemilattice__sup T_b)) (c_Finite__Set_Ofun__left__comm__idem T_b T_b (c_Lattices_Osemilattice__sup__class_Osup T_b))) ) 97.69/108.04 ( tc_Nat_Onat ) 97.69/108.04 ( tc_HOL_Obool ) 97.69/108.04 ( tc_Int_Oint ) 97.69/108.04 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.69/108.04 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (forall ((B_k $$unsorted)) (not (= V_na_2 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m_2) B_k))) )) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_na_2))) ) 97.69/108.04 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.69/108.04 ) 97.69/108.04 (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_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_List_Olinorder__class_Osorted__list__of__set T_b (hAPP _let_1 V_A_2)) (hAPP (hAPP (c_List_Olinorder__class_Oinsort__key T_b T_b (c_COMBI T_b)) V_x_2) (c_List_Olinorder__class_Osorted__list__of__set T_b (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP _let_1 (c_Orderings_Obot__class_Obot _let_0))))))) ))) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.69/108.04 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.04 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.69/108.04 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.04 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (c_Orderings_Oord__class_Omin T_b) (c_Orderings_Oord_Omin T_b (c_Orderings_Oord__class_Oless__eq T_b)))) ) 97.69/108.04 ( tc_Nat_Onat ) 97.69/108.04 ( tc_HOL_Obool ) 97.69/108.04 ( tc_Int_Oint ) 97.69/108.04 ( tc_Code__Numeral_Ocode__numeral ) 97.69/108.04 ( (tc_fun t_a tc_HOL_Obool) ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_na_2 $$unsorted)) (= (hAPP (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) V_na_2) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_na_2)) ) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2) (hAPP (c_Finite__Set_Ofold1 T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b)) V_A_2))) ) 97.69/108.04 ( v_U, tc_Com_Opname ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (= (hAPP (c_SetInterval_Oord__class_OatLeastLessThan T_b V_a_2) V_b_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_a_2) V_b_2))))) ) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.04 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_x) V_y))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) ) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.69/108.04 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.69/108.04 ) 97.69/108.04 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (let ((_let_1 (hAPP (c_Orderings_Oord__class_Oless T_a) _let_0))) (forall ((V_b $$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)))) ))) 97.69/108.04 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_m $$unsorted)) (= V_m (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_m) (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.69/108.04 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.69/108.04 ) 97.69/108.04 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (let ((_let_1 (hAPP _let_0 V_x))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP _let_1 V_y))) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_z))) (hBOOL (hAPP _let_1 V_z))) ))) 97.69/108.04 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_y_2 $$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)))) ) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.04 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.69/108.04 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.04 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.69/108.04 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.04 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.04 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.04 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.69/108.04 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.04 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.04 ) 97.69/108.04 (instantiation (forall ((V_Pa_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (c_Relation_ORange T_c T_b) (hAPP (c_Set_OCollect (tc_prod T_c T_b)) (hAPP (c_Product__Type_Oprod_Oprod__case T_c T_b tc_HOL_Obool) V_Pa_2))) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBB (tc_fun T_c tc_HOL_Obool) tc_HOL_Obool T_b) (c_HOL_OEx T_c)) (hAPP (c_COMBC T_c T_b tc_HOL_Obool) V_Pa_2)))) ) 97.69/108.05 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.05 ( c_fequal, tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.05 ( (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc), tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Olinordered__idom T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) (= (c_Groups_Osgn__class_Osgn T_a V_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (c_Groups_Oone__class_Oone T_a)))) ) 97.69/108.05 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.05 ) 97.69/108.05 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OatLeast T_b))) (forall ((V_u_2 $$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))) )) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.05 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.05 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.05 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.05 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (hBOOL (hAPP (hAPP (c_member T_b) V_i_2) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_k_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_k_2) V_i_2)))) ) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.05 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((V_n $$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))) ) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.69/108.05 ( v_n ) 97.69/108.05 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.69/108.05 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.69/108.05 ) 97.69/108.05 (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))) )))) 97.69/108.05 ( v_U, tc_Com_Opname ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((V_A_2 $$unsorted) (V_Abs_2 $$unsorted) (V_Rep_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Typedef_Otype__definition T_b T_c V_Rep_2 V_Abs_2 V_A_2)) (= V_A_2 (hAPP (c_Set_Oimage T_b T_c V_Rep_2) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))))) ) 97.69/108.05 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Onat__of, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral ) 97.69/108.05 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))) c_Int_Ointrel)), c_Int_OAbs__Integ, c_Int_ORep__Integ, (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), tc_Int_Oint ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Ogroup__add T_b)) (= (= V_a_2 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_b_2)) (= (c_Groups_Ozero__class_Ozero T_b) (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_b_2)))) ) 97.69/108.05 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.05 ) 97.69/108.05 (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))) ))) 97.69/108.05 ( (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 ) 97.69/108.05 ( (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 ) 97.69/108.05 ( (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 ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) V_m))) (= V_m (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n)))) ) 97.69/108.05 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.69/108.05 ) 97.69/108.05 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$unsorted)) (= (c_Complete__Lattice_OInf__class_OInf _let_0 (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot _let_0)) )) 97.69/108.05 ( tc_Nat_Onat ) 97.69/108.05 ( tc_Int_Oint ) 97.69/108.05 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.05 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted)) (= (hAPP (c_Finite__Set_Ocard tc_Nat_Onat) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat V_l_2) V_u_2)) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_u_2) V_l_2)) ) 97.69/108.05 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.69/108.05 ) 97.69/108.05 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (forall ((V_m $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (c_Groups_Oone__class_Oone T_a)) (hAPP _let_0 V_m)) (hAPP _let_0 (hAPP c_Nat_OSuc V_m)))) )) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.69/108.05 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), tc_Int_Oint ) 97.69/108.05 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), tc_Int_Oint ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((T_d $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (c_Product__Type_Ointernal__split T_b T_c T_d) (c_Product__Type_Oprod_Oprod__case T_b T_c T_d)) ) 97.69/108.05 ( tc_HOL_Obool, tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.05 ) 97.69/108.05 (instantiation (let ((_let_0 (c_Big__Operators_Olinorder__class_OMax 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 $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (and (or (not _let_3) (= V_x_2 _let_0)) (or _let_3 (= _let_0 (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMax T_b _let_2)))))) ))))) 97.69/108.05 ( v_pn, v_U, tc_Com_Opname ) 97.69/108.05 ) 97.69/108.05 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat T_a))) (forall ((V_m $$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)))) )) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.69/108.05 ) 97.69/108.05 (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))) ) 97.69/108.05 ( (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.05 ( v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.05 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.69/108.05 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Ozero__neq__one T_a)) (not (= (c_Groups_Ozero__class_Ozero T_a) (c_Groups_Oone__class_Oone T_a)))) ) 97.69/108.05 ( tc_Nat_Onat ) 97.69/108.05 ( tc_Code__Numeral_Ocode__numeral ) 97.69/108.05 ) 97.69/108.05 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 V_i))) (forall ((V_k $$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))) ))) 97.69/108.05 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.69/108.05 ) 97.69/108.05 (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)))) ) 97.69/108.05 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 97.69/108.05 ) 97.69/108.05 (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))) )) 97.69/108.05 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.05 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.05 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.05 ) 97.69/108.05 (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))) ) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.05 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.05 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.05 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.05 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.05 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.69/108.05 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.05 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ) 97.69/108.05 (instantiation (let ((_let_0 (c_Relation_ODomain T_b T_c))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert (tc_prod T_b T_c)) (hAPP (hAPP (c_Product__Type_OPair T_b T_c) V_a_2) V_b_2)) V_r_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (hAPP _let_0 V_r_2))) )) 97.69/108.05 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.05 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.05 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Otop T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) (c_Orderings_Otop__class_Otop T_a)))) ) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ( (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.05 ( v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.05 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.69/108.05 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.05 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((T_b $$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)))) ) 97.69/108.05 ( tc_Nat_Onat ) 97.69/108.05 ( tc_Int_Oint ) 97.69/108.05 ( tc_Code__Numeral_Ocode__numeral ) 97.69/108.05 ( t_a ) 97.69/108.05 ( tc_Com_Opname ) 97.69/108.05 ) 97.69/108.05 (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 $$unsorted)) (= (c_Set_Othe__elem tc_Nat_Onat (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tc_prod tc_Nat_Onat tc_Nat_Onat) _let_0) (hAPP c_Int_ORep__Integ V_z_2)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat _let_0) (hAPP (hAPP (c_COMBC tc_Nat_Onat _let_0 _let_2) (hAPP (hAPP (c_COMBB _let_3 (tc_fun _let_0 _let_2) tc_Nat_Onat) (c_COMBC tc_Nat_Onat _let_0 _let_0)) (hAPP (hAPP (c_COMBB (tc_fun tc_Nat_Onat tc_Nat_Onat) _let_3 tc_Nat_Onat) (hAPP (c_COMBB tc_Nat_Onat _let_1 tc_Nat_Onat) (c_Set_Oinsert tc_Nat_Onat))) (c_Groups_Ominus__class_Ominus tc_Nat_Onat)))) (c_Orderings_Obot__class_Obot _let_0))))) (hAPP c_Int_Onat V_z_2)) ))))) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.05 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.69/108.05 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.05 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.69/108.05 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.69/108.05 ) 97.69/108.05 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_b_2 $$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_b_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_b_2)) V_a_2)))) ))) 97.69/108.05 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.05 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.05 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2))) (= (= V_y_2 V_x_2) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_x_2) V_y_2))))) ) 97.69/108.05 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.05 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.05 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.05 ) 97.69/108.05 (instantiation (forall ((V_x $$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)))) ) 97.69/108.05 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.69/108.05 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.06 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (= (= (hAPP (c_Groups_Ouminus__class_Ouminus T_b) (c_Groups_Oone__class_Oone T_b)) (c_Groups_Osgn__class_Osgn T_b V_a_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_a_2) (c_Groups_Ozero__class_Ozero T_b))))) ) 97.69/108.06 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.06 ) 97.69/108.06 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (hBOOL (hAPP _let_1 V_x_2))) (not (hBOOL (hAPP _let_1 V_y_2))) (= (hBOOL (hAPP (hAPP _let_0 V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) (hAPP c_Int_Onat V_x_2)) (hAPP c_Int_Onat V_y_2))))) ))) 97.69/108.06 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.06 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.06 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.06 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.06 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) (hAPP (c_Set_Oimage T_c T_b V_f_2) V_A_2))) (hAPP (c_Finite__Set_Ocard T_c) V_A_2)))) (not (c_Fun_Oinj__on T_c T_b V_f_2 V_A_2))) ) 97.69/108.06 ( v_U, v_mgt__call, tc_Com_Opname, t_a ) 97.69/108.06 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.06 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 97.69/108.06 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat ) 97.69/108.06 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((V_X_2 $$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))) ) 97.69/108.06 ( (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) ) 97.69/108.06 ( (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) ) 97.69/108.06 ) 97.69/108.06 (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))) )) 97.69/108.06 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.06 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.06 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.06 ) 97.69/108.06 (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 $$unsorted)) (or (not (class_Rings_Oring__1 T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_b) V_a_2)) _let_1))) ))) 97.69/108.06 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Oab__group__add T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) V_a) (c_Groups_Ozero__class_Ozero T_a))) ) 97.69/108.06 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.06 ) 97.69/108.06 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2)) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_1 V_b_2)) (hAPP _let_1 V_a_2))))) ))) 97.69/108.06 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ) 97.69/108.06 (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_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_b_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_b_2) V_c_2)) (c_Transitive__Closure_Ortrancl T_b V_r_2)))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))) ))))) 97.69/108.06 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (not (class_Orderings_Oord T_c)) (= (forall ((B_x $$unsorted)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_c) (hAPP V_f_2 B_x)) (hAPP V_g_2 B_x))) ) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b T_c)) V_f_2) V_g_2)))) ) 97.69/108.06 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a, tc_HOL_Obool ) 97.69/108.06 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a, tc_HOL_Obool ) 97.69/108.06 ) 97.69/108.06 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 _let_0)) (= (c_Fun_Oid T_b) (hAPP (c_Fun_Ocomp T_c T_b T_b (c_Hilbert__Choice_Oinv__into T_b T_c _let_0 V_f_2)) V_f_2))) )) 97.69/108.06 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.69/108.06 ) 97.69/108.06 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless T_a) V_x))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP _let_0 V_y))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_y) V_z))) (hBOOL (hAPP _let_0 V_z))) )) 97.69/108.06 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.06 ) 97.69/108.06 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (= V_B_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) V_A_2) V_B_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) )) 97.69/108.06 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.69/108.06 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a ) 97.69/108.06 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.06 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.06 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.69/108.06 ) 97.69/108.06 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) (hAPP _let_1 V_b_2))) (hBOOL (hAPP (hAPP _let_0 V_b_2) (hAPP _let_1 V_a_2))))) ))) 97.69/108.06 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.06 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ) 97.69/108.06 (instantiation (let ((_let_0 (c_Relation_Oconverse T_b T_b))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Wellfounded_Owf T_b (hAPP _let_0 V_r_2))) (c_Wellfounded_Owf T_b (hAPP _let_0 (c_Transitive__Closure_Otrancl T_b V_r_2)))) )) 97.69/108.06 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc))), tc_Nat_Onat ) 97.69/108.06 ) 97.69/108.06 (instantiation (let ((_let_0 (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2))) (forall ((V_x_2 $$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))) )) 97.69/108.06 ( v_pn, v_U, tc_Com_Opname ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y))) ) 97.69/108.06 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.06 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.06 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.06 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.06 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((V_c_2 $$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_c_2)) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 97.69/108.06 ( c_fTrue, tc_HOL_Obool, tc_Nat_Onat ) 97.69/108.06 ) 97.69/108.06 (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_c_2 $$unsorted) (V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_b_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_b_2) V_c_2)) _let_3))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))) ))))) 97.69/108.06 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc))), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (not (forall ((B_n $$unsorted) (B_f $$unsorted)) (not (= V_A_2 (hAPP (c_Set_Oimage tc_Nat_Onat T_b B_f) (hAPP (c_Set_OCollect tc_Nat_Onat) (hAPP (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat)) B_n))))) )) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) ) 97.69/108.06 ( v_U, tc_Com_Opname ) 97.69/108.06 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.69/108.06 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), tc_Int_Oint ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_x_2) V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) V_y_2) V_x_2)))) ) 97.69/108.06 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.06 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.69/108.06 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.06 