%   ORIGINAL: 'h4/thm/quotient/LAMBDA_PRS1_'
% 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 ==> (!f. (\x. f x) = 'h4/const/quotient/-->' rep1 abs2 (\x. 'h4/const/quotient/-->' abs1 rep2 f x)))
%   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: !_0. (!abs1 rep2 f x. happ (happ (happ (happ _0 abs1) rep2) f) x = 'h4/const/quotient/-->' abs1 rep2 f x) ==> (!R1 abs1 rep1. 'h4/const/quotient/QUOTIENT' R1 abs1 rep1 ==> (!R2 abs2 rep2. 'h4/const/quotient/QUOTIENT' R2 abs2 rep2 ==> (!f x. happ f x = 'h4/const/quotient/-->' rep1 abs2 (happ (happ (happ _0 abs1) rep2) f) x)))
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_3f75190,V_3f75186]: ![F, G]: (![X]: s(V_3f75186,happ(s(fun(V_3f75190,V_3f75186),F),s(V_3f75190,X))) = s(V_3f75186,happ(s(fun(V_3f75190,V_3f75186),G),s(V_3f75190,X))) => s(fun(V_3f75190,V_3f75186),F) = s(fun(V_3f75190,V_3f75186),G))).
fof('h4/thm/quotient/LAMBDA_PRS1_', conjecture, ![A,B,D,C]: ![V__0]: (![Abs1, Rep2, F, X]: s(B,happ(s(fun(A,B),happ(s(fun(fun(C,D),fun(A,B)),happ(s(fun(fun(D,B),fun(fun(C,D),fun(A,B))),happ(s(fun(fun(A,C),fun(fun(D,B),fun(fun(C,D),fun(A,B)))),V__0),s(fun(A,C),Abs1))),s(fun(D,B),Rep2))),s(fun(C,D),F))),s(A,X))) = s(B,'h4/const/quotient/-->'(s(fun(A,C),Abs1),s(fun(D,B),Rep2),s(fun(C,D),F),s(A,X))) => ![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)))) => ![F, X]: s(D,happ(s(fun(C,D),F),s(C,X))) = s(D,'h4/const/quotient/-->'(s(fun(C,A),Rep1),s(fun(B,D),Abs2),s(fun(A,B),happ(s(fun(fun(C,D),fun(A,B)),happ(s(fun(fun(D,B),fun(fun(C,D),fun(A,B))),happ(s(fun(fun(A,C),fun(fun(D,B),fun(fun(C,D),fun(A,B)))),V__0),s(fun(A,C),Abs1))),s(fun(D,B),Rep2))),s(fun(C,D),F))),s(C,X))))))).
