%   ORIGINAL: 'h4/thm/quotient/K_RSP_'
% 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: !R1 abs1 rep1. 'h4/const/quotient/QUOTIENT' R1 abs1 rep1 ==> (!R2 abs2 rep2. 'h4/const/quotient/QUOTIENT' R2 abs2 rep2 ==> (!x1 x2 y1 y2. R1 x1 x2 /\ R2 y1 y2 ==> R1 ('h4/const/combin/K' x1 y1) ('h4/const/combin/K' x2 y2)))
%   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: !R1 abs1 rep1. 'h4/const/quotient/QUOTIENT' R1 abs1 rep1 ==> (!R2 abs2 rep2. 'h4/const/quotient/QUOTIENT' R2 abs2 rep2 ==> (!x1 x2 y1 y2. happ (happ R1 x1) x2 /\ happ (happ R2 y1) y2 ==> happ (happ R1 ('h4/const/combin/K' x1 y1)) ('h4/const/combin/K' x2 y2)))
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_3f75840,V_3f75836]: ![F, G]: (![X]: s(V_3f75836,happ(s(fun(V_3f75840,V_3f75836),F),s(V_3f75840,X))) = s(V_3f75836,happ(s(fun(V_3f75840,V_3f75836),G),s(V_3f75840,X))) => s(fun(V_3f75840,V_3f75836),F) = s(fun(V_3f75840,V_3f75836),G))).
fof('h4/thm/quotient/K_RSP_', conjecture, ![C,D,A,B]: ![R1, Abs1, Rep1]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(A,fun(A,bool)),R1),s(fun(A,C),Abs1),s(fun(C,A),Rep1)))) => ![R2, Abs2, Rep2]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(B,fun(B,bool)),R2),s(fun(B,D),Abs2),s(fun(D,B),Rep2)))) => ![X1, X2, Y1, Y2]: ((p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R1),s(A,X1))),s(A,X2)))) & p(s(bool,happ(s(fun(B,bool),happ(s(fun(B,fun(B,bool)),R2),s(B,Y1))),s(B,Y2))))) => p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R1),s(A,'h4/const/combin/K'(s(A,X1),s(B,Y1))))),s(A,'h4/const/combin/K'(s(A,X2),s(B,Y2)))))))))).
