%   ORIGINAL: 'h4/thm/option/OPTREL_MONO_'
% 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: !y x Q P. (!x0 y0. P x0 y0 ==> Q x0 y0) ==> 'h4/const/option/OPTREL' P x y ==> 'h4/const/option/OPTREL' Q x 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: !y x Q P. (!x0 y0. happ (happ P x0) y0 ==> happ (happ Q x0) y0) ==> 'h4/const/option/OPTREL' P x y ==> 'h4/const/option/OPTREL' Q 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_3f100707,V_3f100703]: ![F, G]: (![X]: s(V_3f100703,happ(s(fun(V_3f100707,V_3f100703),F),s(V_3f100707,X))) = s(V_3f100703,happ(s(fun(V_3f100707,V_3f100703),G),s(V_3f100707,X))) => s(fun(V_3f100707,V_3f100703),F) = s(fun(V_3f100707,V_3f100703),G))).
fof('h4/thm/option/OPTREL_MONO_', conjecture, ![A,B]: ![Y, X, Q, P]: (![X0, Y0]: (p(s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),P),s(A,X0))),s(B,Y0)))) => p(s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),Q),s(A,X0))),s(B,Y0))))) => (p(s(bool,'h4/const/option/OPTREL'(s(fun(A,fun(B,bool)),P),s('h4/type/option/option'(A),X),s('h4/type/option/option'(B),Y)))) => p(s(bool,'h4/const/option/OPTREL'(s(fun(A,fun(B,bool)),Q),s('h4/type/option/option'(A),X),s('h4/type/option/option'(B),Y))))))).
