%   ORIGINAL: 'h4/thm/hreal/HREAL_LT_LEMMA_'
% 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. 'h4/const/hreal/hreal_lt' X Y ==> (?x. ~'h4/const/hreal/cut' X x /\ 'h4/const/hreal/cut' Y x)
%   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. 'h4/const/hreal/hreal_lt' X Y ==> (?x. ~'h4/const/hreal/cut' X x /\ 'h4/const/hreal/cut' Y x)
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_3f37179,V_3f37175]: ![F, G]: (![X]: s(V_3f37175,happ(s(fun(V_3f37179,V_3f37175),F),s(V_3f37179,X))) = s(V_3f37175,happ(s(fun(V_3f37179,V_3f37175),G),s(V_3f37179,X))) => s(fun(V_3f37179,V_3f37175),F) = s(fun(V_3f37179,V_3f37175),G))).
fof('h4/thm/hreal/HREAL_LT_LEMMA_', conjecture, ![X, Y]: (p(s(bool,'h4/const/hreal/hreal_lt'(s('h4/type/hreal/hreal',X),s('h4/type/hreal/hreal',Y)))) => ?[X0]: (~ (p(s(bool,'h4/const/hreal/cut'(s('h4/type/hreal/hreal',X),s('h4/type/hrat/hrat',X0))))) & p(s(bool,'h4/const/hreal/cut'(s('h4/type/hreal/hreal',Y),s('h4/type/hrat/hrat',X0))))))).
