%   ORIGINAL: 'h4/thm/hreal/HREAL_MUL_ISACUT_'
% 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/isacut' (\w. ?x y. w = 'h4/const/hrat/hrat_mul' x y /\ 'h4/const/hreal/cut' X x /\ 'h4/const/hreal/cut' Y 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: !_0. (!X Y w. happ (happ (happ _0 X) Y) w <=> (?x y. w = 'h4/const/hrat/hrat_mul' x y /\ 'h4/const/hreal/cut' X x /\ 'h4/const/hreal/cut' Y y)) ==> (!X Y. 'h4/const/hreal/isacut' (happ (happ _0 X) 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_3f36954,V_3f36950]: ![F, G]: (![X]: s(V_3f36950,happ(s(fun(V_3f36954,V_3f36950),F),s(V_3f36954,X))) = s(V_3f36950,happ(s(fun(V_3f36954,V_3f36950),G),s(V_3f36954,X))) => s(fun(V_3f36954,V_3f36950),F) = s(fun(V_3f36954,V_3f36950),G))).
fof('h4/thm/hreal/HREAL_MUL_ISACUT_', conjecture, ![V__0]: (![X, Y, W]: (p(s(bool,happ(s(fun('h4/type/hrat/hrat',bool),happ(s(fun('h4/type/hreal/hreal',fun('h4/type/hrat/hrat',bool)),happ(s(fun('h4/type/hreal/hreal',fun('h4/type/hreal/hreal',fun('h4/type/hrat/hrat',bool))),V__0),s('h4/type/hreal/hreal',X))),s('h4/type/hreal/hreal',Y))),s('h4/type/hrat/hrat',W)))) <=> ?[X0, Y0]: (s('h4/type/hrat/hrat',W) = s('h4/type/hrat/hrat','h4/const/hrat/hrat_mul'(s('h4/type/hrat/hrat',X0),s('h4/type/hrat/hrat',Y0))) & (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',Y0))))))) => ![X, Y]: p(s(bool,'h4/const/hreal/isacut'(s(fun('h4/type/hrat/hrat',bool),happ(s(fun('h4/type/hreal/hreal',fun('h4/type/hrat/hrat',bool)),happ(s(fun('h4/type/hreal/hreal',fun('h4/type/hreal/hreal',fun('h4/type/hrat/hrat',bool))),V__0),s('h4/type/hreal/hreal',X))),s('h4/type/hreal/hreal',Y)))))))).
