0.10/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.12 % Command : do_CVC4 %s %d 0.11/0.32 % Computer : n028.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Thu Jul 2 07:59:51 EDT 2020 0.11/0.32 % CPUTime : 0.17/0.49 %----Proving TF0_NAR, FOF, or CNF 0.17/0.50 ------- cvc4-fof casc j10 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 960... 0.17/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 1.15/1.37 % SZS status Theorem for theBenchmark 1.15/1.37 % SZS output start Proof for theBenchmark 1.15/1.37 (skolem (forall ((B_x $$unsorted)) (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) B_x) c_Arrow__Order__Mirabelle_OProf))) (hBOOL (hAPP (hAPP (c_member _let_1) (hAPP v_F B_x)) c_Arrow__Order__Mirabelle_OLin))))) ) 1.15/1.37 ( skv_1 ) 1.15/1.37 ) 1.15/1.37 (skolem (forall ((B_x $$unsorted)) (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (or (not (hBOOL (hAPP (hAPP (c_member _let_2) B_x) c_Arrow__Order__Mirabelle_OProf))) (hBOOL (hAPP (hAPP (c_member _let_1) (hAPP v_F B_x)) (hAPP (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin) B_x))))))) ) 1.15/1.37 ( skv_2 ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_prod T_a T_a))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun T_a tc_HOL_Obool))) (let ((_let_3 (tc_fun _let_1 tc_HOL_Obool))) (let ((_let_4 (tc_fun T_a _let_3))) (= (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) (c_Wellfounded_Oacc T_a V_r_2))) (hBOOL (hAPP (c_Wellfounded_Oaccp T_a (hAPP (hAPP (c_COMBC T_a _let_1 _let_2) (hAPP (c_COMBB _let_4 (tc_fun _let_1 _let_2) T_a (c_COMBC T_a _let_1 tc_HOL_Obool)) (hAPP (c_COMBB (tc_fun T_a _let_0) _let_4 T_a (c_COMBB _let_0 _let_3 T_a (c_member _let_0))) (c_Product__Type_OPair T_a T_a)))) V_r_2)) V_x_2)))))))) ) 1.15/1.37 ( v_a_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_a____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_a____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_b____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_b____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_b_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_prod T_a T_a) tc_HOL_Obool) (c_Relation_OId__on T_a V_A_2) (c_Product__Type_OSigma T_a T_a V_A_2 (c_COMBK (tc_fun T_a tc_HOL_Obool) T_a V_A_2))) ) 1.15/1.37 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) c_fFalse), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) c_fFalse), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_prod T_a T_a))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (= (c_Wellfounded_Oacyclic T_a (c_Set_Oinsert _let_0 (hAPP (hAPP _let_1 V_y_2) V_x_2) V_r_2)) (and (c_Wellfounded_Oacyclic T_a V_r_2) (not (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP _let_1 V_x_2) V_y_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))))))) ) 1.15/1.37 ( (hAPP v_F v_Q____), v_a_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_Q____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_Q____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_P____), v_a____, v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_P____), v_b____, v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_prod T_a T_a))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun T_a tc_HOL_Obool))) (let ((_let_3 (tc_fun _let_1 tc_HOL_Obool))) (let ((_let_4 (tc_fun T_a _let_3))) (= (c_Wellfounded_Owf T_a V_r_2) (c_Wellfounded_OwfP T_a (hAPP (hAPP (c_COMBC T_a _let_1 _let_2) (hAPP (c_COMBB _let_4 (tc_fun _let_1 _let_2) T_a (c_COMBC T_a _let_1 tc_HOL_Obool)) (hAPP (c_COMBB (tc_fun T_a _let_0) _let_4 T_a (c_COMBB _let_0 _let_3 T_a (c_member _let_0))) (c_Product__Type_OPair T_a T_a)))) V_r_2)))))))) ) 1.15/1.37 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (c_Relation_Osingle__valued T_a T_a (c_Relation_OId__on T_a V_A_2)) ) 1.15/1.37 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((T_a $$unsorted)) (c_Relation_Orefl__on T_a (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)) (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_a T_a) tc_HOL_Obool))) ) 1.15/1.37 ( tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_aa_2 $$unsorted) (T_a $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member T_a) V_aa_2) (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool))))) ) 1.15/1.37 ( v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.37 ( v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.37 ( (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.37 ( v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.37 ( v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.37 ( (hAPP v_F v_P____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.37 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_a_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi (hAPP v_F v_Q____)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.37 ( skv_1, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.37 ( (hAPP v_F skv_1), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.37 ( skv_2, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.37 ( (hAPP v_F skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (c_Relation_Oantisym T_a (c_Relation_OId__on T_a V_A_2)) ) 1.15/1.37 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_prod T_a T_b))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (tc_fun _let_1 tc_HOL_Obool))) (let ((_let_4 (tc_fun T_b _let_3))) (= (c_Predicate_ORangeP T_a T_b (hAPP (hAPP (c_COMBC T_a _let_1 _let_2) (hAPP (c_COMBB _let_4 (tc_fun _let_1 _let_2) T_a (c_COMBC T_b _let_1 tc_HOL_Obool)) (hAPP (c_COMBB (tc_fun T_b _let_0) _let_4 T_a (c_COMBB _let_0 _let_3 T_b (c_member _let_0))) (c_Product__Type_OPair T_a T_b)))) V_r_2) V_x_2) (hBOOL (hAPP (hAPP (c_member T_b) V_x_2) (c_Relation_ORange T_a T_b V_r_2))))))))) ) 1.15/1.37 ( v_a____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_b____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_b____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_b_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_prod T_a T_b))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun T_b tc_HOL_Obool))) (let ((_let_3 (tc_fun _let_1 tc_HOL_Obool))) (let ((_let_4 (tc_fun T_b _let_3))) (= (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) (c_Relation_ODomain T_a T_b V_r_2))) (c_Predicate_ODomainP T_a T_b (hAPP (hAPP (c_COMBC T_a _let_1 _let_2) (hAPP (c_COMBB _let_4 (tc_fun _let_1 _let_2) T_a (c_COMBC T_b _let_1 tc_HOL_Obool)) (hAPP (c_COMBB (tc_fun T_b _let_0) _let_4 T_a (c_COMBB _let_0 _let_3 T_b (c_member _let_0))) (c_Product__Type_OPair T_a T_b)))) V_r_2) V_x_2))))))) ) 1.15/1.37 ( v_a_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_a____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_a____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( v_b____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_prod T_a T_a))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (= (c_Wellfounded_Owf T_a (c_Set_Oinsert _let_0 (hAPP (hAPP _let_1 V_y_2) V_x_2) V_r_2)) (and (not (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP _let_1 V_x_2) V_y_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (c_Wellfounded_Owf T_a V_r_2))))) ) 1.15/1.37 ( (hAPP v_F v_Q____), v_a_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_Q____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_Q____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_P____), v_a____, v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_P____), v_b____, v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_Q $$unsorted) (V_P $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= V_P (hAPP (c_COMBK T_a T_b V_P) V_Q)) ) 1.15/1.37 ( v_Q____, c_Arrow__Order__Mirabelle_OLin, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 1.15/1.37 ( skv_2, c_Arrow__Order__Mirabelle_OLin, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((T_a $$unsorted)) (c_Relation_Oantisym T_a (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_a T_a) tc_HOL_Obool))) ) 1.15/1.37 ( tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (forall ((B_x $$unsorted)) (hBOOL (hAPP (hAPP (c_member T_a) B_x) (c_Wellfounded_Oacc T_a V_r_2))) ) (c_Wellfounded_Owf T_a V_r_2)) ) 1.15/1.37 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) (c_FuncSet_Ocompose T_a T_c T_b V_A_2 V_f_2 V_g_2)) (c_FuncSet_Oextensional T_a T_b V_A_2))) ) 1.15/1.37 ( v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Orestrict _let_1 _let_1 (c_COMBI _let_1) c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OProf, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.37 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_Orestrict _let_2 _let_2 (c_COMBI _let_2) c_Arrow__Order__Mirabelle_OProf)))), v_F, c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (forall ((B_x1 $$unsorted)) (hBOOL (hAPP (c_Wellfounded_Oaccp T_a V_r_2) B_x1)) ) (c_Wellfounded_OwfP T_a V_r_2)) ) 1.15/1.37 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (c_COMBK (tc_fun _let_0 tc_HOL_Obool) _let_0 (c_COMBK tc_HOL_Obool _let_0 c_fFalse))), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_1 (c_COMBK tc_HOL_Obool _let_1 c_fFalse)))), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_aa_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (c_Orderings_Oord__class_Oless__eq (tc_fun T_a tc_HOL_Obool) V_B_2 (c_Set_Oinsert T_a V_aa_2 V_B_2)) ) 1.15/1.37 ( v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.37 ( v_Q____, c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.37 ( (hAPP v_F v_Q____), c_Arrow__Order__Mirabelle_OLin, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.37 ( v_P_H____, c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.37 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP v_F v_Q____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP v_F v_Q____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP v_F v_P____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( v_P____, c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.37 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (hAPP v_F v_Q____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.37 ( (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.37 ( (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 1.15/1.37 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.37 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (c_Orderings_Oord__class_Oless__eq _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2) V_A_2)) ) 1.15/1.37 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.37 ) 1.15/1.37 (instantiation (forall ((V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Set_Oinsert T_a V_x_2 V_A_2))) (= _let_0 (c_Set_Oinsert T_a V_x_2 _let_0))) ) 1.15/1.38 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OProf, v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OProf, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OProf, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_R_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (hBOOL (hAPP (hAPP (c_FunDef_Oin__rel T_a T_b V_R_2) V_x_2) V_y_2)) (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_b)) (hAPP (hAPP (c_Product__Type_OPair T_a T_b) V_x_2) V_y_2)) V_R_2))) ) 1.15/1.38 ( v_a_H____, v_a____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_a_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_a_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_b____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_b____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_b_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_a____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_a____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_b____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_b____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((T_a $$unsorted)) (c_Wellfounded_Owf T_a (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_a T_a) tc_HOL_Obool))) ) 1.15/1.38 ( tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (let ((_let_1 (c_Orderings_Obot__class_Obot _let_0))) (= _let_1 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) _let_1)))) ) 1.15/1.38 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_a)) (c_COMBI T_a)) (c_FuncSet_OPi T_a T_a V_A_2 (c_COMBK (tc_fun T_a tc_HOL_Obool) T_a V_A_2)))) ) 1.15/1.38 ( (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) c_fFalse), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) c_fFalse), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_xa_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_prod T_a T_a))) (let ((_let_1 (c_member _let_0))) (let ((_let_2 (c_Product__Type_OPair T_a T_a))) (let ((_let_3 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_4 (tc_fun T_a tc_HOL_Obool))) (let ((_let_5 (tc_fun _let_3 tc_HOL_Obool))) (let ((_let_6 (tc_fun T_a _let_5))) (= (hBOOL (hAPP (hAPP _let_1 (hAPP (hAPP _let_2 V_x_2) V_xa_2)) (c_Transitive__Closure_Otrancl T_a V_r_2))) (hBOOL (hAPP (hAPP (c_Transitive__Closure_Otranclp T_a (hAPP (hAPP (c_COMBC T_a _let_3 _let_4) (hAPP (c_COMBB _let_6 (tc_fun _let_3 _let_4) T_a (c_COMBC T_a _let_3 tc_HOL_Obool)) (hAPP (c_COMBB (tc_fun T_a _let_0) _let_6 T_a (c_COMBB _let_0 _let_5 T_a _let_1)) _let_2))) V_r_2)) V_x_2) V_xa_2)))))))))) ) 1.15/1.38 ( v_a____, v_a_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_a____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_b____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_B_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (hBOOL (hAPP (hAPP (c_member T_a) V_aa_2) (c_Set_Oinsert T_a V_aa_2 V_B_2))) ) 1.15/1.38 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OProf, v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OProf, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OProf, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.38 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (c_Orderings_Oord__class_Oless__eq _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2) V_B_2)) ) 1.15/1.38 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) (c_FuncSet_Orestrict T_a T_b V_f_2 V_A_2)) (c_FuncSet_Oextensional T_a T_b V_A_2))) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OLin, (c_COMBI (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OProf, (c_COMBI (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((T_a $$unsorted)) (c_Wellfounded_OwfP T_a (c_COMBK (tc_fun T_a tc_HOL_Obool) T_a (c_COMBK tc_HOL_Obool T_a c_fFalse))) ) 1.15/1.38 ( tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( tc_Arrow__Order__Mirabelle_Oindi ) 1.15/1.38 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.38 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (= (or (hBOOL (hAPP V_A_2 V_x_2)) (= V_x_2 V_y_2)) (hBOOL (hAPP (c_Set_Oinsert T_a V_y_2 V_A_2) V_x_2))) ) 1.15/1.38 ( v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.38 ( v_Q____, c_Arrow__Order__Mirabelle_OProf, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( (hAPP v_F v_Q____), c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( v_P_H____, c_Arrow__Order__Mirabelle_OProf, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( v_P____, c_Arrow__Order__Mirabelle_OProf, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (c_Relation_Orefl__on T_a V_A_2 (c_Relation_OId__on T_a V_A_2)) ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_A_2 $$unsorted) (V_x_2 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c_Arrow__Order__Mirabelle_OLin) skv_2))), (hAPP v_F skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)))) (= (hBOOL (hAPP _let_0 V_x_2)) (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) _let_0)))) ) 1.15/1.38 ( v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.38 ( v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( (hAPP v_F v_P____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_a_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.38 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi (hAPP v_F v_Q____)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( skv_1, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( (hAPP v_F skv_1), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( skv_2, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( (hAPP v_F skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (= V_ba_2 V_aa_2) (not (forall ((B_y $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_aa_2) B_y)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_y) V_ba_2)) V_r_2)))))) ))) ) 1.15/1.38 ( (hAPP v_F v_Q____), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_P____), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((T_a $$unsorted) (T_b $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)) (c_Relation_ORange T_b T_a (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_a) tc_HOL_Obool)))) ) 1.15/1.38 ( tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__inf__class_Oinf T_a))) (or (not (class_Lattices_Olattice T_a)) (= (hAPP (hAPP _let_0 V_y) V_x) (hAPP (hAPP _let_0 V_x) V_y)))) ) 1.15/1.38 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.15/1.38 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_Oextensional T_a T_b V_A_2)))) (= V_f_2 (c_FuncSet_Orestrict T_a T_b V_f_2 V_A_2))) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OLin, (c_COMBI (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OProf, v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ( c_Arrow__Order__Mirabelle_OProf, (c_COMBI (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((T_a $$unsorted)) (let ((_let_0 (tc_prod T_a T_a))) (let ((_let_1 (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool)))) (= _let_1 (c_Transitive__Closure_Otrancl T_a _let_1)))) ) 1.15/1.38 ( tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_x_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (or (not (c_Wellfounded_Owf T_a V_r_2)) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_aa_2) V_x_2)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_x_2) V_aa_2)) V_r_2)))))) ) 1.15/1.38 ( v_a_H____, v_a____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a_H____, v_a____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a_H____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a_H____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_a_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_a_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_b____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_b____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_b_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, v_b_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_a____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_b_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_b_H____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_b_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_b_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, v_b_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_a____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_a____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_b____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_b____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_b)) (hAPP (hAPP (c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) V_r_2))) (hBOOL (hAPP (hAPP (c_member T_a) V_aa_2) (c_Relation_ODomain T_a T_b V_r_2)))) ) 1.15/1.38 ( (hAPP v_F v_Q____), v_a_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_Q____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_Q____), v_b____, v_b_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_Q____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_P____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (let ((_let_3 (hAPP _let_2 V_ba_2))) (let ((_let_4 (hAPP _let_0 _let_3))) (or (not (hBOOL (hAPP _let_4 V_r_2))) (hBOOL (hAPP _let_4 (c_Transitive__Closure_Otrancl T_a V_r_2))))))))) ) 1.15/1.38 ( (hAPP v_F v_Q____), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_P____), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_b)) (hAPP (hAPP (c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2)) V_r_2))) (hBOOL (hAPP (hAPP (c_member T_b) V_ba_2) (c_Relation_ORange T_a T_b V_r_2)))) ) 1.15/1.38 ( (hAPP v_F v_Q____), v_a_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_Q____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_Q____), v_b____, v_b_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_Q____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_P____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_B_2 $$unsorted) (V_C_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__inf__class_Oinf (tc_fun T_a tc_HOL_Obool)))) (or (not (hBOOL (hAPP (hAPP (c_member T_a) V_aa_2) V_C_2))) (= (c_Set_Oinsert T_a V_aa_2 (hAPP (hAPP _let_0 V_B_2) V_C_2)) (hAPP (hAPP _let_0 (c_Set_Oinsert T_a V_aa_2 V_B_2)) V_C_2)))) ) 1.15/1.38 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Osemilattice__inf (tc_fun T_2 T_1))) ) 1.15/1.38 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 1.15/1.38 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.15/1.38 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 1.15/1.38 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 1.15/1.38 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.15/1.38 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))), tc_HOL_Obool ) 1.15/1.38 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (c_Wellfounded_Owf T_a V_r_2) (forall ((B_Q $$unsorted) (BOUND_VARIABLE_9789 $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) BOUND_VARIABLE_9789) B_Q))) (not (forall ((B_x $$unsorted)) (or (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) B_y) B_x)) V_r_2))) (not (hBOOL (hAPP (hAPP (c_member T_a) B_y) B_Q)))) )) (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) B_Q)))) ))) )) ) 1.15/1.38 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (let ((_let_3 (c_Transitive__Closure_Otrancl T_a V_r_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ba_2)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_c_2)) _let_3))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))))))) ) 1.15/1.38 ( v_a_H____, (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, (hAPP v_F v_Q____), v_a_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_a____, (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, (hAPP v_F v_Q____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b____, (hAPP v_F v_P____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, (hAPP v_F v_Q____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ( v_b_H____, (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Oord T_1)) (class_Orderings_Oord (tc_fun T_2 T_1))) ) 1.15/1.38 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 1.15/1.38 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.15/1.38 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 1.15/1.38 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 1.15/1.38 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.15/1.38 