%   ORIGINAL: 'h4/thm/quotient/COND_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: !R abs rep. 'h4/const/quotient/QUOTIENT' R abs rep ==> (!a1 a2 b1 b2 c1 c2. (a1 <=> a2) /\ R b1 b2 /\ R c1 c2 ==> R ('h4/const/bool/COND' a1 b1 c1) ('h4/const/bool/COND' a2 b2 c2))
%   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: !R abs rep. 'h4/const/quotient/QUOTIENT' R abs rep ==> (!a1 a2 b1 b2 c1 c2. (a1 <=> a2) /\ happ (happ R b1) b2 /\ happ (happ R c1) c2 ==> happ (happ R ('h4/const/bool/COND' a1 b1 c1)) ('h4/const/bool/COND' a2 b2 c2))
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_3f75590,V_3f75586]: ![F, G]: (![X]: s(V_3f75586,happ(s(fun(V_3f75590,V_3f75586),F),s(V_3f75590,X))) = s(V_3f75586,happ(s(fun(V_3f75590,V_3f75586),G),s(V_3f75590,X))) => s(fun(V_3f75590,V_3f75586),F) = s(fun(V_3f75590,V_3f75586),G))).
fof('h4/thm/quotient/COND_RSP_', conjecture, ![B,A]: ![R, Abs, Rep]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(A,fun(A,bool)),R),s(fun(A,B),Abs),s(fun(B,A),Rep)))) => ![A1, A2, B1, B2, C1, C2]: ((s(bool,A1) = s(bool,A2) & (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,B1))),s(A,B2)))) & p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,C1))),s(A,C2)))))) => p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,'h4/const/bool/COND'(s(bool,A1),s(A,B1),s(A,C1))))),s(A,'h4/const/bool/COND'(s(bool,A2),s(A,B2),s(A,C2))))))))).
