%   ORIGINAL: h4/fmapal/ORL__bt0_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/ORL__bt__tupled__primitive: h4/fmapal/ORL__bt__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\ORL__bt__tupled a. h4/pair/pair__CASE a (\cmp v1. h4/enumeral/bt__CASE v1 (h4/combin/I T) (\l v3 r. h4/pair/pair__CASE v3 (\x y. h4/combin/I (h4/fmapal/ORL__bt__ub cmp l x /\ h4/fmapal/ORL__bt__lb cmp x r)))))
% Assm: h4/fmapal/ORL__bt__curried: !x1 x. h4/fmapal/ORL__bt x x1 <=> h4/fmapal/ORL__bt__tupled (h4/pair/_2C x x1)
% Goal: !y x r l cmp. h4/fmapal/ORL__bt cmp (h4/enumeral/node l (h4/pair/_2C x y) r) <=> h4/fmapal/ORL__bt__ub cmp l x /\ h4/fmapal/ORL__bt__lb cmp x r
%   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_ORLu_u_btu_u_tupledu_u_primitive]: !_9. (!l cmp x r y. ?v. (v <=> h4/fmapal/ORL__bt__ub cmp l x /\ h4/fmapal/ORL__bt__lb cmp x r) /\ (happ (happ (happ (happ (happ _9 l) cmp) x) r) y <=> h4/combin/I v)) ==> (!_8. (!l cmp r x. happ (happ (happ (happ _8 l) cmp) r) x = happ (happ (happ (happ _9 l) cmp) x) r) ==> (!_7. (!v3 l cmp r. happ (happ (happ (happ _7 v3) l) cmp) r <=> h4/pair/pair__CASE v3 (happ (happ (happ _8 l) cmp) r)) ==> (!_6. (!l cmp v3. happ (happ (happ _6 l) cmp) v3 = happ (happ (happ _7 v3) l) cmp) ==> (!_5. (!cmp l. happ (happ _5 cmp) l = happ (happ _6 l) cmp) ==> (!_4. (!cmp v1. happ (happ _4 cmp) v1 <=> h4/enumeral/bt__CASE v1 (h4/combin/I T) (happ _5 cmp)) ==> (!_3. (!cmp. happ _3 cmp = happ _4 cmp) ==> (!_2. (!a. happ _2 a <=> h4/pair/pair__CASE a _3) ==> (!_1. (!ORL__bt__tupled. happ _1 ORL__bt__tupled = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/fmapal/ORL__bt__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))))
% Assm [h4s_fmapals_ORLu_u_btu_u_curried]: !x1 x. h4/fmapal/ORL__bt x x1 <=> happ h4/fmapal/ORL__bt__tupled (h4/pair/_2C x x1)
% Goal: !y x r l cmp. h4/fmapal/ORL__bt cmp (h4/enumeral/node l (h4/pair/_2C x y) r) <=> h4/fmapal/ORL__bt__ub cmp l x /\ h4/fmapal/ORL__bt__lb cmp x r
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_Q221061,TV_Q221057]: ![V_f, V_g]: (![V_x]: s(TV_Q221057,happ(s(t_fun(TV_Q221061,TV_Q221057),V_f),s(TV_Q221061,V_x))) = s(TV_Q221057,happ(s(t_fun(TV_Q221061,TV_Q221057),V_g),s(TV_Q221061,V_x))) => s(t_fun(TV_Q221061,TV_Q221057),V_f) = s(t_fun(TV_Q221061,TV_Q221057),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_ORLu_u_btu_u_tupledu_u_primitive, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_9]: (![V_l, V_cmp, V_x, V_r, V_y]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_fmapals_orlu_u_btu_u_ub(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)))) & p(s(t_bool,h4s_fmapals_orlu_u_btu_u_lb(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_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_bool)),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(TV_u_27b,t_bool))),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(TV_u_27b,t_bool)))),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(TV_u_27b,t_bool))))),V_uu_9),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(TV_u_27b,V_y))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_8]: (![V_l, V_cmp, V_r, V_x]: s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),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(TV_u_27a,t_fun(TV_u_27b,t_bool)))),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(TV_u_27a,t_fun(TV_u_27b,t_bool))))),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_bool)),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(TV_u_27b,t_bool))),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(TV_u_27b,t_bool)))),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(TV_u_27b,t_bool))))),V_uu_9),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))) => ![V_uu_7]: (![V_v3, V_l, V_cmp, V_r]: s(t_bool,happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),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_bool)),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_bool))),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)))),V_uu_7),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v3))),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_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v3),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),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(TV_u_27a,t_fun(TV_u_27b,t_bool)))),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(TV_u_27a,t_fun(TV_u_27b,t_bool))))),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))))) => ![V_uu_6]: (![V_l, V_cmp, V_v3]: s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),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_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),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_bool))),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_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_bool)))),V_uu_6),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_pairs_prod(TV_u_27a,TV_u_27b),V_v3))) = s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),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_bool)),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_bool))),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)))),V_uu_7),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v3))),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))) => ![V_uu_5]: (![V_cmp, 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_bool)),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_bool))),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_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_bool)))),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_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_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),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_bool))),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_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_bool)))),V_uu_6),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))) => ![V_uu_4]: (![V_cmp, V_v1]: s(t_bool,happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),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_bool)),V_uu_4),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_v1))) = s(t_bool,h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v1),s(t_bool,h4s_combins_i(s(t_bool,t))),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_bool))),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_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_bool)))),V_uu_5),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_cmp]: s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),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_bool)),V_uu_3),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),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_bool)),V_uu_4),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_a]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_uu_2),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_a))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),V_uu_3))) => ![V_uu_1]: (![V_ORLu_u_btu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_btu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),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_enumerals_bt(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_enumerals_bt(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_enumerals_bt(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_enumerals_bt(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_enumerals_bt(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_enumerals_bt(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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),h4s_fmapals_orlu_u_btu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(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_enumerals_bt(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_enumerals_bt(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_enumerals_bt(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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_uu_1)))))))))))))).
fof(ah4s_fmapals_ORLu_u_btu_u_curried, axiom, ![TV_u_27a,TV_u_27b]: ![V_x1, V_x]: s(t_bool,h4s_fmapals_orlu_u_bt(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_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),h4s_fmapals_orlu_u_btu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1)))))).
fof(ch4s_fmapals_ORLu_u_bt0u_c1, conjecture, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_r, V_l, V_cmp]: (p(s(t_bool,h4s_fmapals_orlu_u_bt(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)))))) <=> (p(s(t_bool,h4s_fmapals_orlu_u_btu_u_ub(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)))) & p(s(t_bool,h4s_fmapals_orlu_u_btu_u_lb(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))))))).