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ) 97.69/108.06 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (forall ((V_v $$unsorted)) (or (hBOOL (hAPP c_Nat__Numeral_Oneg (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_v))) (= (hAPP _let_0 (c_Int_Osucc V_v)) (hAPP c_Nat_OSuc (hAPP _let_0 V_v)))) )) 97.69/108.06 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.69/108.06 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.06 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((V_v $$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)))) ) 97.69/108.06 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.69/108.06 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.06 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (= V_a_2 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_a_2) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)))) ) 97.69/108.06 ( v_pn, v_U, tc_Com_Opname ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((T_a $$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))))) ) 97.69/108.06 ( tc_Nat_Onat ) 97.69/108.06 ( tc_Int_Oint ) 97.69/108.06 ( tc_Code__Numeral_Ocode__numeral ) 97.69/108.06 ) 97.69/108.06 (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)))) ))) 97.69/108.06 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.69/108.06 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.06 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.69/108.06 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.69/108.06 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Obot T_1)) (class_Orderings_Obot (tc_fun T_2 T_1))) ) 97.69/108.06 ( tc_Nat_Onat, tc_HOL_Obool ) 97.69/108.06 ( tc_HOL_Obool, tc_HOL_Obool ) 97.69/108.06 ( tc_Int_Oint, tc_HOL_Obool ) 97.69/108.06 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.69/108.06 ( t_a, tc_HOL_Obool ) 97.69/108.06 ( (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 ) 97.69/108.06 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.69/108.06 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.69/108.06 ) 97.69/108.06 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_b)) (c_Finite__Set_Ofun__left__comm__idem T_b T_b (c_Lattices_Osemilattice__inf__class_Oinf T_b))) ) 97.69/108.07 ( tc_Nat_Onat ) 97.69/108.07 ( tc_HOL_Obool ) 97.69/108.07 ( tc_Int_Oint ) 97.69/108.07 ) 97.69/108.07 (instantiation (forall ((V_u_2 $$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))) ) 97.69/108.07 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.07 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.07 ) 97.69/108.07 (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))) ))) 97.69/108.07 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.07 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.07 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.69/108.07 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.07 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.07 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.69/108.07 ( (c_Groups_Ominus__class_Ominus tc_Nat_Onat), (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.69/108.07 ( (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) ) 97.69/108.07 ( (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)) ) 97.69/108.07 ( (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)) ) 97.69/108.07 ( (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)) ) 97.69/108.07 ( (c_Set_Oinsert t_a), v_G, (hAPP v_mgt__call v_pn) ) 97.69/108.07 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.69/108.07 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.69/108.07 ( (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)) ) 97.69/108.07 ( (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)) ) 97.69/108.07 ( (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) ) 97.69/108.07 ( (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) ) 97.69/108.07 ( (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)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)) ) 97.69/108.07 ( (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) ) 97.69/108.07 ( (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 ) 97.69/108.07 ( (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G) ) 97.69/108.07 ( (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) ) 97.69/108.07 ( (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)) ) 97.69/108.07 ( (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)) ) 97.69/108.07 ( (c_member t_a), v_G, (hAPP v_mgt__call v_pn) ) 97.69/108.07 ( (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)), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.69/108.07 ( (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)), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.69/108.07 ( (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)) ) 97.69/108.07 ( (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)) ) 97.69/108.07 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 97.69/108.07 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_Int_Onat ) 97.69/108.07 ) 97.69/108.07 (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_member _let_0) V_A_2) (hAPP (c_Set_OPow T_b) V_B_2)))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) )) 97.69/108.07 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a ) 97.69/108.07 ) 97.69/108.07 (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))) ) 97.69/108.07 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.07 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.69/108.07 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.07 ) 97.69/108.07 (instantiation (forall ((V_u_2 $$unsorted)) (= (hAPP (c_Finite__Set_Ocard tc_Int_Oint) (hAPP (c_SetInterval_Oord__class_OatLeastLessThan tc_Int_Oint (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_u_2)) (hAPP c_Int_Onat V_u_2)) ) 97.69/108.07 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.07 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.69/108.07 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.07 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.69/108.07 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.69/108.07 ) 97.69/108.07 (instantiation (forall ((V_r_2 $$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)))) ) 97.69/108.07 ( 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) ) 97.69/108.07 ) 97.69/108.07 (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)) )) 97.69/108.07 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.69/108.07 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.69/108.07 ) 97.69/108.07 (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))) (= (hAPP (hAPP (c_Orderings_Oord__class_Omax T_b) (c_Big__Operators_Olinorder__class_OMax T_b V_A_2)) (c_Big__Operators_Olinorder__class_OMax T_b V_B_2)) (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) V_A_2) V_B_2)))) )))) 97.69/108.07 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.07 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.07 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.69/108.07 ) 97.69/108.07 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_S_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_S_2))) (= V_S_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP _let_0 (c_Big__Operators_Olinorder__class_OMin T_b V_S_2)) (c_Big__Operators_Olinorder__class_OMax T_b (hAPP (c_Set_Oimage T_b T_b _let_0) V_S_2)))) )) 97.69/108.07 ( v_U, tc_Com_Opname ) 97.69/108.07 ) 97.69/108.07 (instantiation (let ((_let_0 (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP _let_0 (c_Groups_Oone__class_Oone tc_Nat_Onat))) V_n) (hAPP _let_0 (hAPP c_Nat_OSuc V_n))) )) 97.69/108.07 ( v_n, (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.69/108.07 ) 97.69/108.07 (instantiation (forall ((V_x $$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))) ) 97.69/108.07 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) ) 97.69/108.07 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.07 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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)) ) 97.69/108.07 ) 97.69/108.07 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Oord T_b)) (= (c_Orderings_Oord_Omax T_b (c_Orderings_Oord__class_Oless__eq T_b)) (c_Orderings_Oord__class_Omax T_b))) ) 97.69/108.07 ( tc_Nat_Onat ) 97.69/108.07 ( tc_HOL_Obool ) 97.69/108.07 ( tc_Int_Oint ) 97.69/108.07 ( tc_Code__Numeral_Ocode__numeral ) 97.69/108.07 ( (tc_fun t_a tc_HOL_Obool) ) 97.69/108.07 ) 97.69/108.07 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_2 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted)) (= (or (= _let_0 V_k_2) (and (hBOOL (hAPP (hAPP _let_1 V_k_2) V_i_2)) (hBOOL (hAPP (hAPP _let_2 V_i_2) _let_0))) (and (hBOOL (hAPP (hAPP _let_1 V_i_2) V_k_2)) (hBOOL (hAPP (hAPP _let_2 _let_0) V_i_2)))) (= _let_0 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_i_2) V_k_2))) )))) 97.69/108.07 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.07 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.69/108.07 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.69/108.07 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.07 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.07 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.69/108.07 ) 97.69/108.07 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (forall ((V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 _let_0)) (not (= (hAPP (c_Set_Oimage T_b T_c V_f_2) _let_0) _let_1)) (c_Fun_Obij__betw T_b T_c V_f_2 _let_0 _let_1)) ))) 97.69/108.07 ( c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.07 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.69/108.07 ( c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.69/108.07 ( v_mgt__call, t_a, tc_Com_Opname ) 97.69/108.07 ) 97.69/108.07 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Orderings_Oord__class_Omin T_b))) (let ((_let_2 (c_Set_Oinsert T_b))) (let ((_let_3 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (forall ((V_A_2 $$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 $$unsorted)) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_x) B_y)) (hAPP (hAPP _let_2 B_x) (hAPP (hAPP _let_2 B_y) _let_3)))) )) (hBOOL (hAPP (hAPP _let_0 (c_Big__Operators_Olattice_OInf__fin T_b _let_1 V_A_2)) V_A_2))) ))))) 97.69/108.07 ( v_U, tc_Com_Opname ) 97.69/108.07 ) 97.69/108.07 (instantiation (forall ((V_na_2 $$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_na_2))) (hAPP (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) V_na_2)) ) 97.69/108.07 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.69/108.07 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.69/108.07 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.69/108.07 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.69/108.07 ) 97.69/108.07 (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))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_B_2 (c_Orderings_Obot__class_Obot _let_2)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_2) V_B_2) V_A_2))) (= _let_1 (hAPP (hAPP _let_0 (c_Big__Operators_Olattice_OSup__fin T_b _let_0 V_B_2)) _let_1))) )))) 97.69/108.08 ( v_G, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_v_2 $$unsorted) (V_d_2 $$unsorted) (V_c_2 $$unsorted) (T_e $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_d $$unsorted)) (or (not (= (hAPP (c_Fun_Ocomp T_d T_c T_b V_a_2) V_b_2) (hAPP (c_Fun_Ocomp T_e T_c T_b V_c_2) V_d_2))) (= (hAPP V_a_2 (hAPP V_b_2 V_v_2)) (hAPP V_c_2 (hAPP V_d_2 V_v_2)))) ) 97.69/108.08 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), tc_Nat_Onat, c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 97.69/108.08 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), tc_Nat_Onat, c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 97.69/108.08 ) 97.69/108.08 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_z $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_0) V_z))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Groups_Oone__class_Oone tc_Int_Oint)) V_z)))) )) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.08 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.69/108.08 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.69/108.08 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= V_x_2 (c_Big__Operators_Olattice_OInf__fin T_b (c_Orderings_Oord__class_Omin T_b) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))))) ) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.08 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.08 ( (hAPP v_mgt__call v_pn), t_a ) 97.69/108.08 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.08 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_k_2 $$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))) ) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.08 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.08 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.08 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.08 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.08 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.08 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_a_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_a_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP (c_Finite__Set_Ofold1 T_b (c_Orderings_Oord__class_Omin T_b)) V_A_2)) V_a_2))) ) 97.69/108.08 ( v_pn, v_U, tc_Com_Opname ) 97.69/108.08 ) 97.69/108.08 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_b))) (let ((_let_1 (c_Groups_Ozero__class_Ozero T_b))) (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Olinordered__ab__group__add T_b)) (= (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_b) V_a_2) V_a_2)) _let_1)) (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1)))) ))) 97.69/108.08 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_B_2 $$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)) ) 97.69/108.08 ( v_G, (hAPP v_mgt__call v_pn), t_a ) 97.69/108.08 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.08 ( (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) ) 97.69/108.08 ( (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) ) 97.69/108.08 ( (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)) ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Olinorder T_a)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x) V_y))) (= V_x (hAPP (hAPP (c_Orderings_Oord__class_Omin T_a) V_x) V_y))) ) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.08 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.08 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.08 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.08 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.08 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.08 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.08 ) 97.69/108.08 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless T_a))) (let ((_let_1 (hAPP _let_0 V_x))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Opreorder T_a)) (not (hBOOL (hAPP _let_1 V_y))) (not (hBOOL (hAPP (hAPP _let_0 V_y) V_z))) (hBOOL (hAPP _let_1 V_z))) ))) 97.69/108.08 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.08 ) 97.69/108.08 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (forall ((V_x_2 $$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 _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP c_Nat_OSuc (hAPP _let_0 V_A_2)))) )) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.69/108.08 ( (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)) ) 97.69/108.08 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.69/108.08 ( (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) ) 97.69/108.08 ( (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) ) 97.69/108.08 ) 97.69/108.08 (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 $$unsorted)) (or (not (class_Groups_Oordered__comm__monoid__add T_a)) (not (hBOOL (hAPP (hAPP _let_0 V_a) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 V_b) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_1))) ))) 97.69/108.08 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.08 ) 97.69/108.08 (instantiation (let ((_let_0 (c_Relation_ORange T_b T_b))) (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (hAPP _let_0 V_r_2) (hAPP _let_0 (c_Transitive__Closure_Otrancl T_b V_r_2))) )) 97.69/108.08 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc))), tc_Nat_Onat ) 97.69/108.08 ) 97.69/108.08 (instantiation (let ((_let_0 (c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted)) (= _let_0 (c_List_Obutlast T_a _let_0)) )) 97.69/108.08 ( tc_Nat_Onat ) 97.69/108.08 ( tc_Int_Oint ) 97.69/108.08 ) 97.69/108.08 (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 $$unsorted)) (or (not (class_Rings_Oring__1 T_b)) (= (hAPP (c_Int_Oring__1__class_Oof__int T_b) (hAPP c_Int_OAbs__Integ (hAPP (c_Relation_OImage _let_0 _let_0 c_Int_Ointrel) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_i_2) V_j_2)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))))) (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) (hAPP _let_1 V_i_2)) (hAPP _let_1 V_j_2)))) ))) 97.69/108.08 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_r_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_d $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (c_Set_Oimage T_d T_b V_f_2) (hAPP (c_Set_Oimage T_c T_d V_g_2) V_r_2)) (hAPP (c_Set_Oimage T_c T_b (hAPP (c_Fun_Ocomp T_d T_b T_c V_f_2) V_g_2)) V_r_2)) ) 97.69/108.08 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Nat_Onat, tc_Int_Oint, tc_Int_Oint ) 97.69/108.08 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), c_Int_Onat, tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Ocomm__semiring__1 T_a)) (= V_a (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (c_Groups_Ozero__class_Ozero T_a)))) ) 97.69/108.08 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((T_b $$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))))) ) 97.69/108.08 ( tc_Int_Oint ) 97.69/108.08 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.08 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_j $$unsorted) (V_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_i) V_j))) (= (c_List_Oupt V_i (hAPP c_Nat_OSuc V_j)) (hAPP (hAPP (c_List_Oappend tc_Nat_Onat) (c_List_Oupt V_i V_j)) (hAPP (hAPP (c_List_Olist_OCons tc_Nat_Onat) V_j) (c_List_Olist_ONil tc_Nat_Onat))))) ) 97.69/108.08 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (= (c_Orderings_Otop__class_Otop T_b) (c_Complete__Lattice_OInf__class_OInf T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 97.69/108.08 ( tc_Nat_Onat ) 97.69/108.08 ( tc_HOL_Obool ) 97.69/108.08 ( tc_Int_Oint ) 97.69/108.08 ( (tc_fun tc_HOL_Obool tc_HOL_Obool) ) 97.69/108.08 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.08 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.69/108.08 ( t_a ) 97.69/108.08 ( (tc_fun tc_Nat_Onat tc_HOL_Obool) ) 97.69/108.08 ( (tc_fun tc_Int_Oint tc_HOL_Obool) ) 97.69/108.08 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.08 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.69/108.08 ( tc_Product__Type_Ounit ) 97.69/108.08 ( (tc_fun tc_Product__Type_Ounit tc_HOL_Obool) ) 97.69/108.08 ) 97.69/108.08 (instantiation (let ((_let_0 (tc_fun T_c tc_HOL_Obool))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Obij__betw T_b T_c V_f_2 (c_Orderings_Otop__class_Otop _let_1) (c_Orderings_Otop__class_Otop _let_0))) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_B_2) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_1) (hAPP (c_Set_Ovimage T_b T_c V_f_2) V_B_2)) V_A_2)))) ))) 97.69/108.08 ( v_U, v_G, v_mgt__call, t_a, tc_Com_Opname ) 97.69/108.08 ( v_U, (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), v_mgt__call, t_a, tc_Com_Opname ) 97.69/108.08 ) 97.69/108.08 (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_Big__Operators_Olattice__class_OSup__fin T_b (hAPP _let_1 V_A_2)))) (let ((_let_4 (= (c_Orderings_Obot__class_Obot _let_0) _let_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or (not _let_4) (= V_x_2 _let_3)) (or _let_4 (= _let_3 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) (c_Big__Operators_Olattice__class_OSup__fin T_b _let_2)))))) )))))) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.69/108.08 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.08 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.69/108.08 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.08 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.08 ) 97.69/108.08 (instantiation (let ((_let_0 (c_Big__Operators_Olinorder__class_OMax T_b V_A_2))) (forall ((V_x_2 $$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))) )) 97.69/108.08 ( v_pn, v_U, tc_Com_Opname ) 97.69/108.08 ) 97.69/108.08 (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 $$unsorted)) (or (not (class_Fields_Olinordered__field T_a)) (not (hBOOL (hAPP _let_0 V_b))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Rings_Oinverse__class_Odivide T_a) (hAPP (hAPP _let_1 V_a) V_b)) (hAPP (hAPP _let_1 _let_2) _let_2))))) )))) 97.69/108.08 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.08 ) 97.69/108.08 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((T_b $$unsorted)) (= (c_Complete__Lattice_OInf__class_OInf _let_0 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Otop__class_Otop _let_0)) )) 97.69/108.08 ( tc_Nat_Onat ) 97.69/108.08 ( tc_HOL_Obool ) 97.69/108.08 ( tc_Int_Oint ) 97.69/108.08 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.08 ( tc_Product__Type_Ounit ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) V_m))) (= (c_Divides_Odiv__class_Omod tc_Nat_Onat V_m V_n) (c_Divides_Odiv__class_Omod tc_Nat_Onat (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n) V_n))) ) 97.69/108.08 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.69/108.08 ) 97.69/108.08 (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 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (= (hAPP _let_0 (hAPP (hAPP _let_1 V_a_2) _let_2)) (hAPP _let_0 (hAPP (hAPP _let_1 V_b_2) _let_2)))) (not (c_Equiv__Relations_Oequiv T_b V_A_2 V_r_2)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_b_2) V_A_2))) (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) V_a_2) V_b_2)) V_r_2))) )))) 97.69/108.08 ( (c_Orderings_Otop__class_Otop (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.08 ) 97.69/108.08 (instantiation (let ((_let_0 (c_Relation_ORange T_c T_b))) (forall ((V_r_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP _let_0 (hAPP (hAPP (c_Set_Oinsert (tc_prod T_c T_b)) (hAPP (hAPP (c_Product__Type_OPair T_c T_b) V_a_2) V_b_2)) V_r_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_b_2) (hAPP _let_0 V_r_2))) )) 97.69/108.08 ( (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 ) 97.69/108.08 ( (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 ) 97.69/108.08 ( (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) ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_x_2) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) ) 97.69/108.08 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.69/108.08 ) 97.69/108.08 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_a))) (let ((_let_1 (c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (hAPP _let_0 V_w))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP _let_1 (hAPP (hAPP _let_1 (c_Groups_Ozero__class_Ozero T_a)) _let_2)) _let_2) (hAPP _let_0 (c_Int_OBit0 V_w)))) )))) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.69/108.08 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.69/108.08 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Set_Oinsert T_b) V_a_2) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (hAPP (c_Set_OCollect T_b) (hAPP (hAPP (c_COMBC T_b T_b tc_HOL_Obool) c_fequal) V_a_2))) ) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.69/108.08 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.69/108.08 ( (hAPP v_mgt__call v_pn), t_a ) 97.69/108.08 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.08 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.69/108.08 ) 97.69/108.08 (instantiation (forall ((V_x $$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))) ) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.08 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.08 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.08 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.69/108.09 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.69/108.09 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.69/108.09 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.09 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.69/108.09 ) 97.69/108.09 (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))) ))) 97.69/108.09 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.09 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.09 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.69/108.09 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.69/108.09 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.69/108.09 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.69/108.09 ( (c_Groups_Ominus__class_Ominus tc_Nat_Onat), (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.69/108.09 ( (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) ) 97.69/108.09 ( (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)) ) 97.69/108.09 ( (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)) ) 97.69/108.09 ( (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)) ) 97.69/108.09 ( (c_Set_Oinsert t_a), v_G, (hAPP v_mgt__call v_pn) ) 97.69/108.09 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.69/108.09 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.69/108.09 ( (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)) ) 97.69/108.09 ( (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)) ) 97.69/108.09 ( (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) ) 97.69/108.09 ( (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) ) 97.69/108.09 ( (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)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)) ) 97.69/108.09 ( (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) ) 97.69/108.09 ( (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 ) 97.69/108.09 ( (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G) ) 97.69/108.09 ( (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) ) 97.69/108.09 ( (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)) ) 97.69/108.09 ( (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)) ) 97.69/108.09 ( (c_member t_a), v_G, (hAPP v_mgt__call v_pn) ) 97.69/108.09 ( (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)), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.85/108.09 ( (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)), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.85/108.09 ( (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)) ) 97.85/108.09 ( (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)) ) 97.85/108.09 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 97.85/108.09 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_Int_Onat ) 97.85/108.09 ) 97.85/108.09 (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))) )) 97.85/108.09 ( tc_Nat_Onat ) 97.85/108.09 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.09 ) 97.85/108.09 (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))) ) 97.85/108.09 ( v_U, tc_Com_Opname ) 97.85/108.09 ) 97.85/108.09 (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)))) ) 97.85/108.09 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.85/108.09 ) 97.85/108.09 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (= (hAPP (c_Int_Oring__1__class_Oof__int T_a) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) (c_Groups_Ozero__class_Ozero T_a))) ) 97.85/108.09 ( tc_Nat_Onat ) 97.85/108.09 ( tc_Int_Oint ) 97.85/108.09 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.09 ) 97.85/108.09 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omax T_b))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_x_2))) (let ((_let_2 (c_Big__Operators_Olattice_OSup__fin T_b _let_0 (hAPP _let_1 V_A_2)))) (let ((_let_3 (tc_fun T_b tc_HOL_Obool))) (let ((_let_4 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_3) V_A_2) (hAPP _let_1 (c_Orderings_Obot__class_Obot _let_3))))) (let ((_let_5 (= (c_Orderings_Obot__class_Obot _let_3) _let_4))) (forall ((V_x_2 $$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 (not _let_5) (= V_x_2 _let_2)) (or _let_5 (= _let_2 (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OSup__fin T_b _let_0 _let_4)))))) ))))))) 97.85/108.09 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.85/108.09 ( (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)) ) 97.85/108.09 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.85/108.09 ( (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) ) 97.85/108.09 ( (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) ) 97.85/108.09 ) 97.85/108.09 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Finite__Set_Ofold1 T_b (c_Orderings_Oord__class_Omin T_b)))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= V_A_2 (c_Orderings_Obot__class_Obot _let_0)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2))) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_B_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (hAPP _let_1 V_B_2)) (hAPP _let_1 V_A_2)))) ))) 97.85/108.09 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.85/108.09 ) 97.85/108.09 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_na_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Oorder T_b)) (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_na_2)) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_na_2)) (hAPP (hAPP (c_Set_Oinsert T_b) V_na_2) (c_Orderings_Obot__class_Obot _let_0)))) )) 97.85/108.09 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.85/108.09 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.09 ( (hAPP v_mgt__call v_pn), t_a ) 97.85/108.09 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.09 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.09 ) 97.85/108.09 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Nat_Onat))) (let ((_let_1 (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (hBOOL (hAPP _let_1 V_n))) (not (hBOOL (hAPP _let_1 V_m))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n)) V_m))) ))) 97.85/108.09 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.85/108.09 ) 97.85/108.09 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)))) (forall ((T_b $$unsorted)) (= _let_0 (c_Transitive__Closure_Otrancl T_b _let_0)) )) 97.85/108.09 ( tc_Nat_Onat ) 97.85/108.09 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.09 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.85/108.09 ) 97.85/108.09 (instantiation (forall ((V_k_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (hAPP (c_SetInterval_Oord__class_OatMost T_b) V_k_2) (hAPP (c_Groups_Ouminus__class_Ouminus (tc_fun T_b tc_HOL_Obool)) (hAPP (c_SetInterval_Oord__class_OgreaterThan T_b) V_k_2)))) ) 97.85/108.09 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.85/108.09 ) 97.85/108.09 (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 $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (= _let_1 (hAPP (hAPP _let_0 V_x_2) _let_1))) ))) 97.85/108.09 ( v_pn, v_U, tc_Com_Opname ) 97.85/108.09 ) 97.85/108.09 (instantiation (forall ((V_v_H $$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)))) ) 97.85/108.09 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.09 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.09 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.09 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.09 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.09 ) 97.85/108.09 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Osym T_b V_r_2)) (c_Relation_Osym T_b (c_Transitive__Closure_Otrancl T_b V_r_2))) ) 97.85/108.09 ( (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) (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 ) 97.85/108.09 ) 97.85/108.09 (instantiation (forall ((V_Pa_2 $$unsorted) (T_b $$unsorted)) (= V_Pa_2 (hAPP (c_Set_OCollect T_b) V_Pa_2)) ) 97.85/108.09 ( (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) ) 97.85/108.09 ( (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) ) 97.85/108.09 ) 97.85/108.09 (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)))) )))) 97.85/108.09 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.09 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.09 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.85/108.09 ) 97.85/108.09 (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_Groups_Otimes__class_Otimes T_b))) (let ((_let_3 (c_Set_Oinsert T_b))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oab__semigroup__mult T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 _let_0) (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (hBOOL (hAPP (hAPP _let_1 (hAPP (hAPP _let_2 B_x) B_y)) (hAPP (hAPP _let_3 B_x) (hAPP (hAPP _let_3 B_y) _let_0)))) )) (hBOOL (hAPP (hAPP _let_1 (hAPP (c_Finite__Set_Ofold1 T_b _let_2) V_A_2)) V_A_2))) ))))) 97.85/108.10 ( v_U, tc_Com_Opname ) 97.85/108.10 ) 97.85/108.10 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_Osucc V_k) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_k) (c_Groups_Oone__class_Oone tc_Int_Oint))) ) 97.85/108.10 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.10 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.10 ) 97.85/108.10 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Otrans T_b V_r_2)) (= V_r_2 (c_Transitive__Closure_Otrancl T_b V_r_2))) ) 97.85/108.10 ( (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) (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 ) 97.85/108.10 ( (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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 ) 97.85/108.10 ) 97.85/108.10 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Olinordered__semidom T_a)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)) (c_Groups_Oone__class_Oone T_a)))) ) 97.85/108.10 ( tc_Nat_Onat ) 97.85/108.10 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.10 ) 97.85/108.10 (instantiation (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_member T_b))) (let ((_let_2 (c_Set_Oinsert T_b))) (forall ((V_A_2 $$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 $$unsorted)) (hBOOL (hAPP (hAPP _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) B_x) B_y)) (hAPP (hAPP _let_2 B_x) (hAPP (hAPP _let_2 B_y) _let_0)))) )) (hBOOL (hAPP (hAPP _let_1 (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)) V_A_2))) )))) 97.85/108.10 ( v_U, tc_Com_Opname ) 97.85/108.10 ) 97.85/108.10 (instantiation (forall ((V_k_2 $$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)) ) 97.85/108.10 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.10 ( v_n ) 97.85/108.10 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.85/108.10 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.85/108.10 ) 97.85/108.10 (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)))) ))) 97.85/108.10 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.85/108.10 ( (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)) ) 97.85/108.10 ( (hAPP v_mgt__call v_pn), t_a ) 97.85/108.10 ( (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) ) 97.85/108.10 ( (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) ) 97.85/108.10 ) 97.85/108.10 (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))) )) 97.85/108.10 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.10 ) 97.85/108.10 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Transitive__Closure_Otrancl T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) (c_Relation_OId T_b))) (c_Transitive__Closure_Ortrancl T_b V_r_2)) ) 97.85/108.10 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.10 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.85/108.10 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.85/108.10 ) 97.85/108.10 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (= (c_List_Olist_ONil T_b) (c_List_Olinorder__class_Osorted__list__of__set T_b (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) ) 97.85/108.10 ( tc_Nat_Onat ) 97.85/108.10 ( tc_HOL_Obool ) 97.85/108.10 ( tc_Int_Oint ) 97.85/108.10 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.10 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.10 ( t_a ) 97.85/108.10 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.10 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.85/108.10 ( tc_Product__Type_Ounit ) 97.85/108.10 ) 97.85/108.10 (instantiation (forall ((V_x_2 $$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))) ) 97.85/108.10 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.85/108.10 ( (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)) ) 97.85/108.10 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.85/108.10 ( (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) ) 97.85/108.10 ( (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) ) 97.85/108.10 ) 97.85/108.10 (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)) )) 97.85/108.10 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.10 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.10 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.85/108.10 ) 97.85/108.10 (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 $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add__abs T_a)) (= (hAPP _let_0 (hAPP (hAPP _let_1 V_a) V_b)) (hAPP _let_0 (hAPP (hAPP _let_1 V_b) V_a)))) ))) 97.85/108.10 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.85/108.10 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.85/108.10 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 97.85/108.10 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 97.85/108.10 ) 97.85/108.10 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (c_Product__Type_Omap__pair T_b T_b T_c T_c (c_Fun_Oid T_b) (c_Fun_Oid T_c)) (c_Fun_Oid (tc_prod T_b T_c))) ) 97.85/108.10 ( tc_Nat_Onat, tc_Nat_Onat ) 97.85/108.10 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.10 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.85/108.10 ) 97.85/108.10 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq T_a))) (forall ((V_b $$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))) )) 97.85/108.10 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.10 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.10 ) 97.85/108.10 (instantiation (forall ((V_n $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_a) V_n) (hAPP (c_Int_Oring__1__class_Oof__int T_a) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) V_n)))) ) 97.85/108.10 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.85/108.10 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.85/108.10 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 97.85/108.10 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.85/108.10 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.85/108.10 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.85/108.10 ) 97.85/108.10 (instantiation (forall ((V_A_2 $$unsorted) (V_Abs_2 $$unsorted) (V_Rep_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Typedef_Otype__definition T_b T_c V_Rep_2 V_Abs_2 V_A_2)) (= (hAPP (c_Set_Oimage T_c T_b V_Abs_2) V_A_2) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) ) 97.85/108.10 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_Onat__of, tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral ) 97.85/108.10 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop (tc_fun _let_0 tc_HOL_Obool))) c_Int_Ointrel)), c_Int_OAbs__Integ, c_Int_ORep__Integ, (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), tc_Int_Oint ) 97.85/108.10 ) 97.85/108.10 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) (c_Transitive__Closure_Otrancl T_b V_r_2)) (c_Relation_OId T_b)) (c_Transitive__Closure_Ortrancl T_b V_r_2)) ) 97.85/108.10 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc))), tc_Nat_Onat ) 97.85/108.10 ) 97.85/108.10 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Set_Oinsert _let_0))) (forall ((V_B_2 $$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)))))) ))) 97.85/108.10 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.10 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.10 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.85/108.10 ) 97.85/108.10 (instantiation (let ((_let_0 (c_member T_b))) (let ((_let_1 (c_Int_Oring__1__class_OInts T_b))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Oring__1 T_b)) (not (hBOOL (hAPP (hAPP _let_0 V_a_2) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 V_b_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus T_b) V_a_2) V_b_2)) _let_1))) ))) 97.85/108.10 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.85/108.10 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 97.85/108.10 ) 97.85/108.10 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (= (c_Wellfounded_Owf T_b V_r_2) (forall ((B_f $$unsorted)) (not (forall ((B_i $$unsorted)) (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_b)) (hAPP (hAPP (c_Product__Type_OPair T_b T_b) (hAPP B_f (hAPP c_Nat_OSuc B_i))) (hAPP B_f B_i))) V_r_2)) )) )) ) 97.85/108.10 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc))), tc_Nat_Onat ) 97.85/108.10 ( (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (c_Orderings_Oord__class_Oless tc_Nat_Onat))), tc_Nat_Onat ) 97.85/108.10 ( (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))), tc_Nat_Onat ) 97.85/108.10 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect (tc_prod tc_Nat_Onat tc_Nat_Onat)) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))))) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.10 ) 97.85/108.10 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (let ((_let_1 (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint))) (let ((_let_2 (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Nitpick_Onorm__frac__rel))) (forall ((V_Pa_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP _let_2 (hAPP (hAPP _let_1 V_a0_2) V_a1_2)))) (not (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (not (hBOOL (hAPP _let_2 (hAPP (hAPP _let_1 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_0 B_a)) (hAPP _let_0 B_b))))) (hBOOL (hAPP (hAPP V_Pa_2 