%   ORIGINAL: 'h4/thm/list/LAST_CONS_e1'
% 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: !x y z. 'h4/const/list/LAST' ('h4/const/list/CONS' x ('h4/const/list/CONS' y z)) = 'h4/const/list/LAST' ('h4/const/list/CONS' y z)
%   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: !x y z. 'h4/const/list/LAST' ('h4/const/list/CONS' x ('h4/const/list/CONS' y z)) = 'h4/const/list/LAST' ('h4/const/list/CONS' y z)
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_3f6814,V_3f6810]: ![F, G]: (![X]: s(V_3f6810,happ(s(fun(V_3f6814,V_3f6810),F),s(V_3f6814,X))) = s(V_3f6810,happ(s(fun(V_3f6814,V_3f6810),G),s(V_3f6814,X))) => s(fun(V_3f6814,V_3f6810),F) = s(fun(V_3f6814,V_3f6810),G))).
fof('h4/thm/list/LAST_CONS_e1', conjecture, ![A]: ![X, Y, Z]: s(A,'h4/const/list/LAST'(s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,X),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,Y),s('h4/type/list/list'(A),Z))))))) = s(A,'h4/const/list/LAST'(s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,Y),s('h4/type/list/list'(A),Z)))))).