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.15/1.38 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))), tc_HOL_Obool ) 1.15/1.38 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 1.15/1.38 ) 1.15/1.38 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_x))) ) 1.15/1.38 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.15/1.38 ) 1.15/1.39 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_x_2))) (or (hBOOL (hAPP _let_1 V_A_2)) (hBOOL (hAPP _let_1 V_B_2)) (= (= V_B_2 V_A_2) (= 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(c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.39 ( (hAPP v_F v_Q____), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.39 ( (hAPP v_F v_Q____), (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.15/1.39 ( c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt 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(tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.39 ( c_Arrow__Order__Mirabelle_OProf, c_Arrow__Order__Mirabelle_OProf, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.39 ( c_Arrow__Order__Mirabelle_OProf, c_Arrow__Order__Mirabelle_OProf, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.39 ( c_Arrow__Order__Mirabelle_OProf, c_Arrow__Order__Mirabelle_OProf, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi (hAPP v_F v_Q____)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.15/1.39 ( c_Arrow__Order__Mirabelle_OProf, 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(hAPP v_F v_Q____)), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Relation_ODomain tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (c_Relation_ODomain tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (c_Relation_ODomain tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_COMBK (tc_fun _let_1 tc_HOL_Obool) (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) c_Arrow__Order__Mirabelle_OLin) v_Q____))), c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OProf, v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OProf, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), c_Arrow__Order__Mirabelle_OProf, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.39 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Relation_ODomain tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_COMBK (tc_fun _let_1 tc_HOL_Obool) (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) c_Arrow__Order__Mirabelle_OLin) skv_2))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_COMBK (tc_fun _let_1 tc_HOL_Obool) (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) c_Arrow__Order__Mirabelle_OLin) skv_2))), (hAPP v_F skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_f_2 $$unsorted) (V_g_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted)) (= (c_FuncSet_Ocompose T_a T_c T_b V_A_2 V_g_2 V_f_2) (c_FuncSet_Orestrict T_a T_b (hAPP (c_COMBB T_c T_b T_a V_g_2) V_f_2) V_A_2)) ) 1.21/1.39 ( v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Orestrict _let_1 _let_1 (c_COMBI _let_1) c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OProf, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_Orestrict _let_2 _let_2 (c_COMBI _let_2) c_Arrow__Order__Mirabelle_OProf)))), v_F, c_Arrow__Order__Mirabelle_OProf, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_r_2 $$unsorted) (V_z_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_x_2))) (let ((_let_3 (hAPP _let_2 V_z_2))) (let ((_let_4 (hAPP _let_0 _let_3))) (or (not (hBOOL (hAPP _let_4 (c_Transitive__Closure_Otrancl T_a V_r_2)))) (hBOOL (hAPP _let_4 V_r_2)) (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 B_y)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_y) V_z_2)) (c_Transitive__Closure_Otrancl T_a V_r_2))))) )))))))) ) 1.21/1.39 ( (hAPP v_F v_Q____), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_P____), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Obounded__lattice T_1)) (class_Lattices_Obounded__lattice__bot (tc_fun T_2 T_1))) ) 1.21/1.39 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 1.21/1.39 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.21/1.39 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.39 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 1.21/1.39 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.39 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.21/1.39 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))), tc_HOL_Obool ) 1.21/1.39 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_A_2 $$unsorted) (V_B_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (or (not (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)))) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (or (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP V_f_2 B_x)) (hAPP V_B_2 B_x)))) )) (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_OPi T_a T_b V_A_2 V_B_2)))) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) c_Arrow__Order__Mirabelle_OLin))), v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)))) (or (not (= (c_Set_Oinsert T_a V_ba_2 _let_0) (c_Set_Oinsert T_a V_aa_2 _let_0))) (= V_ba_2 V_aa_2))) ) 1.21/1.39 ( (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.39 ( (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_r_2 $$unsorted) (V_z_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) V_x_2) V_z_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (= V_z_2 V_x_2) (not (forall ((B_y $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_x_2) B_y)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_y) V_z_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2))))))) ))) ) 1.21/1.39 ( (hAPP v_F v_Q____), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_P____), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= (c_Orderings_Obot__class_Obot (tc_fun (tc_fun T_a T_b) tc_HOL_Obool)) (c_FuncSet_OPi T_a T_b V_A_2 V_B_2)) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (not (= (c_Orderings_Obot__class_Obot (tc_fun T_b tc_HOL_Obool)) (hAPP V_B_2 B_x)))) ))) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OProf, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_OPi T_a T_b V_A_2 V_B_2)))) (not (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP V_f_2 V_x_2)) (hAPP V_B_2 V_x_2)))) ) 1.21/1.39 ( v_Q____, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OProf, v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ( v_P_H____, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) c_Arrow__Order__Mirabelle_OLin))), c_Arrow__Order__Mirabelle_OProf, v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Odistrib__lattice T_1)) (class_Lattices_Odistrib__lattice (tc_fun T_2 T_1))) ) 1.21/1.39 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 1.21/1.39 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.21/1.39 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.39 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 1.21/1.39 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.39 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.21/1.39 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))), tc_HOL_Obool ) 1.21/1.39 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_B_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (or (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP V_f_2 B_x)) V_B_2))) )) (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_OPi T_a T_b V_A_2 (c_COMBK (tc_fun T_b tc_HOL_Obool) T_a V_B_2))))) ) 1.21/1.39 ( c_Arrow__Order__Mirabelle_OLin, v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (hAPP _let_0 V_p_2))) (or (not (hBOOL (hAPP _let_1 V_r_2))) (hBOOL (hAPP _let_1 (c_Transitive__Closure_Otrancl T_a V_r_2)))))) ) 1.21/1.39 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_b____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b_H____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= V_A_2 (c_Relation_ODomain T_a T_a (c_Relation_OId__on T_a V_A_2))) ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_r_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (forall ((B_y $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) B_y) V_x_2)) V_r_2))) (hBOOL (hAPP (hAPP (c_member T_a) B_y) (c_Wellfounded_Oacc T_a V_r_2)))) )) (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) (c_Wellfounded_Oacc T_a V_r_2)))) ) 1.21/1.39 ( (hAPP v_F v_Q____), v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_Q____), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_Q____), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_Q____), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_P____), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_P____), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_x_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (c_Wellfounded_Owf T_a V_r_2)) (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) (c_Wellfounded_Oacc T_a V_r_2)))) ) 1.21/1.39 ( v_a_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (not (= (c_Set_Oinsert T_a V_aa_2 V_A_2) (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)))) ) 1.21/1.39 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.39 ( c_Arrow__Order__Mirabelle_OProf, v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ( c_Arrow__Order__Mirabelle_OProf, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ( c_Arrow__Order__Mirabelle_OProf, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (let ((_let_3 (c_Transitive__Closure_Otrancl T_a V_r_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ba_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_c_2)) V_r_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))))))) ) 1.21/1.39 ( v_b____, (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b_H____, (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__inf__class_Oinf (tc_fun T_a tc_HOL_Obool)))) (= (hAPP (hAPP _let_0 V_B_2) V_A_2) (hAPP (hAPP _let_0 V_A_2) V_B_2))) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.39 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (c_Relation_ODomain T_a T_b (c_Set_Oinsert (tc_prod T_a T_b) (hAPP (hAPP (c_Product__Type_OPair T_a T_b) V_aa_2) V_ba_2) V_r_2)) (c_Set_Oinsert T_a V_aa_2 (c_Relation_ODomain T_a T_b V_r_2))) ) 1.21/1.39 ( (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_Q____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_A_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (c_Relation_OId__on T_a V_A_2))) (and (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_A_2)) (= V_y_2 V_x_2))) ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (let ((_let_3 (c_Transitive__Closure_Otrancl T_a V_r_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ba_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_c_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))))))) ) 1.21/1.39 ( v_b____, (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b_H____, (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_Fa_2 $$unsorted)) (= (forall ((B_x $$unsorted) (BOUND_VARIABLE_10487 $$unsorted) (BOUND_VARIABLE_10488 $$unsorted)) (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun _let_0 tc_HOL_Obool))) B_x) c_Arrow__Order__Mirabelle_OProf))) (not (forall ((B_i $$unsorted)) (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) BOUND_VARIABLE_10487) BOUND_VARIABLE_10488)) (hAPP B_x B_i))) )) (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) BOUND_VARIABLE_10487) BOUND_VARIABLE_10488)) (hAPP V_Fa_2 B_x))))) ) (c_Arrow__Order__Mirabelle_Ounanimity V_Fa_2)) ) 1.21/1.39 ( v_F ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_r_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (or (not (c_Relation_Oantisym T_a V_r_2)) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_aa_2) V_ba_2)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_aa_2)) V_r_2))) (= V_ba_2 V_aa_2)))) ) 1.21/1.39 ( v_a_H____, v_a____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a_H____, v_a____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a_H____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a_H____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a____, v_a_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a____, v_a_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a____, v_b____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a____, v_b____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a____, v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a____, v_b_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_a____, v_b_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, v_a_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, v_a_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, v_a____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, v_a____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, v_a____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, v_a____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, v_a____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, v_b_H____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, v_b_H____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, v_b_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, v_b_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b____, v_b_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b_H____, v_a____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b_H____, v_a____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b_H____, v_b____, (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b_H____, v_b____, (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b_H____, v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b_H____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ( v_b_H____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.39 ) 1.21/1.39 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Olattice T_a)) (c_Orderings_Oord__class_Oless__eq T_a (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_y)) ) 1.21/1.40 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (not (c_Orderings_Oord__class_Oless__eq T_a V_y V_x)) (= V_y (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y))) ) 1.21/1.40 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf (tc_fun T_a tc_HOL_Obool)) V_A_2) V_A_2)) ) 1.21/1.40 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Osemilattice__sup (tc_fun T_2 T_1))) ) 1.21/1.40 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 1.21/1.40 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.21/1.40 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.40 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 1.21/1.40 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.40 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.21/1.40 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.40 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))), tc_HOL_Obool ) 1.21/1.40 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (or (not (c_Wellfounded_Owf T_a V_R_2)) (c_Wellfounded_OwfP T_a (c_FunDef_Oin__rel T_a T_a V_R_2))) ) 1.21/1.40 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_R_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (= V_ba_2 V_aa_2))) (let ((_let_1 (c_member (tc_prod T_a T_a)))) (let ((_let_2 (c_Product__Type_OPair T_a T_a))) (let ((_let_3 (hAPP _let_2 V_aa_2))) (let ((_let_4 (hAPP _let_3 V_ba_2))) (let ((_let_5 (hAPP _let_1 _let_4))) (or (not (hBOOL (hAPP _let_5 (c_Transitive__Closure_Ortrancl T_a V_R_2)))) _let_0 (and (not _let_0) (hBOOL (hAPP _let_5 (c_Transitive__Closure_Otrancl T_a V_R_2))))))))))) ) 1.21/1.40 ( (hAPP v_F v_Q____), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Obot T_1)) (class_Orderings_Obot (tc_fun T_2 T_1))) ) 1.21/1.40 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 1.21/1.40 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.21/1.40 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.40 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 1.21/1.40 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.40 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.21/1.40 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.40 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))), tc_HOL_Obool ) 1.21/1.40 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (c_Relation_ORange T_a T_a (c_Transitive__Closure_Otrancl T_a V_r_2)) (c_Relation_ORange T_a T_a V_r_2)) ) 1.21/1.40 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_x_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (class_Orderings_Obot T_a)) (= (hAPP (c_Orderings_Obot__class_Obot (tc_fun T_b T_a)) V_x_2) (c_Orderings_Obot__class_Obot T_a))) ) 1.21/1.40 ( v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))), tc_HOL_Obool ) 1.21/1.40 ( v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.21/1.40 ( (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.40 ( v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.21/1.40 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.21/1.40 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.21/1.40 ( v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.21/1.40 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) V_ba_2) (c_Relation_ORange T_b T_a V_r_2)))) (not (forall ((B_x $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_a)) (hAPP (hAPP (c_Product__Type_OPair T_b T_a) B_x) V_ba_2)) V_r_2))) ))) ) 1.21/1.40 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_A_2 $$unsorted) (T_a $$unsorted)) (= V_A_2 (c_Relation_ORange T_a T_a (c_Relation_OId__on T_a V_A_2))) ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (c_Relation_ODomain T_a T_a (c_Transitive__Closure_Otrancl T_a V_r_2)) (c_Relation_ODomain T_a T_a V_r_2)) ) 1.21/1.40 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((BOUND_VARIABLE_10732 $$unsorted) (BOUND_VARIABLE_10733 $$unsorted) (BOUND_VARIABLE_10734 $$unsorted) (BOUND_VARIABLE_10735 $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__inf__class_Oinf (tc_fun BOUND_VARIABLE_10735 tc_HOL_Obool)))) (or (hBOOL (hAPP (hAPP (c_member BOUND_VARIABLE_10735) BOUND_VARIABLE_10734) BOUND_VARIABLE_10733)) (= (hAPP (hAPP _let_0 BOUND_VARIABLE_10732) BOUND_VARIABLE_10733) (hAPP (hAPP _let_0 (c_Set_Oinsert BOUND_VARIABLE_10735 BOUND_VARIABLE_10734 BOUND_VARIABLE_10732)) BOUND_VARIABLE_10733)))) ) 1.21/1.40 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_x_2 $$unsorted) (V_T_2 $$unsorted) (V_S_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_Oextensional__funcset T_a T_b V_S_2 V_T_2)))) (not (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_S_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP V_f_2 V_x_2)) V_T_2))) ) 1.21/1.40 ( v_Q____, c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OProf, v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_z_2 $$unsorted) (V_r_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (c_Transitive__Closure_Otrancl T_a V_r_2))) (let ((_let_3 (hAPP _let_1 V_x_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_3 V_y_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_y_2) V_z_2)) _let_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_3 V_z_2)) _let_2))))))) ) 1.21/1.40 ( v_b____, (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_fun T_a T_b)))) (let ((_let_1 (hAPP _let_0 V_f_2))) (or (not (hBOOL (hAPP _let_1 (c_FuncSet_OPi T_a T_b V_A_2 (c_COMBK (tc_fun T_b tc_HOL_Obool) T_a V_B_2))))) (not (hBOOL (hAPP _let_1 (c_FuncSet_Oextensional T_a T_b V_A_2)))) (= V_f_2 (c_FuncSet_Ocompose T_a T_b T_b V_A_2 (c_FuncSet_Orestrict T_b T_b (c_COMBI T_b) V_B_2) V_f_2))))) ) 1.21/1.40 ( c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OProf, v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Lattices_Osemilattice__inf__class_Oinf T_a))) (or (not (class_Lattices_Osemilattice__inf T_a)) (= (hAPP (hAPP _let_0 V_y) V_x) (hAPP (hAPP _let_0 V_x) V_y)))) ) 1.21/1.40 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.21/1.40 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_r_2 $$unsorted) (V_aa_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (c_Wellfounded_Oacc T_a V_r_2))) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) V_ba_2) V_aa_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (not (hBOOL (hAPP (hAPP _let_0 V_aa_2) _let_1))) (hBOOL (hAPP (hAPP _let_0 V_ba_2) _let_1))))) ) 1.21/1.40 ( (hAPP v_F v_Q____), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_b_H $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Product__Type_OPair T_a T_b))) (or (not (= (hAPP (hAPP _let_0 V_a) V_b) (hAPP (hAPP _let_0 V_a_H) V_b_H))) (and (= V_a_H V_a) (= V_b_H V_b)))) ) 1.21/1.40 ( v_a_H____, v_a____, v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_a____, v_a_H____, v_a_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_a____, v_a_H____, v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_a____, v_a_H____, v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_a____, v_a_H____, v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_a____, v_a_H____, v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_a____, v_b____, v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b____, v_a_H____, v_b____, v_b_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b____, v_a____, v_a_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b____, v_a____, v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b____, v_a____, v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b____, v_a____, v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b____, v_b_H____, v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, v_a____, v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, v_b____, v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, v_b____, v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, v_b____, v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, v_b____, v_b____, v_b_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, v_b____, v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_Pa_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (not (hBOOL (hAPP V_Pa_2 V_ba_2))) (not (forall ((B_y $$unsorted) (B_z $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_y) B_z)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_z) V_ba_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (not (hBOOL (hAPP V_Pa_2 B_z))) (hBOOL (hAPP V_Pa_2 B_y))))) )) (hBOOL (hAPP V_Pa_2 V_aa_2))) ) 1.21/1.40 ( (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____), (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____), (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_Pa_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (not (hBOOL (hAPP V_Pa_2 V_aa_2))) (not (forall ((B_y $$unsorted) (BOUND_VARIABLE_11055 $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_aa_2) B_y)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (not (hBOOL (hAPP V_Pa_2 B_y))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_y) BOUND_VARIABLE_11055)) V_r_2))) (hBOOL (hAPP V_Pa_2 BOUND_VARIABLE_11055))))) )) (hBOOL (hAPP V_Pa_2 V_ba_2))) ) 