B_a) B_b))) )) (hBOOL (hAPP (hAPP V_Pa_2 V_a0_2) V_a1_2))) )))) 97.85/108.10 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.10 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.10 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.10 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.10 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.10 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.10 ( (c_Groups_Ominus__class_Ominus tc_Nat_Onat), (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.85/108.10 ( (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) ) 97.85/108.10 ( (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)) ) 97.85/108.10 ( (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)) ) 97.85/108.10 ( (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)) ) 97.85/108.10 ( (c_Set_Oinsert t_a), v_G, (hAPP v_mgt__call v_pn) ) 97.85/108.10 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.85/108.10 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.85/108.10 ( (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)) ) 97.85/108.10 ( (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)) ) 97.85/108.10 ( (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) ) 97.85/108.10 ( (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) ) 97.85/108.10 ( (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)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)) ) 97.85/108.10 ( (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) ) 97.85/108.10 ( (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 ) 97.85/108.11 ( (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G) ) 97.85/108.11 ( (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) ) 97.85/108.11 ( (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)) ) 97.85/108.11 ( (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)) ) 97.85/108.11 ( (c_member t_a), v_G, (hAPP v_mgt__call v_pn) ) 97.85/108.11 ( (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)), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.85/108.11 ( (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)), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.85/108.11 ( (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)) ) 97.85/108.11 ( (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)) ) 97.85/108.11 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 97.85/108.11 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_Int_Onat ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((T_b $$unsorted)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)))) ) 97.85/108.11 ( tc_Nat_Onat ) 97.85/108.11 ( tc_HOL_Obool ) 97.85/108.11 ( tc_Int_Oint ) 97.85/108.11 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.11 ( t_a ) 97.85/108.11 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.11 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.85/108.11 ( tc_Product__Type_Ounit ) 97.85/108.11 ) 97.85/108.11 (instantiation (let ((_let_0 (c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted)) (= _let_0 (hAPP (c_List_Orev T_a) _let_0)) )) 97.85/108.11 ( tc_Nat_Onat ) 97.85/108.11 ( tc_Int_Oint ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (V_B_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun T_b tc_HOL_Obool)) V_B_2) (hAPP (c_Set_Oimage T_c T_b V_f_2) V_A_2)))) (c_Fun_Oinj__on T_b T_c (c_Hilbert__Choice_Oinv__into T_c T_b V_A_2 V_f_2) V_B_2)) ) 97.85/108.11 ( v_U, v_mgt__call, tc_Com_Opname, v_G, t_a ) 97.85/108.11 ) 97.85/108.11 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_1 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_i)))) (let ((_let_2 (c_Groups_Osgn__class_Osgn tc_Int_Oint V_i))) (forall ((V_i $$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)))) )))) 97.85/108.11 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.11 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((T_c $$unsorted) (T_b $$unsorted)) (= (c_Product__Type_Oapfst T_b T_b T_c (c_Fun_Oid T_b)) (c_Fun_Oid (tc_prod T_b T_c))) ) 97.85/108.11 ( tc_Nat_Onat, tc_Nat_Onat ) 97.85/108.11 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.11 ( (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.85/108.11 ) 97.85/108.11 (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)))) ) 97.85/108.11 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.11 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.85/108.11 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((T_a $$unsorted)) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Nat_Osize__class_Osize (tc_List_Olist T_a)) (c_List_Olist_ONil T_a))) ) 97.85/108.11 ( tc_Nat_Onat ) 97.85/108.11 ( tc_Int_Oint ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((V_w_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_w_2)) (c_Int_Oring__1__class_OInts T_b)))) ) 97.85/108.11 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.85/108.11 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.11 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.85/108.11 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.11 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.11 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.11 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.85/108.11 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.11 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.11 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.11 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((V_k_2 $$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_OgreaterThanAtMost T_b V_k_2 V_l_2))) ) 97.85/108.11 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.11 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.11 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.11 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.85/108.11 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.85/108.11 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.11 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.11 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Groups_Oab__semigroup__mult T_b)) (c_Finite__Set_Ofun__left__comm T_b T_b (c_Groups_Otimes__class_Otimes T_b))) ) 97.85/108.11 ( tc_Nat_Onat ) 97.85/108.11 ( tc_Int_Oint ) 97.85/108.11 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((V_A_2 $$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))) ) 97.85/108.11 ( v_U, v_pn, tc_Com_Opname ) 97.85/108.11 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.85/108.11 ( (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) ) 97.85/108.11 ( (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) ) 97.85/108.11 ( (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)) ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Oboolean__algebra T_a)) (= (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_x)) V_x) (c_Orderings_Otop__class_Otop T_a))) ) 97.85/108.11 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.11 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.85/108.11 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((V_s_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Osym T_b V_r_2)) (not (c_Relation_Osym T_b V_s_2)) (c_Relation_Osym T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) V_r_2) V_s_2))) ) 97.85/108.11 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.85/108.11 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) ) 97.85/108.11 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.11 ) 97.85/108.11 (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))) ) 97.85/108.11 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.11 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.11 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.11 ) 97.85/108.11 (instantiation (let ((_let_0 (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_n))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_i) V_n))) (= V_i (hAPP _let_0 (hAPP _let_0 V_i)))) )) 97.85/108.11 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.85/108.11 ) 97.85/108.11 (instantiation (let ((_let_0 (c_Divides_Odiv__class_Odiv tc_Nat_Onat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) V_n))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_n) V_m))) (= (hAPP c_Nat_OSuc (hAPP (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n)) V_n)) (hAPP (hAPP _let_0 V_m) V_n))) )) 97.85/108.11 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.85/108.11 ) 97.85/108.11 (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 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) B_n))) (not (= V_k (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) B_n)))) ))) ) 97.85/108.11 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (c_Big__Operators_Olattice__class_OSup__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_b) V_x_2) (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2)))) ) 97.85/108.11 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((V_M_2 $$unsorted) (T_b $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_M_2))) (not (forall ((B_h $$unsorted)) (not (c_Fun_Obij__betw tc_Nat_Onat T_b B_h (c_SetInterval_Oord__class_OatLeastAtMost tc_Nat_Onat (c_Groups_Oone__class_Oone tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard T_b) V_M_2)) V_M_2)) ))) ) 97.85/108.11 ( v_U, tc_Com_Opname ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((T_b $$unsorted)) (or (not (class_Finite__Set_Ofinite T_b)) (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool))))) ) 97.85/108.11 ( tc_Nat_Onat ) 97.85/108.11 ( tc_HOL_Obool ) 97.85/108.11 ( tc_Int_Oint ) 97.85/108.11 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.11 ( t_a ) 97.85/108.11 ( tc_Com_Opname ) 97.85/108.11 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.11 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.85/108.11 ( tc_Product__Type_Ounit ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((V_x $$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 $$unsorted)) (not (= V_x (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) (hAPP c_Nat_OSuc B_n))))) ))) ) 97.85/108.11 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.11 ) 97.85/108.11 (instantiation (let ((_let_0 (c_Nitpick_Onat__gcd V_x_2 V_y_2))) (let ((_let_1 (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) V_y_2))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Nat_Onat tc_Nat_Onat) c_Nitpick_Onat__gcd__rel) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_x_2) V_y_2)))) (and (or _let_1 (= (c_Nitpick_Onat__gcd V_y_2 (c_Divides_Odiv__class_Omod tc_Nat_Onat V_x_2 V_y_2)) _let_0)) (or (not _let_1) (= V_x_2 _let_0)))) ))) 97.85/108.11 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.11 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.11 ) 97.85/108.11 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (let ((_let_2 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_0) V_A_2) (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) _let_1)))) (let ((_let_3 (= _let_1 _let_2))) (let ((_let_4 (c_Big__Operators_Olattice__class_OSup__fin T_b V_A_2))) (forall ((V_x_2 $$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))) (and (or _let_3 (= _let_4 (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_3) (= V_x_2 _let_4)))) )))))) 97.85/108.11 ( v_pn, v_U, tc_Com_Opname ) 97.85/108.11 ) 97.85/108.11 (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 $$unsorted)) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus _let_2) V_A_2) (hAPP _let_1 (c_Orderings_Obot__class_Obot _let_2))))) (hAPP _let_0 (hAPP _let_1 V_A_2)))) )))) 97.85/108.11 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.85/108.11 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.11 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.85/108.11 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.11 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((T_f $$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))) ) 97.85/108.11 ( tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) ) 97.85/108.11 ( tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), c_Int_Onat, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) ) 97.85/108.11 ( tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_Onat, (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_Onat ) 97.85/108.11 ( tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), c_Int_Onat, (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Int_Oint), c_Int_Onat ) 97.85/108.11 ( 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) ) 97.85/108.11 ( 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_Groups_Ozero__class_Ozero tc_Int_Oint)))), 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) ) 97.85/108.11 ) 97.85/108.11 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2)) (= V_A_2 (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))) (= (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_b) V_x_2) (c_Big__Operators_Olattice__class_OInf__fin T_b V_A_2)) (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) ) 97.85/108.11 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.85/108.11 ) 97.85/108.11 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP c_Nat_OSuc V_m)) V_n))) (hBOOL (hAPP (hAPP _let_0 V_m) V_n))) )) 97.85/108.11 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), v_n ) 97.85/108.12 ) 97.85/108.12 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (tc_fun T_b tc_HOL_Obool))) (let ((_let_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_1) V_A_2) V_B_2))) (let ((_let_3 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_B_2 $$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)))) ))))) 97.85/108.12 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.12 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.12 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.85/108.12 ) 97.85/108.12 (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)))))) ) 97.85/108.12 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.85/108.12 ( (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)) ) 97.85/108.12 ( (hAPP v_mgt__call v_pn), t_a ) 97.85/108.12 ( (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) ) 97.85/108.12 ( (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) ) 97.85/108.12 ) 97.85/108.12 (instantiation (let ((_let_0 (c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted)) (= _let_0 (hAPP (c_List_Orotate1 T_a) _let_0)) )) 97.85/108.12 ( tc_Nat_Onat ) 97.85/108.12 ( tc_Int_Oint ) 97.85/108.12 ) 97.85/108.12 (instantiation (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m) V_n))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m) V_n))) ) 97.85/108.12 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.85/108.12 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.85/108.12 ) 97.85/108.12 (instantiation (forall ((V_i $$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_Ouminus__class_Ouminus tc_Int_Oint) V_i) (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) V_i))) ) 97.85/108.12 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.12 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.12 ) 97.85/108.12 (instantiation (forall ((V_i $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_i) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (= V_i (hAPP (c_Groups_Oabs__class_Oabs tc_Int_Oint) V_i))) ) 97.85/108.12 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.12 ) 97.85/108.12 (instantiation (forall ((T_b $$unsorted)) (= (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Set_OCollect T_b) (hAPP (c_COMBK tc_HOL_Obool T_b) c_fTrue))) ) 97.85/108.12 ( tc_Nat_Onat ) 97.85/108.12 ( tc_HOL_Obool ) 97.85/108.12 ( tc_Int_Oint ) 97.85/108.12 ( (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.12 ( t_a ) 97.85/108.12 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.12 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.85/108.12 ( tc_Product__Type_Ounit ) 97.85/108.12 ) 97.85/108.12 (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 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (not (= (hAPP (hAPP _let_1 V_c_2) V_d_2) (hAPP (hAPP _let_1 V_a_2) V_b_2))) (= (hBOOL (hAPP (hAPP _let_0 V_a_2) V_b_2)) (hBOOL (hAPP (hAPP _let_0 V_c_2) V_d_2)))) ))) 97.85/108.12 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), tc_Nat_Onat ) 97.85/108.12 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral ) 97.85/108.12 ) 97.85/108.12 (instantiation (forall ((V_d $$unsorted)) (= (c_Lazy__Sequence_Osmall__lazy_H V_d (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_d)) (c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy tc_Int_Oint V_d)) ) 97.85/108.12 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.12 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.12 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.12 ) 97.85/108.12 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) V_B_2)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless _let_0) V_A_2) V_B_2)) (= V_B_2 V_A_2))) )) 97.85/108.12 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, t_a ) 97.85/108.12 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a ) 97.85/108.12 ) 97.85/108.12 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (forall ((V_f_2 $$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)))) )) 97.85/108.12 ( (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 ) 97.85/108.12 ) 97.85/108.12 (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 $$unsorted)) (or (not (class_Int_Onumber T_b)) (not (class_Orderings_Olinorder T_b)) (= (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) _let_1) _let_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) _let_2) _let_1)))) )))) 97.85/108.12 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.12 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.12 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.12 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.12 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.12 ) 97.85/108.12 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (let ((_let_1 (c_Lattices_Osemilattice__inf__class_Oinf T_b))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_2) V_A_2) V_B_2))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Lattices_Olattice T_b)) (not (hBOOL (hAPP _let_0 V_A_2))) (not (hBOOL (hAPP _let_0 V_B_2))) (= _let_3 (c_Orderings_Obot__class_Obot _let_2)) (= (hAPP (hAPP _let_1 (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_1 (c_Big__Operators_Olattice__class_OInf__fin T_b (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_2) V_A_2) V_B_2))) (c_Big__Operators_Olattice__class_OInf__fin T_b _let_3)))) ))))) 97.85/108.12 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.12 ( (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 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.12 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)) ) 97.85/108.12 ) 97.85/108.12 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (c_Int_Oiszero T_a (c_Groups_Ozero__class_Ozero T_a))) ) 97.85/108.12 ( tc_Nat_Onat ) 97.85/108.12 ( tc_Int_Oint ) 97.85/108.12 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.12 ) 97.85/108.12 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Omin T_b))) (forall ((V_x_2 $$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))) (= (hAPP (hAPP _let_0 V_x_2) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 V_A_2)) (c_Big__Operators_Olattice_OInf__fin T_b _let_0 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) )) 97.85/108.12 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.85/108.12 ) 97.85/108.12 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OatLeastLessThan tc_Nat_Onat V_m_2))) (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_na_2))) (= (hAPP _let_0 (hAPP c_Nat_OSuc V_na_2)) (hAPP (hAPP (c_Set_Oinsert tc_Nat_Onat) V_na_2) (hAPP _let_0 V_na_2)))) )) 97.85/108.12 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.85/108.12 ) 97.85/108.12 (instantiation (forall ((V_i $$unsorted) (V_j $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_j) V_i))) (= (c_List_Olist_ONil tc_Nat_Onat) (c_List_Oupt V_i V_j))) ) 97.85/108.12 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.85/108.12 ) 97.85/108.12 (instantiation (forall ((V_N_2 $$unsorted)) (= (not (forall ((B_m $$unsorted)) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_x) V_N_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) B_x) B_m))) )) )) (hBOOL (hAPP (c_Finite__Set_Ofinite tc_Nat_Onat) V_N_2))) ) 97.85/108.12 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 97.85/108.12 ) 97.85/108.12 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Oinj__on T_b T_c V_f_2 V_A_2)) (= V_A_2 (hAPP (c_Set_Oimage T_c T_b (c_Fun_Othe__inv__into T_b T_c V_A_2 V_f_2)) (hAPP (c_Set_Oimage T_b T_c V_f_2) V_A_2)))) ) 97.85/108.12 ( v_U, v_mgt__call, t_a, tc_Com_Opname ) 97.85/108.12 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.85/108.12 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.85/108.12 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.85/108.12 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), tc_Int_Oint, tc_Nat_Onat ) 97.85/108.12 ) 97.85/108.12 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (tc_fun T_c tc_HOL_Obool))) (let ((_let_2 (tc_fun T_c _let_0))) (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (hAPP (hAPP (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR T_c _let_0) V_A_2) V_B_2) (c_Complete__Lattice_OSup__class_OSup _let_0 (hAPP (c_Set_OCollect _let_0) (hAPP (hAPP (c_COMBB _let_1 tc_HOL_Obool _let_0) (c_HOL_OEx T_c)) (hAPP (hAPP (c_COMBB _let_1 _let_1 _let_0) (hAPP (c_COMBS T_c tc_HOL_Obool tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_HOL_Obool (tc_fun tc_HOL_Obool tc_HOL_Obool) T_c) c_fconj) (hAPP (hAPP (c_COMBC T_c _let_1 tc_HOL_Obool) (c_member T_c)) V_A_2)))) (hAPP (hAPP (c_COMBC _let_0 _let_2 _let_1) (hAPP (hAPP (c_COMBB (tc_fun _let_0 tc_HOL_Obool) (tc_fun _let_2 _let_1) _let_0) (c_COMBB _let_0 tc_HOL_Obool T_c)) c_fequal)) V_B_2)))))) )))) 97.85/108.12 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.85/108.12 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.85/108.12 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat, tc_Nat_Onat ) 97.85/108.12 ) 97.85/108.12 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of T_b))) (let ((_let_1 (hAPP _let_0 V_u))) (let ((_let_2 (hAPP _let_0 V_v))) (let ((_let_3 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) _let_1) _let_2)))) (let ((_let_4 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) _let_1) _let_2))) (forall ((V_v $$unsorted) (V_u $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber T_b)) (not (class_Orderings_Oord T_b)) (and (or (not _let_3) (= _let_1 _let_4)) (or _let_3 (= _let_2 _let_4)))) )))))) 97.85/108.12 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.12 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.12 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.12 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.12 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.12 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.12 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.12 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.12 ) 97.85/108.12 (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_Big__Operators_Olinorder__class_OMin T_b (hAPP _let_1 V_A_2)))) (let ((_let_4 (= (c_Orderings_Obot__class_Obot _let_0) _let_2))) (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (c_Finite__Set_Ofinite T_b) V_A_2))) (and (or (not _let_4) (= V_x_2 _let_3)) (or _let_4 (= _let_3 (hAPP (hAPP (c_Orderings_Oord__class_Omin T_b) V_x_2) (c_Big__Operators_Olinorder__class_OMin T_b _let_2)))))) )))))) 97.85/108.12 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.85/108.12 ( (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (hAPP (hAPP (c_Product__Type_OPair (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool) (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) _let_0) _let_0)), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool))), (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)) ) 97.85/108.12 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.85/108.12 ( (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) _let_0) _let_0)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.12 ( (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.12 ) 97.85/108.12 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (let ((_let_1 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) _let_0) V_x)))) (let ((_let_2 (c_Groups_Oone__class_Oone T_a))) (let ((_let_3 (c_Groups_Osgn__class_Osgn T_a V_x))) (let ((_let_4 (= V_x _let_0))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Groups_Osgn__if T_a)) (and (or _let_4 (and (or _let_1 (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) _let_2) _let_3)) (or (not _let_1) (= _let_2 _let_3)))) (or (not _let_4) (= _let_0 _let_3)))) )))))) 97.85/108.12 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.85/108.12 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.12 ) 97.85/108.12 (instantiation (forall ((V_na_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Osemiring__1 T_b)) (= (hAPP (c_Nat_Osemiring__1__class_Oof__nat T_b) V_na_2) (c_Nat_Osemiring__1__class_Oof__nat__aux T_b (hAPP (hAPP (c_COMBC T_b T_b T_b) (c_Groups_Oplus__class_Oplus T_b)) (c_Groups_Oone__class_Oone T_b)) V_na_2 (c_Groups_Ozero__class_Ozero T_b)))) ) 97.85/108.12 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Int_Oint ) 97.85/108.12 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.85/108.12 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Int_Oint ) 97.85/108.12 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Code__Numeral_Ocode__numeral ) 97.85/108.12 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.85/108.12 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), tc_Int_Oint ) 97.85/108.12 ) 97.85/108.12 (instantiation (let ((_let_0 (c_Finite__Set_Ofinite T_b))) (forall ((V_a_2 $$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)))) )) 97.85/108.12 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), tc_Nat_Onat ) 97.85/108.12 ( (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)) ) 97.85/108.12 ( (hAPP v_mgt__call v_pn), v_G, t_a ) 97.85/108.12 ( (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) ) 97.85/108.13 ( (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) ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Rings_Osemiring__1 T_a)) (not (c_Int_Oiszero T_a (c_Groups_Oone__class_Oone T_a)))) ) 97.85/108.13 ( tc_Nat_Onat ) 97.85/108.13 ( tc_Int_Oint ) 97.85/108.13 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Groups_Oplus__class_Oplus tc_Int_Oint))) (forall ((V_k $$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)) )) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.13 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.13 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_m_2))) (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (= (hAPP _let_0 (hAPP c_Nat_OSuc V_na_2)) (c_Nat_Onat_Onat__case tc_Nat_Onat (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (c_COMBI tc_Nat_Onat) (hAPP _let_0 V_na_2))) )) 97.85/108.13 ( v_n, (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Groups_Ominus T_1)) (class_Groups_Ominus (tc_fun T_2 T_1))) ) 97.85/108.13 ( tc_Nat_Onat, tc_HOL_Obool ) 97.85/108.13 ( tc_HOL_Obool, tc_HOL_Obool ) 97.85/108.13 ( tc_Int_Oint, tc_HOL_Obool ) 97.85/108.13 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.85/108.13 ( t_a, tc_HOL_Obool ) 97.85/108.13 ( (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 ) 97.85/108.13 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.85/108.13 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.85/108.13 ) 97.85/108.13 (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)))) ) 97.85/108.13 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.85/108.13 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.13 ) 97.85/108.13 (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 (hAPP (c_Groups_Oplus__class_Oplus T_a) (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (c_Groups_Oone__class_Oone T_a))) (hAPP _let_0 V_w)) (hAPP _let_0 (c_Int_Opred V_w)))) )) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_SetInterval_Oord__class_OatMost T_b))) (forall ((V_u_2 $$unsorted) (V_l_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Orderings_Olinorder T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) V_l_2) V_u_2))) (= (hAPP _let_0 V_u_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun T_b tc_HOL_Obool)) (hAPP _let_0 V_l_2)) (c_SetInterval_Oord__class_OgreaterThanAtMost T_b V_l_2 V_u_2)))) )) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.13 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.13 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), v_G, (tc_fun t_a tc_HOL_Obool) ) 97.85/108.13 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.85/108.13 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.13 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.13 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Finite__Set_Ocard T_b))) (forall ((V_k_2 $$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))) (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))))) (not (= V_k_2 (hAPP _let_0 B_B))) (hBOOL (hAPP (hAPP (c_member T_b) B_b) B_B))) ))) )) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), v_G, t_a ) 97.85/108.13 ( v_n, (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), t_a ) 97.85/108.13 ( (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 ) 97.85/108.13 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), tc_HOL_Obool ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (forall ((V_A_2 $$unsorted) (T_b $$unsorted)) (= (= V_A_2 (c_Orderings_Obot__class_Obot _let_0)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq _let_0) V_A_2) (hAPP (c_Groups_Ouminus__class_Ouminus _let_0) V_A_2)))) )) 97.85/108.13 ( v_G, t_a ) 97.85/108.13 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), t_a ) 97.85/108.13 ) 97.85/108.13 (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))) ) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.13 ( (hAPP c_Nat_OSuc v_n), tc_Nat_Onat ) 97.85/108.13 ( v_G, (tc_fun t_a tc_HOL_Obool) ) 97.85/108.13 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.85/108.13 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.13 ) 97.85/108.13 (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))) ) 97.85/108.13 ( v_U, v_mgt__call, t_a, tc_Com_Opname ) 97.85/108.13 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), c_Nat_OSuc, tc_Nat_Onat, tc_Nat_Onat ) 97.85/108.13 ( (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 ) 97.85/108.13 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool)), c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.85/108.13 ( (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 ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Complete__Lattice_Ocomplete__lattice T_b)) (not (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Complete__Lattice_OInf__class_OInf T_b V_A_2)) V_x_2))) ) 97.85/108.13 ( v_U, v_pn, tc_Com_Opname ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq T_a) V_x))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Fields_Olinordered__field T_a)) (not (forall ((B_e $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_a) (c_Groups_Ozero__class_Ozero T_a)) B_e))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_y) B_e)))) )) (hBOOL (hAPP _let_0 V_y))) )) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.13 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (tc_fun t_a tc_HOL_Obool) ) 97.85/108.13 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Osemilattice__inf (tc_fun T_2 T_1))) ) 97.85/108.13 ( tc_Nat_Onat, tc_HOL_Obool ) 97.85/108.13 ( tc_HOL_Obool, tc_HOL_Obool ) 97.85/108.13 ( tc_Int_Oint, tc_HOL_Obool ) 97.85/108.13 ( (tc_prod tc_Nat_Onat tc_Nat_Onat), tc_HOL_Obool ) 97.85/108.13 ( t_a, tc_HOL_Obool ) 97.85/108.13 ( (let ((_let_0 (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.85/108.13 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (tc_prod _let_0 _let_0)), tc_HOL_Obool ) 97.85/108.13 ( tc_Product__Type_Ounit, tc_HOL_Obool ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus T_b))) (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Groups_Oordered__ab__group__add T_b)) (= (hAPP (c_Set_Oimage T_b T_b _let_0) (hAPP (c_SetInterval_Oord__class_OatLeast T_b) V_x_2)) (hAPP (c_SetInterval_Oord__class_OatMost T_b) (hAPP _let_0 V_x_2)))) )) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.13 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.85/108.13 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (V_F_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Finite__Set_Ofolding__one__idem T_b V_f_2 V_F_2)) (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 V_f_2 V_x_2) (hAPP V_F_2 V_A_2)) (hAPP V_F_2 (hAPP (hAPP (c_Set_Oinsert T_b) V_x_2) V_A_2)))) ) 97.85/108.13 ( v_G, v_U, (c_Set_Oimage tc_Com_Opname t_a v_mgt__call), (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)), tc_Com_Opname ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_Pa_2 $$unsorted) (T_b $$unsorted) (B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_b) B_x) (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool))))) (not (hBOOL (hAPP V_Pa_2 B_x)))) ) 97.85/108.13 ( (c_member tc_Com_Opname), tc_Com_Opname, v_pn ) 97.85/108.13 ( (c_member t_a), t_a, (hAPP v_mgt__call v_pn) ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Orderings_Otop__class_Otop (tc_fun T_b tc_HOL_Obool)))) (let ((_let_1 (c_Orderings_Otop__class_Otop (tc_fun T_d tc_HOL_Obool)))) (forall ((V_g_2 $$unsorted) (T_d $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (or (not (c_Fun_Obij__betw T_b T_c V_f_2 _let_0 (c_Orderings_Otop__class_Otop (tc_fun T_c tc_HOL_Obool)))) (not (c_Fun_Obij__betw T_d T_b V_g_2 _let_1 _let_0)) (= (hAPP (c_Fun_Ocomp T_b T_d T_c (c_Hilbert__Choice_Oinv__into T_d T_b _let_1 V_g_2)) (c_Hilbert__Choice_Oinv__into T_b T_c _let_0 V_f_2)) (c_Hilbert__Choice_Oinv__into T_d T_c _let_1 (hAPP (c_Fun_Ocomp T_b T_c T_d V_f_2) V_g_2)))) ))) 97.85/108.13 ( c_Int_Onat, tc_Int_Oint, (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat ) 97.85/108.13 ( 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 ) 97.85/108.13 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), tc_Int_Oint, c_Int_Onat, tc_Nat_Onat, tc_Int_Oint ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_R_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP (c_Relation_OImage T_c T_b V_R_2) (c_Orderings_Obot__class_Obot (tc_fun T_c tc_HOL_Obool)))) ) 97.85/108.13 ( c_Int_Ointrel, (tc_prod tc_Nat_Onat tc_Nat_Onat), (tc_prod tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_w $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (not (class_Int_Oring__char__0 T_a)) (not (c_Int_Oiszero T_a (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit1 V_w))))) ) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.85/108.13 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.13 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.13 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (tc_fun T_b tc_HOL_Obool))) (let ((_let_1 (hAPP (c_Set_Oinsert T_b) V_x_2))) (forall ((V_A_2 $$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))))) ))) 97.85/108.13 ( v_G, (hAPP v_mgt__call v_pn), t_a ) 97.85/108.13 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Groups_Ozero__class_Ozero tc_Nat_Onat), tc_Nat_Onat ) 97.85/108.13 ( (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) ) 97.85/108.13 ( (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) ) 97.85/108.13 ( (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)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted)) (or (not (c_Relation_Otrans T_b V_r_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_prod T_b T_b) tc_HOL_Obool)) (hAPP (hAPP (c_Relation_Orel__comp T_b T_b T_b) V_r_2) V_r_2)) V_r_2))) ) 97.85/108.13 ( (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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 ) 97.85/108.13 ) 97.85/108.13 (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 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_k_2) V_i_2)) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_i_2) V_k_2))))) )) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.13 ) 97.85/108.13 (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 (hAPP (c_Groups_Oplus__class_Oplus T_a) (c_Groups_Oone__class_Oone T_a)) (hAPP _let_0 V_w)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) V_w)))) )) 97.85/108.13 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Divides_Odiv__class_Odiv tc_Nat_Onat))) (let ((_let_1 (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) (forall ((V_m $$unsorted)) (= (hAPP (hAPP _let_0 (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_m))) _let_1) (hAPP c_Nat_OSuc (hAPP (hAPP _let_0 V_m) _let_1))) ))) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.13 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (hAPP _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) V_m)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Code__Numeral_Ocode__numeral) (hAPP _let_0 V_n)) (hAPP _let_0 V_m))) )) 97.85/108.13 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) V_n) V_m) (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP c_Code__Numeral_Onat__of V_n)) (hAPP c_Code__Numeral_Onat__of V_m)))) ) 97.85/108.13 ( (c_Groups_Oone__class_Oone tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) (hAPP _let_0 V_n)) (hAPP _let_0 V_m)) (hAPP _let_0 (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) V_n) V_m))) )) 97.85/108.13 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.13 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (forall ((V_l $$unsorted)) (= (c_Int_OBit1 (hAPP _let_0 V_l)) (hAPP _let_0 (c_Int_OBit0 V_l))) )) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.13 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.13 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_n $$unsorted)) (= (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_n))) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) V_n)) ) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 (c_Int_OBit0 V_k_2))) (hBOOL (hAPP _let_0 V_k_2))) )) 97.85/108.13 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_n $$unsorted)) (= V_n (hAPP c_Code__Numeral_Onat__of (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) V_n))) ) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.13 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_2 (hAPP _let_1 V_v))) (let ((_let_3 (hAPP _let_1 V_w))) (let ((_let_4 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_3) _let_2)))) (let ((_let_5 (c_Divides_OposDivAlg _let_3 _let_2))) (forall ((V_w $$unsorted) (V_v $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) _let_2))) (and (or _let_4 (= _let_5 (hAPP (c_Divides_Oadjust _let_2) (c_Divides_OposDivAlg _let_3 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP _let_1 (c_Int_OBit0 (c_Int_OBit1 _let_0)))) _let_2))))) (or (not _let_4) (= _let_5 (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) _let_0) _let_3))))) ))))))) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 (c_Int_OBit1 V_k_2))) (hBOOL (hAPP _let_0 V_k_2))) )) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.13 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_z) V_z) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) V_z) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))))))) ) 97.85/108.13 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_n $$unsorted)) (= (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_n)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) V_n)) ) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.13 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((T_a $$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) _let_0)) (hAPP (c_Int_Onumber__class_Onumber__of T_a) _let_0))) )) 97.85/108.13 ( tc_Nat_Onat ) 97.85/108.13 ( tc_Int_Oint ) 97.85/108.13 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.13 ) 97.85/108.13 (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_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__eq tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) V_y_2)))) ) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.85/108.13 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.13 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.13 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.13 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.85/108.13 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.13 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.13 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.13 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone T_a))) (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) _let_0) _let_0) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) )) 97.85/108.13 ( tc_Int_Oint ) 97.85/108.13 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_m $$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_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 97.85/108.13 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 V_k_2) _let_1)) (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k_2)) _let_1))) ))) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.13 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (forall ((V_n $$unsorted)) (= (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc V_n)) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.13 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.13 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_k_2) _let_0)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Int_OBit1 V_k_2)) _let_0))) )) 97.85/108.13 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.13 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.13 ) 97.85/108.13 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) 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_Opred _let_0)) V_b))) )) 97.85/108.13 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.13 ) 97.85/108.13 (instantiation (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (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 ((_let_3 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_4 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (forall ((V_X_2 $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP _let_2 V_X_2) _let_3)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_4 _let_4)) (c_Relation_OId _let_0)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP (hAPP _let_2 _let_3) _let_3)) (c_Orderings_Obot__class_Obot _let_1)))))) )))))) 97.85/108.14 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 97.85/108.14 ) 97.85/108.14 (instantiation (forall ((V_z $$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_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 97.85/108.14 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.14 ) 97.85/108.14 (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 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_3 (hAPP _let_2 V_w))) (let ((_let_4 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_1) _let_3)))) (let ((_let_5 (c_Divides_OposDivAlg _let_1 _let_3))) (forall ((V_w $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) _let_3))) (and (or (not _let_4) (= (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) _let_0) _let_1) _let_5)) (or _let_4 (= _let_5 (hAPP (c_Divides_Oadjust _let_3) (c_Divides_OposDivAlg _let_1 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP _let_2 (c_Int_OBit0 (c_Int_OBit1 _let_0)))) _let_3))))))) ))))))) 97.85/108.14 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.14 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.14 ) 97.85/108.14 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 (c_Int_OBit0 V_k_2))) (hBOOL (hAPP _let_0 V_k_2))) )) 97.85/108.14 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ) 97.85/108.14 (instantiation (forall ((V_y_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq T_b) (c_Groups_Ozero__class_Ozero T_b)) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_y_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_y_2)))) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.85/108.14 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.14 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.85/108.14 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.14 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.14 ) 97.85/108.14 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_1 (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit0 V_k_2)) _let_1)) (hBOOL (hAPP (hAPP _let_0 V_k_2) _let_1))) ))) 97.85/108.14 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ) 97.85/108.14 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint))) (let ((_let_2 (c_Divides_OposDivAlg V_a_2 V_b_2))) (let ((_let_3 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_b_2) _let_0)))) (let ((_let_4 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_a_2) V_b_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted)) (or (not (hBOOL (hAPP (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Divides_OposDivAlg__rel) (hAPP (hAPP _let_1 V_a_2) V_b_2)))) (and (or _let_3 _let_4 (= _let_2 (hAPP (c_Divides_Oadjust V_b_2) (c_Divides_OposDivAlg V_a_2 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 _let_0)))) V_b_2))))) (or (and (not _let_3) (not _let_4)) (= _let_2 (hAPP (hAPP _let_1 _let_0) V_a_2))))) )))))) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.14 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.14 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ) 97.85/108.14 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_z) V_z) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) V_z))) ) 97.85/108.14 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.85/108.14 ) 97.85/108.14 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (forall ((V_v $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_v) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (= (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)))) )) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.14 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ) 97.85/108.14 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone tc_Nat_Onat))) (forall ((V_v $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_v) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (= _let_0 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) _let_0) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v)))) )) 97.85/108.14 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.14 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.14 ) 97.85/108.14 (instantiation (forall ((V_z $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_z) (hAPP (hAPP (c_Groups_Otimes__class_Otimes T_a) V_z) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.14 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.85/108.14 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.14 ) 97.85/108.14 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_1 (c_Int_OBit0 V_k_2)) _let_0)) (hBOOL (hAPP (hAPP _let_1 V_k_2) _let_0))) ))) 97.85/108.14 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ) 97.85/108.14 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (forall ((V_b $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_b))) (= _let_0 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) _let_0) V_b))) )) 97.85/108.14 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.14 ) 97.85/108.14 (instantiation (let ((_let_0 (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (forall ((V_l $$unsorted)) (= (c_Int_OBit0 (hAPP _let_0 V_l)) (hAPP _let_0 (c_Int_OBit1 V_l))) )) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.14 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ) 97.85/108.14 (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 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 tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_y_2)))) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.85/108.14 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.14 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.85/108.14 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.14 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.14 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.14 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.14 ) 97.85/108.14 (instantiation (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((V_x_2 $$unsorted) (V_Pa_2 $$unsorted)) (or (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) B_y) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (hBOOL (hAPP V_Pa_2 (hAPP c_Int_OAbs__Integ B_y)))) )) (hBOOL (hAPP V_Pa_2 V_x_2))) ))) 97.85/108.14 ( 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)) ) 97.85/108.14 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 97.85/108.14 ( c_fequal, (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.14 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 97.85/108.14 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_Onat ) 97.85/108.14 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat__Numeral_Oneg ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert tc_Nat_Onat) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (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))) ) 97.85/108.14 ( c_Int_Onat, (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)) ) 97.85/108.14 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.85/108.14 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 97.85/108.14 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) ) 97.85/108.14 ( v_U, (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) ) 97.85/108.14 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (c_Finite__Set_Ocard t_a) ) 97.85/108.14 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G)) ) 97.85/108.14 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (c_Groups_Ominus__class_Ominus tc_Nat_Onat) ) 97.85/108.14 ( v_n, c_Nat_OSuc ) 97.85/108.14 ( (hAPP c_Nat_OSuc v_n), (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) ) 97.85/108.14 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U))) ) 97.85/108.14 ( v_G, (c_Finite__Set_Ocard t_a) ) 97.85/108.14 ( v_G, (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) ) 97.85/108.14 ( v_G, (hAPP (c_member t_a) (hAPP v_mgt__call v_pn)) ) 97.85/108.14 ( v_G, (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Nat_Onat) ) 97.85/108.14 ( (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) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( 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)) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (hAPP (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) ) 97.85/108.14 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) ) 97.85/108.14 ( v_pn, v_mgt__call ) 97.85/108.14 ( v_pn, (c_member tc_Com_Opname) ) 97.85/108.14 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Nat_OSuc ) 97.85/108.14 ( (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) ) 97.85/108.14 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (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) ) 97.85/108.14 ( (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) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (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))) ) 97.85/108.14 ( (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))) ) 97.85/108.14 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (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))) ) 97.85/108.14 ( (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))) ) 97.85/108.14 ( (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))) ) 97.85/108.14 ( (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))) ) 97.85/108.14 ( (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))) ) 97.85/108.14 ( (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))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0))))))) ) 97.85/108.14 ( (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))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0))))))) ) 97.85/108.14 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.85/108.14 ( 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)))) ) 97.85/108.14 ( (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))) ) 97.85/108.14 ( (hAPP v_mgt__call v_pn), (c_Set_Oinsert t_a) ) 97.85/108.14 ( (hAPP v_mgt__call v_pn), (c_member t_a) ) 97.85/108.14 ( c_fTrue, (c_COMBK tc_HOL_Obool tc_Nat_Onat) ) 97.85/108.14 ( c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Int_Oint) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (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 ) 97.85/108.14 ( c_fFalse, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (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)) ) 97.85/108.14 ( (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 ) 97.85/108.14 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Finite__Set_Ocard tc_Product__Type_Ounit) ) 97.85/108.14 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) ) 97.85/108.14 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), (c_Finite__Set_Ocard tc_HOL_Obool) ) 97.85/108.14 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (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))) ) 97.85/108.14 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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))) ) 97.85/108.15 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (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))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))))) ) 97.85/108.15 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.85/108.15 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 97.85/108.15 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 97.85/108.15 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 97.85/108.15 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.15 ( (c_Int_Opred (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)) ) 97.85/108.15 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.85/108.15 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.15 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), c_Int_Onat ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 97.85/108.15 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 97.85/108.15 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.85/108.15 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), c_Int_Onat ) 97.85/108.15 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 97.85/108.15 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.85/108.15 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), c_Int_Onat ) 97.85/108.15 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.85/108.15 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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))) ) 97.85/108.15 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (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))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))))) ) 97.85/108.15 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.85/108.15 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_Nat__Numeral_Oneg ) 97.85/108.15 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 97.85/108.15 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.85/108.15 ) 97.85/108.15 (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 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) V_b))) (and (or _let_1 (= _let_2 (hAPP (c_Divides_Oadjust V_b) (c_Divides_OposDivAlg V_a (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 _let_0)))) V_b))))) (or (not _let_1) (= _let_2 (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) _let_0) V_a))))) )))) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.15 ) 97.85/108.15 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_1 (c_Int_OBit1 V_k_2)) _let_0)) (hBOOL (hAPP (hAPP _let_1 V_k_2) _let_0))) ))) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.15 ) 97.85/108.15 (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_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_1 V_k_2) _let_0)) (hBOOL (hAPP (hAPP _let_1 (c_Int_OBit0 V_k_2)) _let_0))) ))) 97.85/108.15 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.15 ) 97.85/108.15 (instantiation (forall ((V_z $$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) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) V_z)) ) 97.85/108.15 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.15 ) 97.85/108.15 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (not (class_Fields_Ofield__inverse__zero 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_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.15 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.85/108.15 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.15 ) 97.85/108.15 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (not (class_Rings_Olinordered__idom T_a)) (= (c_Groups_Oone__class_Oone T_a) (hAPP (c_Groups_Oabs__class_Oabs T_a) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 97.85/108.15 ( tc_Nat_Onat ) 97.85/108.15 ( tc_Int_Oint ) 97.85/108.15 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.15 ) 97.85/108.15 (instantiation (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_m_2) V_na_2)) (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (hAPP (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) (hAPP (hAPP (c_COMBB tc_Nat_Onat (tc_fun tc_Nat_Onat tc_HOL_Obool) tc_Nat_Onat) (hAPP (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) c_fequal)) c_Nat_OSuc)))))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) V_m_2) V_na_2))) )) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.15 ) 97.85/108.15 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone T_a))) (forall ((T_a $$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_Groups_Ozero__class_Ozero tc_Int_Oint))))))) )) 97.85/108.15 ( tc_Nat_Onat ) 97.85/108.15 ( tc_Int_Oint ) 97.85/108.15 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.15 ) 97.85/108.15 (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_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) V_z))) ) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.15 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.85/108.15 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.15 ) 97.85/108.15 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (c_Groups_Ozero__class_Ozero tc_Nat_Onat)))) (forall ((V_n $$unsorted)) (or (not (hBOOL (hAPP _let_0 V_n))) (hBOOL (hAPP _let_0 (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Nat_Onat) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) V_n) (c_Groups_Oone__class_Oone tc_Nat_Onat))) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))))) )) 97.85/108.15 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.15 ) 97.85/108.15 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) (c_Int_OBit1 V_k_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_0) V_k_2))) )) 97.85/108.15 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.15 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.15 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.15 ) 97.85/108.15 (instantiation (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (forall ((V_na_2 $$unsorted) (V_m_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) V_m_2) V_na_2)) (c_Transitive__Closure_Ortrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_m_2) V_na_2))) )) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.15 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.85/108.15 ) 97.85/108.15 (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_Groups_Ozero__class_Ozero tc_Int_Oint))))) ) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.85/108.15 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.15 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.15 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.15 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.15 ) 97.85/108.15 (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_Ominus__class_Ominus 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) (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))))))) )) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.85/108.15 ) 97.85/108.15 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 (c_Int_OBit1 V_k_2))) (hBOOL (hAPP _let_0 V_k_2))) )) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.15 ) 97.85/108.15 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus tc_Int_Oint))) (let ((_let_1 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_2 (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) V_w))) (forall ((V_w $$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_1) _let_2) (hAPP (c_Product__Type_Ofst tc_Int_Oint tc_Int_Oint) (hAPP (c_Product__Type_Oapsnd tc_Int_Oint tc_Int_Oint tc_Int_Oint _let_0) (c_Divides_OnegDivAlg (hAPP _let_0 _let_1) (hAPP _let_0 _let_2)))))) )))) 97.85/108.15 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.15 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.15 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.15 ) 97.85/108.15 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (not (c_Int_Oiszero T_a (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 97.85/108.15 ( tc_Nat_Onat ) 97.85/108.15 ( tc_Int_Oint ) 97.85/108.15 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.15 ) 97.85/108.15 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_x_2) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_x_2)) (c_Groups_Ozero__class_Ozero T_b))))) ) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.85/108.15 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.15 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.85/108.15 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.15 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.15 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.15 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.15 ) 97.85/108.15 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Orderings_Oord__class_Oless__eq tc_Int_Oint))) (let ((_let_2 (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint))) (let ((_let_3 (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Divides_OnegDivAlg__rel))) (let ((_let_4 (hAPP V_Pa_2 B_a))) (forall ((V_Pa_2 $$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_1 _let_0) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) B_a) B_b)))) (not (hBOOL (hAPP (hAPP _let_1 B_b) _let_0))) (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 _let_0)))) B_b))))) (hBOOL (hAPP _let_4 B_b))) )) (hBOOL (hAPP (hAPP V_Pa_2 V_a0_2) V_a1_2))) )))))) 97.85/108.15 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.15 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.15 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.15 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.15 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.15 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.15 ( (c_Groups_Ominus__class_Ominus tc_Nat_Onat), (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.85/108.15 ( (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) ) 97.85/108.15 ( (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)) ) 97.85/108.15 ( (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)) ) 97.85/108.15 ( (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)) ) 97.85/108.15 ( (c_Set_Oinsert t_a), v_G, (hAPP v_mgt__call v_pn) ) 97.85/108.15 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.85/108.15 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.85/108.15 ( (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)) ) 97.85/108.15 ( (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)) ) 97.85/108.15 ( (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) ) 97.85/108.15 ( (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) ) 97.85/108.15 ( (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)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)) ) 97.85/108.16 ( (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) ) 97.85/108.16 ( (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 ) 97.85/108.16 ( (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G) ) 97.85/108.16 ( (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) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (c_member t_a), v_G, (hAPP v_mgt__call v_pn) ) 97.85/108.16 ( (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)), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.85/108.16 ( (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)), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 97.85/108.16 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_Int_Onat ) 97.85/108.16 ) 97.85/108.16 (instantiation (forall ((V_v_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_v_2) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (= (c_Groups_Ozero__class_Ozero tc_Nat_Onat) (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) V_v_2))) ) 97.85/108.16 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.16 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.16 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.16 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.16 ) 97.85/108.16 (instantiation (forall ((V_y_2 $$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_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) V_y_2)))) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.16 ( (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.16 ) 97.85/108.16 (instantiation (forall ((V_a $$unsorted)) (= (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_a) (hAPP (hAPP (c_Divides_Odiv__class_Odiv tc_Int_Oint) V_a) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.16 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.16 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.16 ) 97.85/108.16 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_Osucc V_k) (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Int_Oint) V_k) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.16 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.16 ) 97.85/108.16 (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_Int_Onumber T_b)) (not (class_Groups_Omonoid__mult 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_Groups_Ozero__class_Ozero tc_Int_Oint))))))) )) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.85/108.16 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.16 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.16 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.16 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.85/108.16 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.16 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.16 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.16 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.16 ) 97.85/108.16 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (forall ((V_k_2 $$unsorted)) (= (= _let_0 V_k_2) (= _let_0 (c_Int_OBit0 V_k_2))) )) 97.85/108.16 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.16 ) 97.85/108.16 (instantiation (forall ((V_w_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_w_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_w_2)) (c_Nat_Osemiring__1__class_ONats T_b)))) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.85/108.16 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.16 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.16 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.85/108.16 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.16 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.16 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.16 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.16 ) 97.85/108.16 (instantiation (let ((_let_0 (c_Power_Opower__class_Opower T_a))) (let ((_let_1 (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Rings_Oring__1 T_a)) (= (hAPP (hAPP _let_0 (hAPP (c_Groups_Ouminus__class_Ouminus T_a) V_a)) _let_1) (hAPP (hAPP _let_0 V_a) _let_1))) ))) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 97.85/108.16 ( (c_Groups_Oone__class_Oone tc_Int_Oint), tc_Int_Oint ) 97.85/108.16 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.16 ) 97.85/108.16 (instantiation (forall ((V_x_2 $$unsorted) (V_Pa_2 $$unsorted)) (or (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Nat_Onat) B_y) (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool))))) (hBOOL (hAPP V_Pa_2 (hAPP (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) B_y)))) )) (hBOOL (hAPP V_Pa_2 V_x_2))) ) 97.85/108.16 ( 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)) ) 97.85/108.16 ( (c_Orderings_Oord__class_Oless tc_Nat_Onat), (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 97.85/108.16 ( c_fequal, (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.16 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 97.85/108.16 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Int_Onat ) 97.85/108.16 ( (c_Groups_Oone__class_Oone tc_Int_Oint), c_Nat__Numeral_Oneg ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), c_Nat_OSuc ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osize__class_Osize tc_Nat_Onat) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OatMost tc_Nat_Onat) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Set_Oinsert tc_Nat_Onat) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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))) ) 97.85/108.16 ( c_Int_Onat, (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)) ) 97.85/108.16 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.85/108.16 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oplus__class_Oplus tc_Nat_Onat) ) 97.85/108.16 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral) ) 97.85/108.16 ( v_U, (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) ) 97.85/108.16 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (c_Finite__Set_Ocard t_a) ) 97.85/108.16 ( (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G)) ) 97.85/108.16 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (c_Groups_Ominus__class_Ominus tc_Nat_Onat) ) 97.85/108.16 ( v_n, c_Nat_OSuc ) 97.85/108.16 ( (hAPP c_Nat_OSuc v_n), (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) ) 97.85/108.16 ( (hAPP c_Nat_OSuc v_n), (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U))) ) 97.85/108.16 ( v_G, (c_Finite__Set_Ocard t_a) ) 97.85/108.16 ( v_G, (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) ) 97.85/108.16 ( v_G, (hAPP (c_member t_a) (hAPP v_mgt__call v_pn)) ) 97.85/108.16 ( v_G, (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Nat_Onat) ) 97.85/108.16 ( (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) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( 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)) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (hAPP (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) ) 97.85/108.16 ( (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral), (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral) ) 97.85/108.16 ( v_pn, v_mgt__call ) 97.85/108.16 ( v_pn, (c_member tc_Com_Opname) ) 97.85/108.16 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)), c_Nat_OSuc ) 97.85/108.16 ( (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) ) 97.85/108.16 ( (c_Groups_Oabs__class_Oabs tc_Int_Oint), (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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) ) 97.85/108.16 ( (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) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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))) ) 97.85/108.16 ( (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))) ) 97.85/108.16 ( (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))), c_Nat_OSuc ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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))) ) 97.85/108.16 ( (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))) ) 97.85/108.16 ( (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))) ) 97.85/108.16 ( (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))) ) 97.85/108.16 ( (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))) ) 97.85/108.16 ( (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))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0))))))) ) 97.85/108.16 ( (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))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0))))))) ) 97.85/108.16 ( (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.85/108.16 ( 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)))) ) 97.85/108.16 ( (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))) ) 97.85/108.16 ( (hAPP v_mgt__call v_pn), (c_Set_Oinsert t_a) ) 97.85/108.16 ( (hAPP v_mgt__call v_pn), (c_member t_a) ) 97.85/108.16 ( c_fTrue, (c_COMBK tc_HOL_Obool tc_Nat_Onat) ) 97.85/108.16 ( c_fTrue, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)), (c_Finite__Set_Ofinite tc_Int_Oint) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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 ) 97.85/108.16 ( c_fFalse, (c_Nat_Osize__class_Osize tc_HOL_Obool) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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)) ) 97.85/108.16 ( (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 ) 97.85/108.16 ( (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)), (c_Finite__Set_Ocard tc_Product__Type_Ounit) ) 97.85/108.16 ( (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G), (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) ) 97.85/108.16 ( (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)), (c_Finite__Set_Ocard tc_HOL_Obool) ) 97.85/108.16 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)), (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))) ) 97.85/108.16 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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))) ) 97.85/108.16 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (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))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))))) ) 97.85/108.17 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.85/108.17 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) ) 97.85/108.17 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Orderings_Oord__class_Oless tc_Int_Oint) ) 97.85/108.17 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 97.85/108.17 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.17 ( (c_Int_Opred (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)) ) 97.85/108.17 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.85/108.17 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.17 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), c_Int_Onat ) 97.85/108.17 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 97.85/108.17 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.85/108.17 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral) ) 97.85/108.17 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 97.85/108.17 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.85/108.17 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), c_Int_Onat ) 97.85/108.17 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) ) 97.85/108.17 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Onumber__class_Onumber__of tc_Int_Oint) ) 97.85/108.17 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), c_Int_Onat ) 97.85/108.17 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.85/108.17 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))), (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))) ) 97.85/108.17 ( (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (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))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))))) ) 97.85/108.17 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint) ) 97.85/108.17 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_Nat__Numeral_Oneg ) 97.85/108.17 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) ) 97.85/108.17 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (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)) ) 97.85/108.17 ) 97.85/108.17 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_Opred V_k) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) V_k)) ) 97.85/108.17 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.17 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.17 ) 97.85/108.17 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= (hAPP (c_Groups_Ouminus__class_Ouminus T_a) (c_Groups_Oone__class_Oone T_a)) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) ) 97.85/108.17 ( tc_Nat_Onat ) 97.85/108.17 ( tc_Int_Oint ) 97.85/108.17 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.17 ) 97.85/108.17 (instantiation (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (forall ((V_Pa_2 $$unsorted) (V_y_2 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) V_y_2) (hAPP (hAPP (c_Equiv__Relations_Oquotient _let_0) (c_Orderings_Otop__class_Otop _let_1)) c_Int_Ointrel)))) (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))) ))) 97.85/108.17 ( c_Nat_OSuc, (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.17 ( c_Nat_OSuc, v_n ) 97.85/108.17 ( c_Nat_OSuc, (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.85/108.17 ( c_Nat_OSuc, (hAPP c_Nat_OSuc (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat))) ) 97.85/108.17 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.17 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.17 ( (c_Groups_Ouminus__class_Ouminus tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.17 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.17 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.17 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.17 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.17 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.17 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.17 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.17 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.17 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.17 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Int_Oint), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.17 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.17 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.17 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.17 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.17 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.17 ( (c_Int_Onumber__class_Onumber__of tc_Nat_Onat), (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.17 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.17 ( 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)))))) ) 97.85/108.17 ( 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))))) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (c_SetInterval_Oord__class_OlessThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.17 ( c_Int_Onat, (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.17 ( c_Int_Onat, (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.17 ( c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.17 ( c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.17 ( c_Int_Onat, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.17 ( (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat), (hAPP c_Nat_OSuc v_n) ) 97.85/108.17 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.17 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.17 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.17 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.17 ( (c_Int_Onumber__class_Onumber__of tc_Int_Oint), (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.17 ( (c_Groups_Ominus__class_Ominus tc_Nat_Onat), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.85/108.17 ( (c_Finite__Set_Ocard t_a), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U) ) 97.85/108.17 ( (c_Finite__Set_Ocard t_a), v_G ) 97.85/108.17 ( v_mgt__call, v_pn ) 97.85/108.17 ( (c_Set_Oimage tc_Com_Opname t_a v_mgt__call), v_U ) 97.85/108.17 ( (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U))), (hAPP c_Nat_OSuc v_n) ) 97.85/108.17 ( (c_Nat_Osize__class_Osize tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 97.85/108.17 ( c_Nat__Numeral_Oneg, (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.17 ( c_Nat__Numeral_Oneg, (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (c_COMBC tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool), c_fequal ) 97.85/108.17 ( (c_member tc_Com_Opname), v_pn ) 97.85/108.17 ( (c_Nat_Osize__class_Osize tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (c_Product__Type_Oprod_Oprod__case tc_Nat_Onat tc_Nat_Onat tc_HOL_Obool), (c_Orderings_Oord__class_Oless tc_Nat_Onat) ) 97.85/108.17 ( (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) ) 97.85/108.17 ( (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) ) 97.85/108.17 ( (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 ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (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) ) 97.85/108.17 ( (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) ) 97.85/108.17 ( (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) ) 97.85/108.17 ( (c_SetInterval_Oord__class_OatLeast tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.17 ( (c_Finite__Set_Ofinite tc_Nat_Onat), (c_Orderings_Otop__class_Otop (tc_fun tc_Nat_Onat tc_HOL_Obool)) ) 97.85/108.17 ( (c_SetInterval_Oord__class_OatMost tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.17 ( (c_Set_Oinsert t_a), (hAPP v_mgt__call v_pn) ) 97.85/108.17 ( (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_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.85/108.17 ( (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_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (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))) ) 97.85/108.17 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.17 ( (c_Product__Type_OPair tc_Nat_Onat tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.17 ( (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))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)) ) 97.85/108.17 ( (c_Set_Oinsert tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (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 ) 97.85/108.17 ( (hAPP (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) ) 97.85/108.17 ( (c_Finite__Set_Ofinite tc_Int_Oint), (c_Orderings_Otop__class_Otop (tc_fun tc_Int_Oint tc_HOL_Obool)) ) 97.85/108.17 ( (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)), v_G ) 97.85/108.17 ( (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G) ) 97.85/108.17 ( (c_Groups_Ominus__class_Ominus tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Code__Numeral_Ocode__numeral) ) 97.85/108.17 ( (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) ) 97.85/108.17 ( (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))))) ) 97.85/108.17 ( (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)))) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (c_SetInterval_Oord__class_OgreaterThan tc_Nat_Onat), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.17 ( (c_member t_a), (hAPP v_mgt__call v_pn) ) 97.85/108.17 ( (hAPP (c_member t_a) (hAPP v_mgt__call v_pn)), v_G ) 97.85/108.17 ( (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) ) 97.85/108.17 ( (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) ) 97.85/108.17 ( (c_COMBK tc_HOL_Obool tc_Nat_Onat), c_fTrue ) 97.85/108.17 ( (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.17 ( (c_Int_Onumber__class_Onumber__of tc_Code__Numeral_Ocode__numeral), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.17 ( (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.17 ( (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) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (c_Nat_Osize__class_Osize tc_HOL_Obool), c_fTrue ) 97.85/108.17 ( (c_Nat_Osize__class_Osize tc_HOL_Obool), c_fFalse ) 97.85/108.17 ( (c_Finite__Set_Ocard tc_Product__Type_Ounit), (c_Orderings_Otop__class_Otop (tc_fun tc_Product__Type_Ounit tc_HOL_Obool)) ) 97.85/108.17 ( (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)), v_G ) 97.85/108.17 ( (hAPP (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)) (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G)), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U) ) 97.85/108.17 ( (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)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.85/108.17 ( (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)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.85/108.17 ( (c_Finite__Set_Ocard tc_HOL_Obool), (c_Orderings_Otop__class_Otop (tc_fun tc_HOL_Obool tc_HOL_Obool)) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (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 ) 97.85/108.17 ( (c_Fun_Ocomp tc_Int_Oint tc_Nat_Onat tc_Int_Oint c_Int_Onat), (c_Groups_Oabs__class_Oabs tc_Int_Oint) ) 97.85/108.17 ( (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)) ) 97.85/108.17 ( (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) ) 97.85/108.17 ( (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))), (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat)) ) 97.85/108.17 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0))))))), (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))))) ) 97.85/108.17 ( (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))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))))), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))) ) 97.85/108.18 ( (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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)))))) (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_1 _let_1) tc_HOL_Obool)) (c_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_2 _let_2)) (c_Relation_OId _let_0))))))), (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))))) ) 97.85/108.18 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), c_Int_Onat ) 97.85/108.18 ( (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.18 ( (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))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (c_Product__Type_OPair _let_0 _let_0) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1))))), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))) ) 97.85/108.18 ( (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.18 ) 97.85/108.18 (instantiation (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (= V_a (hAPP (hAPP (c_Groups_Oplus__class_Oplus T_a) V_a) (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) ) 97.85/108.18 ( (c_Groups_Oone__class_Oone tc_Nat_Onat), tc_Nat_Onat ) 97.85/108.18 ) 97.85/108.18 (instantiation (let ((_let_0 (hAPP (c_Int_Onumber__class_Onumber__of tc_Nat_Onat) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) (forall ((V_m $$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)) )) 97.85/108.18 ( (c_Groups_Ozero__class_Ozero tc_Nat_Onat) ) 97.85/108.18 ( (hAPP c_Nat_OSuc (c_Groups_Ozero__class_Ozero tc_Nat_Onat)) ) 97.85/108.18 ) 97.85/108.18 (instantiation (forall ((V_l $$unsorted)) (not (= (c_Int_OBit0 V_l) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.18 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.18 ) 97.85/108.18 (instantiation (let ((_let_0 (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_0) (c_Int_OBit0 V_k_2))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) V_k_2))) )) 97.85/108.18 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.18 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.18 ) 97.85/108.18 (instantiation (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (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_2))) (let ((_let_4 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (forall ((V_X_2 $$unsorted)) (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (or (not (hBOOL (hAPP (c_Finite__Set_Ofinite _let_0) V_X_2))) (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP _let_3 V_X_2)) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_4 _let_4)) (c_Relation_OId _let_0)))) (hAPP (hAPP (c_Set_Oinsert _let_0) (hAPP _let_3 _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))) )))))) 97.85/108.18 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)) ) 97.85/108.18 ) 97.85/108.18 (instantiation (forall ((V_k $$unsorted)) (= (hAPP (c_Groups_Ouminus__class_Ouminus tc_Int_Oint) V_k) (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint))) V_k)) ) 97.85/108.18 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.18 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.18 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.18 ) 97.85/108.18 (instantiation (let ((_let_0 (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral))) (forall ((V_m_2 $$unsorted) (V_na_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Nat_Onat) V_na_2) V_m_2)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Code__Numeral_Ocode__numeral) (hAPP _let_0 V_na_2)) (hAPP _let_0 V_m_2)))) )) 97.85/108.18 ( (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)), (hAPP c_Nat_OSuc v_n) ) 97.85/108.18 ) 97.85/108.18 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (not (c_Int_Oiszero T_a (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 97.85/108.18 ( tc_Nat_Onat ) 97.85/108.18 ( tc_Int_Oint ) 97.85/108.18 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.18 ) 97.85/108.18 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero T_a))) (forall ((T_a $$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_Groups_Ozero__class_Ozero tc_Int_Oint))))))) )) 97.85/108.18 ( tc_Nat_Onat ) 97.85/108.18 ( tc_Int_Oint ) 97.85/108.18 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.18 ) 97.85/108.18 (instantiation (forall ((T_a $$unsorted)) (or (not (class_Int_Onumber__ring T_a)) (c_Int_Oiszero T_a (hAPP (c_Int_Onumber__class_Onumber__of T_a) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 97.85/108.18 ( tc_Nat_Onat ) 97.85/108.18 ( tc_Int_Oint ) 97.85/108.18 ( tc_Code__Numeral_Ocode__numeral ) 97.85/108.18 ) 97.85/108.18 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Groups_Oone__class_Oone tc_Int_Oint))) (let ((_let_2 (c_Int_Onumber__class_Onumber__of tc_Int_Oint))) (let ((_let_3 (hAPP _let_2 V_w))) (let ((_let_4 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) _let_1) _let_3))) (let ((_let_5 (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) _let_0) _let_4)))) (let ((_let_6 (c_Divides_OnegDivAlg _let_1 _let_3))) (forall ((V_w $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_0) _let_3))) (and (or (not _let_5) (= _let_6 (hAPP (hAPP (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint) (hAPP _let_2 (c_Int_Opred _let_0))) _let_4))) (or _let_5 (= _let_6 (hAPP (c_Divides_Oadjust _let_3) (c_Divides_OnegDivAlg _let_1 (hAPP (hAPP (c_Groups_Otimes__class_Otimes tc_Int_Oint) (hAPP _let_2 (c_Int_OBit0 (c_Int_OBit1 _let_0)))) _let_3))))))) )))))))) 97.85/108.18 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.18 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.18 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.18 ) 97.85/108.18 (instantiation (let ((_let_0 (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP _let_0 V_k_2)) (hBOOL (hAPP _let_0 (c_Int_OBit0 V_k_2)))) )) 97.85/108.18 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.18 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.18 ) 97.85/108.18 (instantiation (let ((_let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (let ((_let_1 (c_Product__Type_OPair tc_Int_Oint tc_Int_Oint))) (let ((_let_2 (c_Wellfounded_Oaccp (tc_prod tc_Int_Oint tc_Int_Oint) c_Divides_OposDivAlg__rel))) (let ((_let_3 (hAPP V_Pa_2 B_a))) (forall ((V_Pa_2 $$unsorted) (V_a1_2 $$unsorted) (V_a0_2 $$unsorted)) (or (not (hBOOL (hAPP _let_2 (hAPP (hAPP _let_1 V_a0_2) V_a1_2)))) (not (forall ((B_a $$unsorted) (B_b $$unsorted)) (or (not (hBOOL (hAPP _let_2 (hAPP (hAPP _let_1 B_a) B_b)))) (and (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) B_b) _let_0))) (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) B_a) B_b))) (not (hBOOL (hAPP _let_3 (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 _let_0)))) B_b))))) (hBOOL (hAPP _let_3 B_b))) )) (hBOOL (hAPP (hAPP V_Pa_2 V_a0_2) V_a1_2))) ))))) 97.85/108.18 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.18 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.18 ( (c_Orderings_Oord__class_Oless tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.18 ( (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_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.18 ( (c_Orderings_Oord__class_Oless__eq tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.18 ( (c_Groups_Oplus__class_Oplus tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat), (c_Groups_Oone__class_Oone tc_Nat_Onat) ) 97.85/108.18 ( (c_Groups_Ominus__class_Ominus tc_Nat_Onat), (hAPP c_Nat_OSuc v_n), (hAPP (c_Finite__Set_Ocard t_a) (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U)) ) 97.85/108.18 ( (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) ) 97.85/108.18 ( (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)) ) 97.85/108.18 ( (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)) ) 97.85/108.18 ( (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)) ) 97.85/108.18 ( (c_Set_Oinsert t_a), v_G, (hAPP v_mgt__call v_pn) ) 97.85/108.18 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omin__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.85/108.18 ( (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))))), (let ((_let_0 (tc_prod tc_Nat_Onat tc_Nat_Onat))) (let ((_let_1 (c_Transitive__Closure_Otrancl tc_Nat_Onat (hAPP (c_Set_OCollect _let_0) (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_Wellfounded_Omax__ext _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod _let_0 _let_0) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_1 _let_1)) (c_Relation_OId _let_0))))) ) 97.85/108.18 ( (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)) ) 97.85/108.18 ( (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)) ) 97.85/108.18 ( (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) ) 97.85/108.18 ( (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) ) 97.85/108.18 ( (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)), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0)) ) 97.85/108.18 ( (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) ) 97.85/108.18 ( (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 ) 97.85/108.18 ( (c_Orderings_Oord__class_Oless__eq (tc_fun t_a tc_HOL_Obool)), (hAPP (c_Set_Oimage tc_Com_Opname t_a v_mgt__call) v_U), (hAPP (hAPP (c_Set_Oinsert t_a) (hAPP v_mgt__call v_pn)) v_G) ) 97.85/108.18 ( (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) ) 97.85/108.18 ( (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)) ) 97.85/108.18 ( (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)) ) 97.85/108.18 ( (c_member t_a), v_G, (hAPP v_mgt__call v_pn) ) 97.85/108.18 ( (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)), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omin__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.85/108.18 ( (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)), (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 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Nat_Onat tc_Nat_Onat) tc_HOL_Obool)))) (let ((_let_3 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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)))))) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_1) (c_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup (tc_fun (tc_prod (tc_prod tc_Nat_Onat tc_Nat_Onat) (tc_prod tc_Nat_Onat tc_Nat_Onat)) tc_HOL_Obool)) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_3 _let_3)) (c_Relation_OId (tc_prod tc_Nat_Onat tc_Nat_Onat))))) (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_2) _let_2)) (c_Orderings_Obot__class_Obot _let_1))))))), (let ((_let_0 (c_Transitive__Closure_Otrancl tc_Nat_Onat (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) (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_Wellfounded_Omax__ext (tc_prod tc_Nat_Onat tc_Nat_Onat) (c_Wellfounded_Olex__prod tc_Nat_Onat tc_Nat_Onat _let_0 _let_0))) ) 97.85/108.18 ( (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)) ) 97.85/108.18 ( (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)) ) 97.85/108.18 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), (c_Groups_Ozero__class_Ozero tc_Int_Oint), c_Int_Onat ) 97.85/108.18 ( (c_Fun_Ocomp tc_Nat_Onat tc_Code__Numeral_Ocode__numeral tc_Int_Oint (c_Nat_Osemiring__1__class_Oof__nat tc_Code__Numeral_Ocode__numeral)), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), c_Int_Onat ) 97.85/108.18 ) 97.85/108.18 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_1 (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP _let_0 V_k_2) _let_1)) (hBOOL (hAPP (hAPP _let_0 (c_Int_OBit1 V_k_2)) _let_1))) ))) 97.85/108.18 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.18 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.18 ) 97.85/108.18 (instantiation (let ((_let_0 (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (forall ((V_k_2 $$unsorted)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_k_2) _let_0)) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) (c_Int_OBit0 V_k_2)) _let_0))) )) 97.85/108.18 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.18 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.18 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.18 ) 97.85/108.18 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (forall ((V_v $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_v) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (= (hAPP (hAPP (c_Groups_Ominus__class_Ominus tc_Nat_Onat) (hAPP _let_0 V_v)) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 (c_Int_Opred V_v)))) )) 97.85/108.18 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.18 ) 97.85/108.18 (instantiation (forall ((V_v $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_v) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (= (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)))) ) 97.85/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.19 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.19 ) 97.85/108.19 (instantiation (let ((_let_0 (c_Orderings_Oord__class_Oless tc_Int_Oint))) (let ((_let_1 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (let ((_let_2 (hBOOL (hAPP (hAPP _let_0 V_v_2) V_v_H_2)))) (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (= (and (or (not _let_2) (hBOOL (hAPP (hAPP _let_0 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) V_v_H_2))) _let_2) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Nat_Onat) (hAPP _let_1 V_v_2)) (hAPP _let_1 V_v_H_2)))) )))) 97.85/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ) 97.85/108.19 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Int_Onumber__ring T_b)) (not (class_Rings_Olinordered__idom T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) V_x_2) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (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))))) ) 97.85/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.85/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.85/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.85/108.19 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.19 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.19 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.19 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.19 ) 97.85/108.19 (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)) (= (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))) (or (hBOOL (hAPP _let_1 V_v_H_2)) (hBOOL (hAPP _let_1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))))) ))) 97.85/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.19 ( (c_Groups_Oone__class_Oone tc_Int_Oint), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.19 ( (hAPP (c_Int_Onumber__class_Onumber__of tc_Int_Oint) (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))), (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.19 ) 97.85/108.19 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (or (not (class_Rings_Olinordered__idom T_b)) (not (class_Int_Onumber__ring T_b)) (= (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless T_b) (hAPP (c_Int_Onumber__class_Onumber__of T_b) V_x_2)) (c_Groups_Oone__class_Oone T_b))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_x_2) (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)))))) ) 97.85/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 97.85/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 97.85/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 97.85/108.19 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.19 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.19 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 97.85/108.19 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 97.85/108.19 ) 97.85/108.19 (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_Groups_Ozero__class_Ozero tc_Int_Oint)))) (= _let_1 (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP _let_0 V_v)) _let_1))) ))) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ) 97.85/108.19 (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_Groups_Ozero__class_Ozero tc_Int_Oint))))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_v) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (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)))))) )))) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ) 97.85/108.19 (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_Groups_Ozero__class_Ozero tc_Int_Oint)))))) )) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 97.85/108.19 ) 97.85/108.19 (instantiation (let ((_let_0 (c_Int_Onumber__class_Onumber__of tc_Nat_Onat))) (forall ((V_v $$unsorted)) (or (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_v) (c_Groups_Ozero__class_Ozero tc_Int_Oint))) (= (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Nat_Onat) (hAPP _let_0 V_v)) (c_Groups_Oone__class_Oone tc_Nat_Onat)) (hAPP _let_0 (c_Int_Osucc V_v)))) )) 97.85/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ) 97.85/108.19 (instantiation (let ((_let_0 (c_Groups_Oone__class_Oone tc_Nat_Onat))) (forall ((V_v $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) V_v) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (= _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))) )) 97.85/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.19 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.19 ) 97.85/108.19 (instantiation (let ((_let_0 (c_Groups_Ouminus__class_Ouminus 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))) (forall ((V_w $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless tc_Int_Oint) _let_2) (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) (= (c_Divides_Odiv__class_Omod tc_Int_Oint _let_1 _let_2) (hAPP (c_Product__Type_Osnd tc_Int_Oint tc_Int_Oint) (hAPP (c_Product__Type_Oapsnd tc_Int_Oint tc_Int_Oint tc_Int_Oint _let_0) (c_Divides_OnegDivAlg (hAPP _let_0 _let_1) (hAPP _let_0 _let_2)))))) )))) 97.85/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.19 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.19 ) 97.85/108.19 (instantiation (forall ((V_v_2 $$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_Groups_Ozero__class_Ozero tc_Int_Oint)) V_v_2))) ) 97.85/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 97.85/108.19 ( (c_Groups_Oone__class_Oone tc_Int_Oint) ) 97.85/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 97.85/108.19 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.19 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))) ) 97.85/108.19 ) 97.85/108.19 (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_Groups_Ozero__class_Ozero tc_Int_Oint))) V_y_2)))) ) 98.02/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Nat_Onat ) 98.02/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Int_Oint ) 98.02/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint), tc_Code__Numeral_Ocode__numeral ) 98.02/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 98.02/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Nat_Onat ) 98.02/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Int_Oint ) 98.02/108.19 ( (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint)), tc_Code__Numeral_Ocode__numeral ) 98.02/108.19 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 98.02/108.19 ( (c_Int_OBit0 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 98.02/108.19 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Nat_Onat ) 98.02/108.19 ( (c_Int_OBit1 (c_Int_OBit1 (c_Groups_Ozero__class_Ozero tc_Int_Oint))), tc_Int_Oint ) 98.02/108.19 ) 98.02/108.19 (instantiation (forall ((V_k $$unsorted)) (= (c_Int_Opred V_k) (hAPP (hAPP (c_Groups_Oplus__class_Oplus tc_Int_Oint) V_k) (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)))) ) 98.02/108.19 ( (c_Groups_Ozero__class_Ozero tc_Int_Oint) ) 98.02/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 98.02/108.19 ) 98.02/108.19 (instantiation (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member tc_Int_Oint) B_x) (c_Orderings_Obot__class_Obot (tc_fun tc_Int_Oint tc_HOL_Obool))))) (hBOOL (hAPP (hAPP (c_Orderings_Oord__class_Oless__eq tc_Int_Oint) (c_Groups_Ozero__class_Ozero tc_Int_Oint)) B_x))) ) 98.02/108.19 ( (c_Int_Opred (c_Groups_Ozero__class_Ozero tc_Int_Oint)) ) 98.02/108.19 ) 98.02/108.19 % SZS output end Proof for theBenchmark 98.03/108.22 EOF