%   ORIGINAL: h4/realax/TREAL__LT__WELLDEF
% 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/TRUTH: T
% Assm: h4/bool/EQ__TRANS: !z y x. x = y /\ y = z ==> x = z
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/realax/TREAL__LT__WELLDEFR: !y x2 x1. h4/realax/treal__eq x1 x2 ==> (h4/realax/treal__lt x1 y <=> h4/realax/treal__lt x2 y)
% Assm: h4/realax/TREAL__LT__WELLDEFL: !y2 y1 x. h4/realax/treal__eq y1 y2 ==> (h4/realax/treal__lt x y1 <=> h4/realax/treal__lt x y2)
% Goal: !y2 y1 x2 x1. h4/realax/treal__eq x1 x2 /\ h4/realax/treal__eq y1 y2 ==> (h4/realax/treal__lt x1 y1 <=> h4/realax/treal__lt x2 y2)
%   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_TRUTH]: T
% Assm [h4s_bools_EQu_u_TRANS]: !z y x. x = y /\ y = z ==> x = z
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_realaxs_TREALu_u_LTu_u_WELLDEFR]: !y x2 x1. h4/realax/treal__eq x1 x2 ==> (h4/realax/treal__lt x1 y <=> h4/realax/treal__lt x2 y)
% Assm [h4s_realaxs_TREALu_u_LTu_u_WELLDEFL]: !y2 y1 x. h4/realax/treal__eq y1 y2 ==> (h4/realax/treal__lt x y1 <=> h4/realax/treal__lt x y2)
% Goal: !y2 y1 x2 x1. h4/realax/treal__eq x1 x2 /\ h4/realax/treal__eq y1 y2 ==> (h4/realax/treal__lt x1 y1 <=> h4/realax/treal__lt x2 y2)
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_Q329191,TV_Q329187]: ![V_f, V_g]: (![V_x]: s(TV_Q329187,happ(s(t_fun(TV_Q329191,TV_Q329187),V_f),s(TV_Q329191,V_x))) = s(TV_Q329187,happ(s(t_fun(TV_Q329191,TV_Q329187),V_g),s(TV_Q329191,V_x))) => s(t_fun(TV_Q329191,TV_Q329187),V_f) = s(t_fun(TV_Q329191,TV_Q329187),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EQu_u_TRANS, axiom, ![TV_u_27a]: ![V_z, 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_z)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_z))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_realaxs_TREALu_u_LTu_u_WELLDEFR, axiom, ![V_y, V_x2, V_x1]: (p(s(t_bool,h4s_realaxs_trealu_u_eq(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x1),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x2)))) => s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x1),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_y))) = s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x2),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_y))))).
fof(ah4s_realaxs_TREALu_u_LTu_u_WELLDEFL, axiom, ![V_y2, V_y1, V_x]: (p(s(t_bool,h4s_realaxs_trealu_u_eq(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_y1),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_y2)))) => s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_y1))) = s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_y2))))).
fof(ch4s_realaxs_TREALu_u_LTu_u_WELLDEF, conjecture, ![V_y2, V_y1, V_x2, V_x1]: ((p(s(t_bool,h4s_realaxs_trealu_u_eq(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x1),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x2)))) & p(s(t_bool,h4s_realaxs_trealu_u_eq(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_y1),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_y2))))) => s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x1),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_y1))) = s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_x2),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_y2))))).