1.21/1.40 ( (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____), (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (or (not (c_Relation_Orefl__on T_a V_A_2 V_r_2)) (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2))) (hBOOL (hAPP (hAPP (c_member T_a) V_y_2) V_A_2))) ) 1.21/1.40 ( v_a____, v_a_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_ba_2 $$unsorted) (V_B_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_aa_2))) (or (not (hBOOL (hAPP _let_1 V_B_2))) (hBOOL (hAPP _let_1 (c_Set_Oinsert T_a V_ba_2 V_B_2)))))) ) 1.21/1.40 ( v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.40 ( (hAPP v_F v_Q____), c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.40 ( (hAPP v_F v_Q____), c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_P____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.40 ( (hAPP v_F v_Q____), c_Arrow__Order__Mirabelle_OLin, (hAPP v_F skv_1), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.40 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_a_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( v_P____, c_Arrow__Order__Mirabelle_OProf, v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( v_P____, c_Arrow__Order__Mirabelle_OProf, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( v_P____, c_Arrow__Order__Mirabelle_OProf, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( v_P____, c_Arrow__Order__Mirabelle_OProf, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi (hAPP v_F v_Q____)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( v_P____, c_Arrow__Order__Mirabelle_OProf, skv_1, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( v_P____, c_Arrow__Order__Mirabelle_OProf, skv_2, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (= (c_Set_Oinsert T_a V_aa_2 V_A_2) (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup _let_0) (c_Set_Oinsert T_a V_aa_2 (c_Orderings_Obot__class_Obot _let_0))) V_A_2))) ) 1.21/1.40 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.40 ( c_Arrow__Order__Mirabelle_OProf, v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( c_Arrow__Order__Mirabelle_OProf, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( c_Arrow__Order__Mirabelle_OProf, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.40 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.40 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi (c_HOL_Oundefined _let_1)))), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (let ((_let_3 (c_Transitive__Closure_Ortrancl T_a V_r_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ba_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_c_2)) _let_3))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))))))) ) 1.21/1.40 ( v_b____, (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Orderings_Obot__class_Obot T_a))) (or (not (class_Lattices_Obounded__lattice__bot T_a)) (= _let_0 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) _let_0)))) ) 1.21/1.40 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (let ((_let_3 (hAPP _let_2 V_ba_2))) (let ((_let_4 (hAPP _let_0 _let_3))) (or (not (hBOOL (hAPP _let_4 (c_Transitive__Closure_Otrancl T_a V_r_2)))) (hBOOL (hAPP _let_4 (c_Transitive__Closure_Ortrancl T_a V_r_2))))))))) ) 1.21/1.40 ( (hAPP v_F v_Q____), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_x_2))) (let ((_let_3 (hAPP _let_2 V_y_2))) (let ((_let_4 (hAPP _let_0 _let_3))) (let ((_let_5 (= V_y_2 V_x_2))) (= (hBOOL (hAPP _let_4 (c_Transitive__Closure_Ortrancl T_a V_R_2))) (or (and (hBOOL (hAPP _let_4 (c_Transitive__Closure_Otrancl T_a V_R_2))) (not _let_5)) _let_5)))))))) ) 1.21/1.40 ( (hAPP v_F v_Q____), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_r_2 $$unsorted) (V_p_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (hAPP _let_0 V_p_2))) (or (not (hBOOL (hAPP _let_1 V_r_2))) (hBOOL (hAPP _let_1 (c_Transitive__Closure_Ortrancl T_a V_r_2)))))) ) 1.21/1.40 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_b____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b_H____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (= (c_Relation_Orefl__on T_a V_A_2 V_r_2) (and (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) B_x) B_x)) V_r_2))) ) (c_Orderings_Oord__class_Oless__eq (tc_fun (tc_prod T_a T_a) tc_HOL_Obool) V_r_2 (c_Product__Type_OSigma T_a T_a V_A_2 (c_COMBK (tc_fun T_a tc_HOL_Obool) T_a V_A_2))))) ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_Fa_2 $$unsorted)) (= (c_Arrow__Order__Mirabelle_OIIA V_Fa_2) (forall ((B_x $$unsorted) (BOUND_VARIABLE_11398 $$unsorted) (BOUND_VARIABLE_11399 $$unsorted) (BOUND_VARIABLE_11400 $$unsorted)) (let ((_let_0 (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool))) (let ((_let_1 (c_member (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_0)))) (let ((_let_2 (c_member (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_3 (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (hAPP _let_3 BOUND_VARIABLE_11399))) (let ((_let_5 (hAPP _let_4 BOUND_VARIABLE_11400))) (let ((_let_6 (hAPP _let_2 _let_5))) (or (not (hBOOL (hAPP (hAPP _let_1 B_x) c_Arrow__Order__Mirabelle_OProf))) (not (hBOOL (hAPP (hAPP _let_1 BOUND_VARIABLE_11398) c_Arrow__Order__Mirabelle_OProf))) (not (forall ((B_i $$unsorted)) (= (hBOOL (hAPP _let_6 (hAPP B_x B_i))) (hBOOL (hAPP _let_6 (hAPP BOUND_VARIABLE_11398 B_i)))) )) (= (hBOOL (hAPP _let_6 (hAPP V_Fa_2 BOUND_VARIABLE_11398))) (hBOOL (hAPP _let_6 (hAPP V_Fa_2 B_x)))))))))))) )) ) 1.21/1.40 ( v_F ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (c_Wellfounded_Owf T_a V_r_2)) (c_Wellfounded_Owf T_a (c_Transitive__Closure_Otrancl T_a V_r_2))) ) 1.21/1.40 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ba_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_c_2)) V_r_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) (c_Transitive__Closure_Otrancl T_a V_r_2))))))) ) 1.21/1.40 ( v_b____, (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (let ((_let_3 (c_Transitive__Closure_Otrancl T_a V_r_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ba_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_c_2)) _let_3))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))))))) ) 1.21/1.40 ( v_b____, (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_T_2 $$unsorted) (V_S_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (c_FuncSet_Oextensional__funcset T_a T_b V_S_2 V_T_2) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf (tc_fun (tc_fun T_a T_b) tc_HOL_Obool)) (c_FuncSet_OPi T_a T_b V_S_2 (c_COMBK (tc_fun T_b tc_HOL_Obool) T_a V_T_2))) (c_FuncSet_Oextensional T_a T_b V_S_2))) ) 1.21/1.40 ( c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OProf, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (let ((_let_3 (c_Transitive__Closure_Ortrancl T_a V_r_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ba_2)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_c_2)) _let_3))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))))))) ) 1.21/1.40 ( v_a_H____, (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_a____, (hAPP v_F v_Q____), v_a_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_a____, (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b____, (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b____, (hAPP v_F v_Q____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b____, (hAPP v_F v_P____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, (hAPP v_F v_Q____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( v_b_H____, (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) V_aa_2) (c_Relation_ODomain T_a T_b V_r_2)))) (not (forall ((B_y $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_b)) (hAPP (hAPP (c_Product__Type_OPair T_a T_b) V_aa_2) B_y)) V_r_2))) ))) ) 1.21/1.40 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.40 ) 1.21/1.40 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_L_2 $$unsorted)) (let ((_let_0 (c_member (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_1 (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) V_L_2) c_Arrow__Order__Mirabelle_OLin))) (= V_y_2 V_x_2) (= (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_y_2) V_x_2)) V_L_2)) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_x_2) V_y_2)) V_L_2))))))) ) 1.21/1.40 ( v_a_H____, v_a____, (hAPP v_F v_Q____) ) 1.21/1.40 ( v_a_H____, v_a____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( v_a_H____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.40 ( v_a_H____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.40 ( v_a____, v_a_H____, (hAPP v_F v_Q____) ) 1.21/1.40 ( v_a____, v_a_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( v_a____, v_b____, (hAPP v_F v_Q____) ) 1.21/1.40 ( v_a____, v_b____, (hAPP v_F v_P____) ) 1.21/1.40 ( v_a____, v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( v_a____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.40 ( v_a____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.40 ( v_a____, v_b_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.40 ( v_a____, v_b_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.40 ( v_b____, v_a_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.40 ( v_b____, v_a_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.40 ( v_b____, v_a____, (hAPP v_F v_Q____) ) 1.21/1.40 ( v_b____, v_a____, (hAPP v_F v_P____) ) 1.21/1.40 ( v_b____, v_a____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( v_b____, v_a____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.40 ( v_b____, v_a____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.40 ( v_b____, v_b_H____, (hAPP v_F v_Q____) ) 1.21/1.40 ( v_b____, v_b_H____, (hAPP v_F v_P____) ) 1.21/1.40 ( v_b____, v_b_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( v_b____, v_b_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.40 ( v_b____, v_b_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.40 ( v_b_H____, v_a____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.40 ( v_b_H____, v_a____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.40 ( v_b_H____, v_b____, (hAPP v_F v_Q____) ) 1.21/1.40 ( v_b_H____, v_b____, (hAPP v_F v_P____) ) 1.21/1.40 ( v_b_H____, v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.40 ( v_b_H____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.40 ( v_b_H____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.40 ) 1.21/1.41 (instantiation (forall ((V_x_2 $$unsorted) (V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_OPi T_a T_b V_A_2 (c_COMBK (tc_fun T_b tc_HOL_Obool) T_a V_B_2))))) (not (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_A_2))) (hBOOL (hAPP (hAPP (c_member T_b) (hAPP V_f_2 V_x_2)) V_B_2))) ) 1.21/1.41 ( v_Q____, c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OProf, v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( v_P_H____, c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OProf, v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (c_Wellfounded_Owf T_a V_r_2)) (c_Wellfounded_Oacyclic T_a V_r_2)) ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (c_Orderings_Oord__class_Oless__eq T_a (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_y)) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (or (not (c_Orderings_Oord__class_Oless__eq _let_0 V_A_2 V_B_2)) (= V_A_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2)))) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (let ((_let_3 (c_Transitive__Closure_Ortrancl T_a