%   ORIGINAL: 'h4/thm/relation/EQC_MONOTONE_'
% 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 'R\'' R. (!x0 y0. R x0 y0 ==> 'R\'' x0 y0) ==> 'h4/const/relation/EQC' R x y ==> 'h4/const/relation/EQC' 'R\'' 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 'R\'' R. (!x0 y0. happ (happ R x0) y0 ==> happ (happ 'R\'' x0) y0) ==> 'h4/const/relation/EQC' R x y ==> 'h4/const/relation/EQC' 'R\'' 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_3f27753,V_3f27749]: ![F, G]: (![X]: s(V_3f27749,happ(s(fun(V_3f27753,V_3f27749),F),s(V_3f27753,X))) = s(V_3f27749,happ(s(fun(V_3f27753,V_3f27749),G),s(V_3f27753,X))) => s(fun(V_3f27753,V_3f27749),F) = s(fun(V_3f27753,V_3f27749),G))).
fof('h4/thm/relation/EQC_MONOTONE_', conjecture, ![A]: ![Y, X, V_27R_5c_27_27, R]: (![X0, Y0]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,X0))),s(A,Y0)))) => p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),V_27R_5c_27_27),s(A,X0))),s(A,Y0))))) => (p(s(bool,'h4/const/relation/EQC'(s(fun(A,fun(A,bool)),R),s(A,X),s(A,Y)))) => p(s(bool,'h4/const/relation/EQC'(s(fun(A,fun(A,bool)),V_27R_5c_27_27),s(A,X),s(A,Y))))))).
