%   ORIGINAL: 'h4/thm/hreal/CUT_NEARTOP_MUL_'
% 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 u. 'h4/const/hreal/hrat_lt' 'h4/const/hrat/hrat_1' u ==> (?x. 'h4/const/hreal/cut' X x /\ ~'h4/const/hreal/cut' X ('h4/const/hrat/hrat_mul' u 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 u. 'h4/const/hreal/hrat_lt' 'h4/const/hrat/hrat_1' u ==> (?x. 'h4/const/hreal/cut' X x /\ ~'h4/const/hreal/cut' X ('h4/const/hrat/hrat_mul' u 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_3f36879,V_3f36875]: ![F, G]: (![X]: s(V_3f36875,happ(s(fun(V_3f36879,V_3f36875),F),s(V_3f36879,X))) = s(V_3f36875,happ(s(fun(V_3f36879,V_3f36875),G),s(V_3f36879,X))) => s(fun(V_3f36879,V_3f36875),F) = s(fun(V_3f36879,V_3f36875),G))).
fof('h4/thm/hreal/CUT_NEARTOP_MUL_', conjecture, ![X, U]: (p(s(bool,'h4/const/hreal/hrat_lt'(s('h4/type/hrat/hrat','h4/const/hrat/hrat_1'),s('h4/type/hrat/hrat',U)))) => ?[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',X),s('h4/type/hrat/hrat','h4/const/hrat/hrat_mul'(s('h4/type/hrat/hrat',U),s('h4/type/hrat/hrat',X0)))))))))).