V_r_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ba_2)) _let_3))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_c_2)) V_r_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) _let_3))))))) ) 1.21/1.41 ( v_b____, (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b_H____, (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_A_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) V_aa_2) V_A_2))) (= V_A_2 (c_Set_Oinsert T_a V_aa_2 V_A_2))) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_a_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_P____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F skv_1), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi (hAPP v_F v_Q____)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, skv_1, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, skv_2, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (c_Relation_ODomain tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Relation_ODomain tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Relation_ODomain tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Relation_ODomain tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Relation_ORange tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool)))), v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK _let_1 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) (c_HOL_Oundefined _let_1)))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_COMBK (tc_fun _let_1 tc_HOL_Obool) (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) c_Arrow__Order__Mirabelle_OLin) v_Q____))), (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt 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(c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) tc_HOL_Obool)), (c_COMBK tc_HOL_Obool (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) (c_HOL_Oundefined tc_HOL_Obool)), (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 1.21/1.41 ( (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Wellfounded_Oacc tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (hAPP (c_COMBK (tc_fun _let_1 tc_HOL_Obool) (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) c_Arrow__Order__Mirabelle_OLin) skv_2))), (hAPP v_F skv_2), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member T_a) V_aa_2) (c_Relation_ODomain T_a T_b V_r_2))) (not (forall ((B_y $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_b)) (hAPP (hAPP (c_Product__Type_OPair T_a T_b) V_aa_2) B_y)) V_r_2))) ))) ) 1.21/1.41 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (not (c_Orderings_Oord__class_Oless__eq T_a V_x V_y)) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y))) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (= (= V_x_2 (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x_2) V_y_2)) (c_Orderings_Oord__class_Oless__eq T_a V_x_2 V_y_2))) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (= V_r_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_b T_a) tc_HOL_Obool))) (= (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)) (c_Relation_ORange T_b T_a V_r_2))) ) 1.21/1.41 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_x_2 $$unsorted) (V_T_2 $$unsorted) (V_S_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_Oextensional__funcset T_a T_b V_S_2 V_T_2)))) (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_S_2)) (= (hAPP V_f_2 V_x_2) (c_HOL_Oundefined T_b))) ) 1.21/1.41 ( v_Q____, c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OProf, v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_r_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (or (not (c_Relation_Orefl__on T_a V_A_2 V_r_2)) (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) V_r_2))) (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_A_2))) ) 1.21/1.41 ( v_a____, v_a_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((T_b $$unsorted) (T_a $$unsorted)) (= (c_Relation_ODomain T_a T_b (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_a T_b) tc_HOL_Obool))) (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool))) ) 1.21/1.41 ( tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Opreorder T_1)) (class_Orderings_Opreorder (tc_fun T_2 T_1))) ) 1.21/1.41 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 1.21/1.41 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.21/1.41 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.41 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 1.21/1.41 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.21/1.41 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))), tc_HOL_Obool ) 1.21/1.41 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_y_2 $$unsorted) (V_R_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) (c_Relation_ODomain T_a T_a V_R_2))) (= (= V_y_2 V_x_2) (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (c_Transitive__Closure_Ortrancl T_a V_R_2))))) ) 1.21/1.41 ( v_b____, (hAPP v_F v_Q____), v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b____, (hAPP v_F v_Q____), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b_H____, (hAPP v_F v_P____), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b_H____, (hAPP v_F v_P____), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Olattice T_a)) (= V_x (hAPP (hAPP (c_Lattices_Osemilattice__sup__class_Osup T_a) V_x) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y)))) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Transitive__Closure_Ortrancl T_a V_R_2))) (= _let_0 (c_Transitive__Closure_Otrancl T_a _let_0))) ) 1.21/1.41 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (V_g_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_fun T_a T_b)))) (let ((_let_1 (hAPP _let_0 V_g_2))) (or (not (hBOOL (hAPP _let_1 (c_FuncSet_OPi T_a T_b V_A_2 (c_COMBK (tc_fun T_b tc_HOL_Obool) T_a V_B_2))))) (not (hBOOL (hAPP _let_1 (c_FuncSet_Oextensional T_a T_b V_A_2)))) (= V_g_2 (c_FuncSet_Ocompose T_a T_a T_b V_A_2 V_g_2 (c_FuncSet_Orestrict T_a T_a (c_COMBI T_a) V_A_2)))))) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OLin, c_Arrow__Order__Mirabelle_OProf, v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_A_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (= (c_Set_Oinsert T_a V_x_2 (c_Set_Oinsert T_a V_y_2 V_A_2)) (c_Set_Oinsert T_a V_y_2 (c_Set_Oinsert T_a V_x_2 V_A_2))) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_Q____, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_Q____, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P_H____, v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P_H____, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P_H____, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P____, v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P____, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P____, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), v_F, v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Orderings_Oorder T_1)) (class_Orderings_Oorder (tc_fun T_2 T_1))) ) 1.21/1.41 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 1.21/1.41 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.21/1.41 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.41 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 1.21/1.41 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.21/1.41 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))), tc_HOL_Obool ) 1.21/1.41 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Osemilattice__inf T_a)) (c_Orderings_Oord__class_Oless__eq T_a (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_x)) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_B_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a tc_HOL_Obool))) (= (forall ((B_x $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 B_x))) (or (not (hBOOL (hAPP _let_1 V_A_2))) (not (hBOOL (hAPP _let_1 V_B_2)))))) ) (= (c_Orderings_Obot__class_Obot _let_0) (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf _let_0) V_A_2) V_B_2)))) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_R_2 $$unsorted) (T_a $$unsorted)) (= (c_Transitive__Closure_Ortrancl T_a V_R_2) (c_Transitive__Closure_Ortrancl T_a (c_Transitive__Closure_Otrancl T_a V_R_2))) ) 1.21/1.41 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_x) B_y)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_y) B_x)) V_r_2))) (= B_x B_y)))) )) (c_Relation_Oantisym T_a V_r_2)) ) 1.21/1.41 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (tc_fun T_a T_b))) (= (c_Set_Oinsert _let_0 (c_COMBK T_b T_a (c_HOL_Oundefined T_b)) (c_Orderings_Obot__class_Obot (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional T_a T_b (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool))))) ) 1.21/1.41 ( tc_HOL_Obool, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( tc_HOL_Obool, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( tc_HOL_Obool, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( tc_HOL_Obool, tc_Arrow__Order__Mirabelle_Oindi ) 1.21/1.41 ( tc_HOL_Obool, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( tc_HOL_Obool, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.41 ( tc_HOL_Obool, (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool) ) 1.21/1.41 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 1.21/1.41 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (class_Lattices_Olattice T_a)) (c_Orderings_Oord__class_Oless__eq T_a (hAPP (hAPP (c_Lattices_Osemilattice__inf__class_Oinf T_a) V_x) V_y) V_x)) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_FuncSet_Oextensional (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1 c_Arrow__Order__Mirabelle_OProf))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1) tc_HOL_Obool))) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (= (c_Relation_Oantisym T_a V_r_2) (forall ((B_x $$unsorted) (B_y $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_x) B_y)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_y) B_x)) V_r_2))) (= B_x B_y)))) )) ) 1.21/1.41 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_aa_2))) (or (not (hBOOL (hAPP _let_1 (c_Set_Oinsert T_a V_ba_2 V_A_2)))) (= V_ba_2 V_aa_2) (hBOOL (hAPP _let_1 V_A_2))))) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_a_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (hAPP v_F v_P____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (hAPP v_F skv_1), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P_H____, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P____, v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P____, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P____, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P____, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi (hAPP v_F v_Q____)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P____, skv_1, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( c_Arrow__Order__Mirabelle_OProf, v_P____, skv_2, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.41 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), v_F, v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_L_2 $$unsorted)) (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member _let_1) V_L_2) c_Arrow__Order__Mirabelle_OLin))) (hBOOL (hAPP (hAPP (c_member (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1)) (c_COMBK _let_1 tc_Arrow__Order__Mirabelle_Oindi V_L_2)) c_Arrow__Order__Mirabelle_OProf))))) ) 1.21/1.41 ( (hAPP v_F v_Q____) ) 1.21/1.41 ( (hAPP v_F v_P____) ) 1.21/1.41 ( (c_HOL_Oundefined (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.41 ( (hAPP