%   ORIGINAL: 'h4/thm/list/list_Axiom_'
% 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: !f0 f1. ?fn. fn 'h4/const/list/NIL' = f0 /\ (!a0 a1. fn ('h4/const/list/CONS' a0 a1) = f1 a0 a1 (fn a1))
%   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: !f0 f1. ?fn. happ fn 'h4/const/list/NIL' = f0 /\ (!a0 a1. happ fn ('h4/const/list/CONS' a0 a1) = happ (happ (happ f1 a0) a1) (happ fn a1))
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_3f2488,V_3f2484]: ![F, G]: (![X]: s(V_3f2484,happ(s(fun(V_3f2488,V_3f2484),F),s(V_3f2488,X))) = s(V_3f2484,happ(s(fun(V_3f2488,V_3f2484),G),s(V_3f2488,X))) => s(fun(V_3f2488,V_3f2484),F) = s(fun(V_3f2488,V_3f2484),G))).
fof('h4/thm/list/list_Axiom_', conjecture, ![B,A]: ![F0, F1]: ?[Fn]: (s(B,happ(s(fun('h4/type/list/list'(A),B),Fn),s('h4/type/list/list'(A),'h4/const/list/NIL'))) = s(B,F0) & ![A0, A1]: s(B,happ(s(fun('h4/type/list/list'(A),B),Fn),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,A0),s('h4/type/list/list'(A),A1))))) = s(B,happ(s(fun(B,B),happ(s(fun('h4/type/list/list'(A),fun(B,B)),happ(s(fun(A,fun('h4/type/list/list'(A),fun(B,B))),F1),s(A,A0))),s('h4/type/list/list'(A),A1))),s(B,happ(s(fun('h4/type/list/list'(A),B),Fn),s('h4/type/list/list'(A),A1))))))).
