%   ORIGINAL: 'h4/thm/hreal/HRAT_DOWN2_'
% 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: !x y. ?z. 'h4/const/hreal/hrat_lt' z x /\ 'h4/const/hreal/hrat_lt' z y
%   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: !x y. ?z. 'h4/const/hreal/hrat_lt' z x /\ 'h4/const/hreal/hrat_lt' z y
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_3f36579,V_3f36575]: ![F, G]: (![X]: s(V_3f36575,happ(s(fun(V_3f36579,V_3f36575),F),s(V_3f36579,X))) = s(V_3f36575,happ(s(fun(V_3f36579,V_3f36575),G),s(V_3f36579,X))) => s(fun(V_3f36579,V_3f36575),F) = s(fun(V_3f36579,V_3f36575),G))).
fof('h4/thm/hreal/HRAT_DOWN2_', conjecture, ![X, Y]: ?[Z]: (p(s(bool,'h4/const/hreal/hrat_lt'(s('h4/type/hrat/hrat',Z),s('h4/type/hrat/hrat',X)))) & p(s(bool,'h4/const/hreal/hrat_lt'(s('h4/type/hrat/hrat',Z),s('h4/type/hrat/hrat',Y)))))).
