%   ORIGINAL: 'h4/thm/quotient_list/CONS_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 ==> (!t1 t2 h1 h2. R h1 h2 /\ 'h4/const/list/LIST_REL' R t1 t2 ==> 'h4/const/list/LIST_REL' R ('h4/const/list/CONS' h1 t1) ('h4/const/list/CONS' h2 t2))
%   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 ==> (!t1 t2 h1 h2. happ (happ R h1) h2 /\ 'h4/const/list/LIST_REL' R t1 t2 ==> 'h4/const/list/LIST_REL' R ('h4/const/list/CONS' h1 t1) ('h4/const/list/CONS' h2 t2))
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_3f67436,V_3f67432]: ![F, G]: (![X]: s(V_3f67432,happ(s(fun(V_3f67436,V_3f67432),F),s(V_3f67436,X))) = s(V_3f67432,happ(s(fun(V_3f67436,V_3f67432),G),s(V_3f67436,X))) => s(fun(V_3f67436,V_3f67432),F) = s(fun(V_3f67436,V_3f67432),G))).
fof('h4/thm/quotient_list/CONS_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)))) => ![T1, T2, H1, H2]: ((p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,H1))),s(A,H2)))) & p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(A,bool)),R),s('h4/type/list/list'(A),T1),s('h4/type/list/list'(A),T2))))) => p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(A,bool)),R),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H1),s('h4/type/list/list'(A),T1))),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H2),s('h4/type/list/list'(A),T2))))))))).
