%   ORIGINAL: 'h4/thm/quotient/LAMBDA_REP_ABS_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: !REL1 abs1 rep1 REL2 abs2 rep2 f1 f2. ((!r 'r\''. REL1 r 'r\'' ==> REL1 r (rep1 (abs1 'r\''))) /\ (!r 'r\''. REL2 r 'r\'' ==> REL2 r (rep2 (abs2 'r\'')))) /\ 'h4/const/quotient/===>' REL1 REL2 f1 f2 ==> 'h4/const/quotient/===>' REL1 REL2 f1 ('h4/const/quotient/-->' abs1 rep2 ('h4/const/quotient/-->' rep1 abs2 f2))
%   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: !REL1 abs1 rep1 REL2 abs2 rep2 f1 f2. ((!r 'r\''. happ (happ REL1 r) 'r\'' ==> happ (happ REL1 r) (happ rep1 (happ abs1 'r\''))) /\ (!r 'r\''. happ (happ REL2 r) 'r\'' ==> happ (happ REL2 r) (happ rep2 (happ abs2 'r\'')))) /\ 'h4/const/quotient/===>' REL1 REL2 f1 f2 ==> 'h4/const/quotient/===>' REL1 REL2 f1 ('h4/const/quotient/-->' abs1 rep2 ('h4/const/quotient/-->' rep1 abs2 f2))
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_3f75315,V_3f75311]: ![F, G]: (![X]: s(V_3f75311,happ(s(fun(V_3f75315,V_3f75311),F),s(V_3f75315,X))) = s(V_3f75311,happ(s(fun(V_3f75315,V_3f75311),G),s(V_3f75315,X))) => s(fun(V_3f75315,V_3f75311),F) = s(fun(V_3f75315,V_3f75311),G))).
fof('h4/thm/quotient/LAMBDA_REP_ABS_RSP_', conjecture, ![C,D,A,B]: ![REL1, Abs1, Rep1, REL2, Abs2, Rep2, F1, F2]: (((![R, V_27r_5c_27_27]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),REL1),s(A,R))),s(A,V_27r_5c_27_27)))) => p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),REL1),s(A,R))),s(A,happ(s(fun(C,A),Rep1),s(C,happ(s(fun(A,C),Abs1),s(A,V_27r_5c_27_27))))))))) & ![R, V_27r_5c_27_27]: (p(s(bool,happ(s(fun(B,bool),happ(s(fun(B,fun(B,bool)),REL2),s(B,R))),s(B,V_27r_5c_27_27)))) => p(s(bool,happ(s(fun(B,bool),happ(s(fun(B,fun(B,bool)),REL2),s(B,R))),s(B,happ(s(fun(D,B),Rep2),s(D,happ(s(fun(B,D),Abs2),s(B,V_27r_5c_27_27)))))))))) & p(s(bool,'h4/const/quotient/===>'(s(fun(A,fun(A,bool)),REL1),s(fun(B,fun(B,bool)),REL2),s(fun(A,B),F1),s(fun(A,B),F2))))) => p(s(bool,'h4/const/quotient/===>'(s(fun(A,fun(A,bool)),REL1),s(fun(B,fun(B,bool)),REL2),s(fun(A,B),F1),s(fun(A,B),'h4/const/quotient/-->'(s(fun(A,C),Abs1),s(fun(D,B),Rep2),s(fun(C,D),'h4/const/quotient/-->'(s(fun(C,A),Rep1),s(fun(B,D),Abs2),s(fun(A,B),F2)))))))))).
