%   ORIGINAL: 'h4/thm/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
% Goal: !x1 x2 y1 y2. 'h4/const/realax/treal_eq' x1 x2 /\ 'h4/const/realax/treal_eq' y1 y2 ==> ('h4/const/realax/treal_lt' x1 y1 <=> 'h4/const/realax/treal_lt' x2 y2)
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !x1 x2 y1 y2. 'h4/const/realax/treal_eq' x1 x2 /\ 'h4/const/realax/treal_eq' y1 y2 ==> ('h4/const/realax/treal_lt' x1 y1 <=> 'h4/const/realax/treal_lt' x2 y2)
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f49836,V_3f49832]: ![F, G]: (![X]: s(V_3f49832,happ(s(fun(V_3f49836,V_3f49832),F),s(V_3f49836,X))) = s(V_3f49832,happ(s(fun(V_3f49836,V_3f49832),G),s(V_3f49836,X))) => s(fun(V_3f49836,V_3f49832),F) = s(fun(V_3f49836,V_3f49832),G))).
fof('h4/thm/realax/TREAL_LT_WELLDEF_', conjecture, ![X1, X2, Y1, Y2]: ((p(s(bool,'h4/const/realax/treal_eq'(s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),X1),s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),X2)))) & p(s(bool,'h4/const/realax/treal_eq'(s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),Y1),s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),Y2))))) => s(bool,'h4/const/realax/treal_lt'(s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),X1),s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),Y1))) = s(bool,'h4/const/realax/treal_lt'(s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),X2),s('h4/type/pair/prod'('h4/type/hreal/hreal','h4/type/hreal/hreal'),Y2))))).
