%   ORIGINAL: 'h4/thm/list/LIST_REL_CONS1_'
% 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: !xs t h R. 'h4/const/list/LIST_REL' R ('h4/const/list/CONS' h t) xs <=> (?'h\'' 't\''. xs = 'h4/const/list/CONS' 'h\'' 't\'' /\ R h 'h\'' /\ 'h4/const/list/LIST_REL' R t 't\'')
%   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: !xs t h R. 'h4/const/list/LIST_REL' R ('h4/const/list/CONS' h t) xs <=> (?'h\'' 't\''. xs = 'h4/const/list/CONS' 'h\'' 't\'' /\ happ (happ R h) 'h\'' /\ 'h4/const/list/LIST_REL' R t 't\'')
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_3f5814,V_3f5810]: ![F, G]: (![X]: s(V_3f5810,happ(s(fun(V_3f5814,V_3f5810),F),s(V_3f5814,X))) = s(V_3f5810,happ(s(fun(V_3f5814,V_3f5810),G),s(V_3f5814,X))) => s(fun(V_3f5814,V_3f5810),F) = s(fun(V_3f5814,V_3f5810),G))).
fof('h4/thm/list/LIST_REL_CONS1_', conjecture, ![A,B]: ![Xs, T, H, R]: (p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),R),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H),s('h4/type/list/list'(A),T))),s('h4/type/list/list'(B),Xs)))) <=> ?[V_27h_5c_27_27, V_27t_5c_27_27]: (s('h4/type/list/list'(B),Xs) = s('h4/type/list/list'(B),'h4/const/list/CONS'(s(B,V_27h_5c_27_27),s('h4/type/list/list'(B),V_27t_5c_27_27))) & (p(s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),R),s(A,H))),s(B,V_27h_5c_27_27)))) & p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),R),s('h4/type/list/list'(A),T),s('h4/type/list/list'(B),V_27t_5c_27_27)))))))).
