%   ORIGINAL: 'h4/thm/quotient_list/FOLDL_PRS_'
% 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 ==> (!l f e. 'h4/const/list/FOLDL' f e l = abs1 ('h4/const/list/FOLDL' ('h4/const/quotient/-->' abs1 ('h4/const/quotient/-->' abs2 rep1) f) (rep1 e) ('h4/const/list/MAP' rep2 l))))
%   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 ==> (!l f e. 'h4/const/list/FOLDL' f e l = happ abs1 ('h4/const/list/FOLDL' (happ ('h4/const/quotient/-->' abs1 ('h4/const/quotient/-->' abs2 rep1)) f) (happ rep1 e) ('h4/const/list/MAP' rep2 l))))
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_3f67961,V_3f67957]: ![F, G]: (![X]: s(V_3f67957,happ(s(fun(V_3f67961,V_3f67957),F),s(V_3f67961,X))) = s(V_3f67957,happ(s(fun(V_3f67961,V_3f67957),G),s(V_3f67961,X))) => s(fun(V_3f67961,V_3f67957),F) = s(fun(V_3f67961,V_3f67957),G))).
fof('h4/thm/quotient_list/FOLDL_PRS_', conjecture, ![A,C,B,D]: ![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)))) => ![L, F, E]: s(C,'h4/const/list/FOLDL'(s(fun(C,fun(D,C)),F),s(C,E),s('h4/type/list/list'(D),L))) = s(C,happ(s(fun(A,C),Abs1),s(A,'h4/const/list/FOLDL'(s(fun(A,fun(B,A)),happ(s(fun(fun(C,fun(D,C)),fun(A,fun(B,A))),'h4/const/quotient/-->'(s(fun(A,C),Abs1),s(fun(fun(D,C),fun(B,A)),'h4/const/quotient/-->'(s(fun(B,D),Abs2),s(fun(C,A),Rep1))))),s(fun(C,fun(D,C)),F))),s(A,happ(s(fun(C,A),Rep1),s(C,E))),s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(D,B),Rep2),s('h4/type/list/list'(D),L)))))))))).
