%   ORIGINAL: h4/fmapal/bt__to__orl__ac0_c1
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/relation/WF__EMPTY__REL: h4/relation/WF h4/relation/EMPTY__REL
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/enumeral/bt__case__def_c0: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% Assm: h4/enumeral/bt__case__def_c1: !v f a2 a1 a0. h4/enumeral/bt__CASE (h4/enumeral/node a0 a1 a2) v f = f a0 a1 a2
% Assm: h4/fmapal/bt__to__orl__ac__tupled__primitive: h4/fmapal/bt__to__orl__ac__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\bt__to__orl__ac__tupled a. h4/pair/pair__CASE a (\cmp v1. h4/pair/pair__CASE v1 (\v2 m. h4/enumeral/bt__CASE v2 (h4/combin/I m) (\l v5 r. h4/pair/pair__CASE v5 (\x y. h4/combin/I (h4/fmapal/bt__to__orl__ub__ac cmp l x (h4/list/CONS (h4/pair/_2C x y) (h4/fmapal/bt__to__orl__lb__ac cmp x r m))))))))
% Assm: h4/fmapal/bt__to__orl__ac__curried: !x2 x1 x. h4/fmapal/bt__to__orl__ac x x1 x2 = h4/fmapal/bt__to__orl__ac__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Goal: !y x r m l cmp. h4/fmapal/bt__to__orl__ac cmp (h4/enumeral/node l (h4/pair/_2C x y) r) m = h4/fmapal/bt__to__orl__ub__ac cmp l x (h4/list/CONS (h4/pair/_2C x y) (h4/fmapal/bt__to__orl__lb__ac cmp x r m))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_relations_WFu_u_EMPTYu_u_REL]: h4/relation/WF h4/relation/EMPTY__REL
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_enumerals_btu_u_caseu_u_defu_c0]: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% Assm [h4s_enumerals_btu_u_caseu_u_defu_c1]: !v f a2 a1 a0. h4/enumeral/bt__CASE (h4/enumeral/node a0 a1 a2) v f = happ (happ (happ f a0) a1) a2
% Assm [h4s_fmapals_btu_u_tou_u_orlu_u_acu_u_tupledu_u_primitive]: !_11. (!l cmp x r m y. happ (happ (happ (happ (happ (happ _11 l) cmp) x) r) m) y = h4/combin/I (h4/fmapal/bt__to__orl__ub__ac cmp l x (h4/list/CONS (h4/pair/_2C x y) (h4/fmapal/bt__to__orl__lb__ac cmp x r m)))) ==> (!_10. (!l cmp r m x. happ (happ (happ (happ (happ _10 l) cmp) r) m) x = happ (happ (happ (happ (happ _11 l) cmp) x) r) m) ==> (!_9. (!v5 l cmp m r. happ (happ (happ (happ (happ _9 v5) l) cmp) m) r = h4/pair/pair__CASE v5 (happ (happ (happ (happ _10 l) cmp) r) m)) ==> (!_8. (!l cmp m v5. happ (happ (happ (happ _8 l) cmp) m) v5 = happ (happ (happ (happ _9 v5) l) cmp) m) ==> (!_7. (!cmp m l. happ (happ (happ _7 cmp) m) l = happ (happ (happ _8 l) cmp) m) ==> (!_6. (!v2 cmp m. happ (happ (happ _6 v2) cmp) m = h4/enumeral/bt__CASE v2 (h4/combin/I m) (happ (happ _7 cmp) m)) ==> (!_5. (!cmp v2. happ (happ _5 cmp) v2 = happ (happ _6 v2) cmp) ==> (!_4. (!cmp v1. happ (happ _4 cmp) v1 = h4/pair/pair__CASE v1 (happ _5 cmp)) ==> (!_3. (!cmp. happ _3 cmp = happ _4 cmp) ==> (!_2. (!a. happ _2 a = h4/pair/pair__CASE a _3) ==> (!_1. (!bt__to__orl__ac__tupled. happ _1 bt__to__orl__ac__tupled = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/fmapal/bt__to__orl__ac__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))))))
% Assm [h4s_fmapals_btu_u_tou_u_orlu_u_acu_u_curried]: !x2 x1 x. h4/fmapal/bt__to__orl__ac x x1 x2 = happ h4/fmapal/bt__to__orl__ac__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Goal: !y x r m l cmp. h4/fmapal/bt__to__orl__ac cmp (h4/enumeral/node l (h4/pair/_2C x y) r) m = h4/fmapal/bt__to__orl__ub__ac cmp l x (h4/list/CONS (h4/pair/_2C x y) (h4/fmapal/bt__to__orl__lb__ac cmp x r m))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q219870,TV_Q219866]: ![V_f, V_g]: (![V_x]: s(TV_Q219866,happ(s(t_fun(TV_Q219870,TV_Q219866),V_f),s(TV_Q219870,V_x))) = s(TV_Q219866,happ(s(t_fun(TV_Q219870,TV_Q219866),V_g),s(TV_Q219870,V_x))) => s(t_fun(TV_Q219870,TV_Q219866),V_f) = s(t_fun(TV_Q219870,TV_Q219866),V_g))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_relations_WFu_u_EMPTYu_u_REL, axiom, ![TV_u_27a]: p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_emptyu_u_rel))))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_enumerals_btu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_enumerals_btu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a2, V_a1, V_a0]: s(TV_u_27b,h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_node(s(t_h4s_enumerals_bt(TV_u_27a),V_a0),s(TV_u_27a,V_a1),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2)))).
fof(ah4s_fmapals_btu_u_tou_u_orlu_u_acu_u_tupledu_u_primitive, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_11]: (![V_l, V_cmp, V_x, V_r, V_m, V_y]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_11),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))),s(TV_u_27b,V_y))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))))))))) => ![V_uu_10]: (![V_l, V_cmp, V_r, V_m, V_x]: s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_10),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_11),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))) => ![V_uu_9]: (![V_v5, V_l, V_cmp, V_m, V_r]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_9),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v5))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v5),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_10),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))))) => ![V_uu_8]: (![V_l, V_cmp, V_m, V_v5]: s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_8),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v5))) = s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_9),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v5))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))) => ![V_uu_7]: (![V_cmp, V_m, V_l]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_7),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_8),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))) => ![V_uu_6]: (![V_v2, V_cmp, V_m]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_6),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))),s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_7),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))))) => ![V_uu_5]: (![V_cmp, V_v2]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_5),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_6),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_4]: (![V_cmp, V_v1]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_4),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_v1))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_v1),s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_5),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_cmp]: s(t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_3),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_4),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_a]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_uu_2),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_a))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_a),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_3))) => ![V_uu_1]: (![V_btu_u_tou_u_orlu_u_acu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_acu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_uu_2) => ![V_uu_0]: (![V_R]: s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_bool)),V_R))) = s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_bool)),V_R))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_fmapals_btu_u_tou_u_orlu_u_acu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_1)))))))))))))))).
fof(ah4s_fmapals_btu_u_tou_u_orlu_u_acu_u_curried, axiom, ![TV_u_27a,TV_u_27b]: ![V_x2, V_x1, V_x]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x2))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_fmapals_btu_u_tou_u_orlu_u_acu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x2)))))))).
fof(ch4s_fmapals_btu_u_tou_u_orlu_u_ac0u_c1, conjecture, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_r, V_m, V_l, V_cmp]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_m)))))))).