v_F skv_1) ) 1.21/1.41 ( (hAPP v_F skv_2) ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_c_2 $$unsorted) (V_R_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ba_2)) V_R_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_c_2)) V_R_2))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) (c_Transitive__Closure_Otrancl T_a V_R_2))))))) ) 1.21/1.41 ( v_a_H____, (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a____, (hAPP v_F v_Q____), v_a_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a____, (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b____, (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b____, (hAPP v_F v_Q____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b____, (hAPP v_F v_P____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b_H____, (hAPP v_F v_Q____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b_H____, (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b_H____, (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_aa_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (c_Wellfounded_Oacc T_a V_r_2))) (or (not (hBOOL (hAPP (hAPP _let_0 V_ba_2) _let_1))) (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) V_aa_2) V_ba_2)) V_r_2))) (hBOOL (hAPP (hAPP _let_0 V_aa_2) _let_1))))) ) 1.21/1.41 ( v_a_H____, (hAPP v_F v_Q____), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a____, (hAPP v_F v_Q____), v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a____, (hAPP v_F v_Q____), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a____, (hAPP v_F v_P____), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_a____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b____, (hAPP v_F v_Q____), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b____, (hAPP v_F v_Q____), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b____, (hAPP v_F v_P____), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b____, (hAPP v_F v_P____), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( v_b_H____, (hAPP v_F v_Q____), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (= (not (forall ((B_y $$unsorted)) (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_b T_a)) (hAPP (hAPP (c_Product__Type_OPair T_b T_a) B_y) V_aa_2)) V_r_2))) )) (hBOOL (hAPP (hAPP (c_member T_a) V_aa_2) (c_Relation_ORange T_b T_a V_r_2)))) ) 1.21/1.41 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ) 1.21/1.41 (instantiation (forall ((V_r_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (= V_r_2 (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_a T_b) tc_HOL_Obool))) (= (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)) (c_Relation_ODomain T_a T_b V_r_2))) ) 1.21/1.41 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.41 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_A_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member T_a))) (let ((_let_1 (hAPP _let_0 V_aa_2))) (= (hBOOL (hAPP _let_1 (c_Set_Oinsert T_a V_ba_2 V_A_2))) (or (= V_ba_2 V_aa_2) (hBOOL (hAPP _let_1 V_A_2)))))) ) 1.21/1.42 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.42 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.42 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.42 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_a_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.42 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.42 ( (hAPP v_F v_Q____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b_H____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.42 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (hAPP v_F v_Q____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.42 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (hAPP v_F v_P____), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.42 ( c_Arrow__Order__Mirabelle_OLin, (hAPP v_F v_Q____), (hAPP v_F skv_1), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.42 ( c_Arrow__Order__Mirabelle_OProf, v_P____, v_Q____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( c_Arrow__Order__Mirabelle_OProf, v_P____, v_P_H____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( c_Arrow__Order__Mirabelle_OProf, v_P____, v_P____, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( c_Arrow__Order__Mirabelle_OProf, v_P____, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi (hAPP v_F v_Q____)), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( c_Arrow__Order__Mirabelle_OProf, v_P____, skv_1, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( c_Arrow__Order__Mirabelle_OProf, v_P____, skv_2, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.42 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.42 ( (hAPP v_F v_P____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_a____), (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.42 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (c_FuncSet_OPi _let_2 _let_1 c_Arrow__Order__Mirabelle_OProf (c_COMBK (tc_fun _let_1 tc_HOL_Obool) _let_2 c_Arrow__Order__Mirabelle_OLin))))), v_F, v_F, (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))) ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_r_2 $$unsorted) (T_a $$unsorted)) (or (not (c_Wellfounded_Oacyclic T_a V_r_2)) (c_Relation_Oantisym T_a (c_Transitive__Closure_Ortrancl T_a V_r_2))) ) 1.21/1.42 ( (hAPP v_F v_Q____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_P____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (c_Relation_ORange T_b T_a (c_Set_Oinsert (tc_prod T_b T_a) (hAPP (hAPP (c_Product__Type_OPair T_b T_a) V_aa_2) V_ba_2) V_r_2)) (c_Set_Oinsert T_a V_ba_2 (c_Relation_ORange T_b T_a V_r_2))) ) 1.21/1.42 ( (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_Q____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_g_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_fun T_a T_b)))) (let ((_let_1 (c_FuncSet_Oextensional T_a T_b V_A_2))) (or (not (hBOOL (hAPP (hAPP _let_0 V_f_2) _let_1))) (not (hBOOL (hAPP (hAPP _let_0 V_g_2) _let_1))) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (= (hAPP V_f_2 B_x) (hAPP V_g_2 B_x))) )) (= V_g_2 V_f_2)))) ) 1.21/1.42 ( v_F, c_Arrow__Order__Mirabelle_OProf, v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( v_F, (c_Orderings_Obot__class_Obot (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) tc_HOL_Obool)), v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( v_Q____, (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), v_Q____, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 1.21/1.42 ( (hAPP v_F v_Q____), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (hAPP v_F v_Q____), tc_HOL_Obool, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.42 ( v_P_H____, (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oindi tc_HOL_Obool)), v_Q____, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi ) 1.21/1.42 ( (hAPP v_F v_P____), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (hAPP v_F v_Q____), tc_HOL_Obool, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_c_2 $$unsorted) (V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_ba_2)) V_r_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_c_2)) (c_Transitive__Closure_Ortrancl T_a V_r_2)))) (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 V_c_2)) (c_Transitive__Closure_Otrancl T_a V_r_2))))))) ) 1.21/1.42 ( v_a_H____, (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_a____, (hAPP v_F v_Q____), v_a_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_a____, (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b____, (hAPP v_F v_Q____), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b____, (hAPP v_F v_Q____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b____, (hAPP v_F v_P____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b_H____, (hAPP v_F v_Q____), v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b_H____, (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b_H____, (hAPP v_F v_P____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (c_Transitive__Closure_Otrancl T_a V_R_2)))) (not (forall ((B_z $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_x_2) B_z)) (c_Transitive__Closure_Ortrancl T_a V_R_2)))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_z) V_y_2)) V_R_2)))))) ))) ) 1.21/1.42 ( (hAPP v_F v_Q____), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_P____), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (V_L_2 $$unsorted)) (let ((_let_0 (c_member (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_1 (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) V_L_2) c_Arrow__Order__Mirabelle_OLin))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_aa_2) V_ba_2)) V_L_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_ba_2) V_aa_2)) V_L_2)))))) ) 1.21/1.42 ( v_a_H____, v_a____, (hAPP v_F v_Q____) ) 1.21/1.42 ( v_a_H____, v_a____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( v_a_H____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.42 ( v_a_H____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.42 ( v_a____, v_a_H____, (hAPP v_F v_Q____) ) 1.21/1.42 ( v_a____, v_a_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( v_a____, v_b____, (hAPP v_F v_Q____) ) 1.21/1.42 ( v_a____, v_b____, (hAPP v_F v_P____) ) 1.21/1.42 ( v_a____, v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( v_a____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.42 ( v_a____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.42 ( v_a____, v_b_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.42 ( v_a____, v_b_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.42 ( v_b____, v_a_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.42 ( v_b____, v_a_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.42 ( v_b____, v_a____, (hAPP v_F v_Q____) ) 1.21/1.42 ( v_b____, v_a____, (hAPP v_F v_P____) ) 1.21/1.42 ( v_b____, v_a____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( v_b____, v_a____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.42 ( v_b____, v_a____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_Q____)) ) 1.21/1.42 ( v_b____, v_b_H____, (hAPP v_F v_Q____) ) 1.21/1.42 ( v_b____, v_b_H____, (hAPP v_F v_P____) ) 1.21/1.42 ( v_b____, v_b_H____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( v_b____, v_b_H____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.42 ( v_b____, v_b_H____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.42 ( v_b_H____, v_a____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.42 ( v_b_H____, v_a____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.42 ( v_b_H____, v_b____, (hAPP v_F v_Q____) ) 1.21/1.42 ( v_b_H____, v_b____, (hAPP v_F v_P____) ) 1.21/1.42 ( v_b_H____, v_b____, (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( v_b_H____, v_b____, (c_Transitive__Closure_Otrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.42 ( v_b_H____, v_b____, (c_Transitive__Closure_Ortrancl tc_Arrow__Order__Mirabelle_Oalt (hAPP v_F v_P____)) ) 1.21/1.42 ) 1.21/1.42 (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))) ) 1.21/1.42 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 1.21/1.42 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.21/1.42 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.42 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 1.21/1.42 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.42 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.21/1.42 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.42 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))), tc_HOL_Obool ) 1.21/1.42 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (class_Lattices_Olattice T_1)) (class_Lattices_Olattice (tc_fun T_2 T_1))) ) 1.21/1.42 ( tc_Arrow__Order__Mirabelle_Oalt, tc_HOL_Obool ) 1.21/1.42 ( (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool ) 1.21/1.42 ( (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.42 ( tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool ) 1.21/1.42 ( tc_Arrow__Order__Mirabelle_Oindi, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.42 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), tc_HOL_Obool ) 1.21/1.42 ( (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) ) 1.21/1.42 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (tc_fun (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) _let_1))), tc_HOL_Obool ) 1.21/1.42 ( (tc_fun (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_HOL_Obool), tc_HOL_Obool ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_R_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) V_x_2) V_y_2)) (c_Transitive__Closure_Otrancl T_a V_R_2)))) (not (forall ((B_z $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 V_x_2) B_z)) V_R_2))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_z) V_y_2)) (c_Transitive__Closure_Ortrancl T_a V_R_2))))))) ))) ) 1.21/1.42 ( (hAPP v_F v_Q____), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_P____), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_b_Ha_2 $$unsorted) (V_a_Ha_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_Product__Type_OPair T_a T_b))) (= (and (= V_b_Ha_2 V_ba_2) (= V_a_Ha_2 V_aa_2)) (= (hAPP (hAPP _let_0 V_aa_2) V_ba_2) (hAPP (hAPP _let_0 V_a_Ha_2) V_b_Ha_2)))) ) 1.21/1.42 ( v_a_H____, v_a____, v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_a____, v_a_H____, v_a_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_a____, v_a_H____, v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_a____, v_a_H____, v_a____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_a____, v_a_H____, v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_a____, v_a_H____, v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_a____, v_b____, v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b____, v_a_H____, v_b____, v_b_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b____, v_a____, v_a_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b____, v_a____, v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b____, v_a____, v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b____, v_a____, v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b____, v_b_H____, v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b_H____, v_a____, v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b_H____, v_b____, v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b_H____, v_b____, v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b_H____, v_b____, v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b_H____, v_b____, v_b____, v_b_H____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( v_b_H____, v_b____, v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_x_2 $$unsorted) (V_A_2 $$unsorted) (V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun T_a T_b)) V_f_2) (c_FuncSet_Oextensional T_a T_b V_A_2)))) (hBOOL (hAPP (hAPP (c_member T_a) V_x_2) V_A_2)) (= (c_HOL_Oundefined T_b) (hAPP V_f_2 V_x_2))) ) 1.21/1.42 ( v_Q____, c_Arrow__Order__Mirabelle_OProf, v_F, (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ( (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), (hAPP v_F v_Q____), tc_HOL_Obool, (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_r_2 $$unsorted) (V_ba_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_prod T_a T_a)))) (let ((_let_1 (c_Product__Type_OPair T_a T_a))) (let ((_let_2 (hAPP _let_1 V_aa_2))) (let ((_let_3 (hAPP _let_2 V_ba_2))) (let ((_let_4 (hAPP _let_0 _let_3))) (or (not (hBOOL (hAPP _let_4 (c_Transitive__Closure_Otrancl T_a V_r_2)))) (hBOOL (hAPP _let_4 V_r_2)) (not (forall ((B_c $$unsorted)) (or (not (hBOOL (hAPP (hAPP _let_0 (hAPP _let_2 B_c)) (c_Transitive__Closure_Otrancl T_a V_r_2)))) (not (hBOOL (hAPP (hAPP _let_0 (hAPP (hAPP _let_1 B_c) V_ba_2)) V_r_2)))) )))))))) ) 1.21/1.42 ( (hAPP v_F v_Q____), v_b____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_Q____), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_P____), v_b_H____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_P____), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_a____, v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b____, v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)), v_b_H____, v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_A_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) V_c_2) (c_Relation_OId__on T_a V_A_2)))) (not (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_x) V_A_2))) (not (= V_c_2 (hAPP (hAPP (c_Product__Type_OPair T_a T_a) B_x) B_x)))) ))) ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a_H____) v_a____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_a____) v_b____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (c_Orderings_Obot__class_Obot (tc_fun tc_Arrow__Order__Mirabelle_Oalt tc_HOL_Obool)), (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) v_b____) v_b_H____), tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_B_2 $$unsorted) (T_b $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (V_A_2 $$unsorted) (T_a $$unsorted)) (let ((_let_0 (c_member (tc_fun T_a T_b)))) (let ((_let_1 (c_FuncSet_OPi T_a T_b V_A_2 V_B_2))) (or (not (forall ((B_w $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member T_a) B_w) V_A_2))) (= (hAPP V_f_2 B_w) (hAPP V_g_2 B_w))) )) (= (hBOOL (hAPP (hAPP _let_0 V_g_2) _let_1)) (hBOOL (hAPP (hAPP _let_0 V_f_2) _let_1)))))) ) 1.21/1.42 ( (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (c_COMBK (tc_fun _let_1 tc_HOL_Obool) (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1) c_Arrow__Order__Mirabelle_OLin))), (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool), v_F, v_F, c_Arrow__Order__Mirabelle_OProf, (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool)) ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((T_a $$unsorted)) (= (c_Orderings_Obot__class_Obot (tc_fun (tc_prod T_a T_a) tc_HOL_Obool)) (c_Relation_OId__on T_a (c_Orderings_Obot__class_Obot (tc_fun T_a tc_HOL_Obool)))) ) 1.21/1.42 ( tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((V_r_2 $$unsorted) (V_aa_2 $$unsorted) (T_a $$unsorted)) (= (hBOOL (hAPP (hAPP (c_member T_a) V_aa_2) (c_Wellfounded_Oacc T_a V_r_2))) (forall ((B_x $$unsorted)) (or (not (hBOOL (hAPP (hAPP (c_member (tc_prod T_a T_a)) (hAPP (hAPP (c_Product__Type_OPair T_a T_a) B_x) V_aa_2)) V_r_2))) (hBOOL (hAPP (hAPP (c_member T_a) B_x) (c_Wellfounded_Oacc T_a V_r_2)))) )) ) 1.21/1.42 ( (hAPP v_F v_Q____), v_a_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_Q____), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_Q____), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_Q____), v_b_H____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_P____), v_a____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ( (hAPP v_F v_P____), v_b____, tc_Arrow__Order__Mirabelle_Oalt ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((B_x $$unsorted)) (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_1 (tc_fun _let_0 tc_HOL_Obool))) (let ((_let_2 (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_1))) (let ((_let_3 (tc_fun _let_1 tc_HOL_Obool))) (or (not (hBOOL (hAPP (hAPP (c_member _let_2) B_x) c_Arrow__Order__Mirabelle_OProf))) (not (= (c_Orderings_Obot__class_Obot _let_3) (hAPP (c_COMBK _let_3 _let_2 c_Arrow__Order__Mirabelle_OLin) B_x)))))))) ) 1.21/1.42 ( v_Q____ ) 1.21/1.42 ( v_P_H____ ) 1.21/1.42 ( v_P____ ) 1.21/1.42 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi (hAPP v_F v_Q____)) ) 1.21/1.42 ( skv_1 ) 1.21/1.42 ( skv_2 ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((B_x $$unsorted) (BOUND_VARIABLE_10487 $$unsorted) (BOUND_VARIABLE_10488 $$unsorted)) (let ((_let_0 (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (or (not (hBOOL (hAPP (hAPP (c_member (tc_fun tc_Arrow__Order__Mirabelle_Oindi (tc_fun _let_0 tc_HOL_Obool))) B_x) c_Arrow__Order__Mirabelle_OProf))) (not (forall ((B_i $$unsorted)) (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) BOUND_VARIABLE_10487) BOUND_VARIABLE_10488)) (hAPP B_x B_i))) )) (hBOOL (hAPP (hAPP (c_member _let_0) (hAPP (hAPP (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) BOUND_VARIABLE_10487) BOUND_VARIABLE_10488)) (hAPP v_F B_x))))) ) 1.21/1.42 ( v_Q____, v_a_H____, v_a____ ) 1.21/1.42 ( v_Q____, v_a____, v_a_H____ ) 1.21/1.42 ( v_Q____, v_a____, v_b____ ) 1.21/1.42 ( v_Q____, v_b____, v_a____ ) 1.21/1.42 ( v_Q____, v_b____, v_b_H____ ) 1.21/1.42 ( v_Q____, v_b_H____, v_b____ ) 1.21/1.42 ( v_P____, v_a____, v_b____ ) 1.21/1.42 ( v_P____, v_b____, v_a____ ) 1.21/1.42 ( v_P____, v_b____, v_b_H____ ) 1.21/1.42 ) 1.21/1.42 (instantiation (forall ((B_x $$unsorted) (BOUND_VARIABLE_11398 $$unsorted) (BOUND_VARIABLE_11399 $$unsorted) (BOUND_VARIABLE_11400 $$unsorted)) (let ((_let_0 (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool))) (let ((_let_1 (c_member (tc_fun tc_Arrow__Order__Mirabelle_Oindi _let_0)))) (let ((_let_2 (c_member (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_3 (c_Product__Type_OPair tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_4 (hAPP _let_3 BOUND_VARIABLE_11399))) (let ((_let_5 (hAPP _let_4 BOUND_VARIABLE_11400))) (let ((_let_6 (hAPP _let_2 _let_5))) (or (not (hBOOL (hAPP (hAPP _let_1 B_x) c_Arrow__Order__Mirabelle_OProf))) (not (hBOOL (hAPP (hAPP _let_1 BOUND_VARIABLE_11398) c_Arrow__Order__Mirabelle_OProf))) (not (forall ((B_i $$unsorted)) (= (hBOOL (hAPP _let_6 (hAPP B_x B_i))) (hBOOL (hAPP _let_6 (hAPP BOUND_VARIABLE_11398 B_i)))) )) (= (hBOOL (hAPP _let_6 (hAPP v_F BOUND_VARIABLE_11398))) (hBOOL (hAPP _let_6 (hAPP v_F B_x)))))))))))) ) 1.21/1.42 ( v_Q____, v_Q____, v_a_H____, v_a____ ) 1.21/1.42 ( v_Q____, v_Q____, v_a_H____, v_b____ ) 1.21/1.42 ( v_Q____, v_Q____, v_a____, v_a_H____ ) 1.21/1.42 ( v_Q____, v_Q____, v_a____, v_b____ ) 1.21/1.42 ( v_Q____, v_Q____, v_a____, v_b_H____ ) 1.21/1.42 ( v_Q____, v_Q____, v_b____, v_a____ ) 1.21/1.42 ( v_Q____, v_Q____, v_b____, v_b_H____ ) 1.21/1.42 ( v_Q____, v_Q____, v_b_H____, v_b____ ) 1.21/1.42 ( v_Q____, v_P_H____, v_a_H____, v_a____ ) 1.21/1.42 ( v_P_H____, v_Q____, v_a____, v_b____ ) 1.21/1.42 ( v_P____, v_P____, v_a_H____, v_b____ ) 1.21/1.42 ( v_P____, v_P____, v_a____, v_a_H____ ) 1.21/1.42 ( v_P____, v_P____, v_a____, v_b_H____ ) 1.21/1.42 ( v_P____, v_P____, v_b____, v_a____ ) 1.21/1.42 ( v_P____, v_P____, v_b____, v_b_H____ ) 1.21/1.42 ( v_P____, v_P____, v_b_H____, v_b____ ) 1.21/1.42 ( v_P____, (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi (hAPP v_F v_Q____)), v_b____, v_b_H____ ) 1.21/1.42 ( (c_COMBK (tc_fun (tc_prod tc_Arrow__Order__Mirabelle_Oalt tc_Arrow__Order__Mirabelle_Oalt) tc_HOL_Obool) tc_Arrow__Order__Mirabelle_Oindi (hAPP v_F v_Q____)), v_P____, v_a____, v_a_H____ ) 1.21/1.42 ( skv_1, skv_1, v_a_H____, v_b____ ) 1.21/1.42 ( skv_1, skv_1, v_a____, v_b_H____ ) 1.21/1.42 ( skv_1, skv_1, v_b____, v_a____ ) 1.21/1.42 ( skv_1, skv_1, v_b_H____, v_b____ ) 1.21/1.42 ( skv_1, skv_2, v_b____, v_a____ ) 1.21/1.42 ( skv_2, skv_1, v_b_H____, v_b____ ) 1.21/1.42 ) 1.21/1.42 % SZS output end Proof for theBenchmark 1.21/1.43 EOF