%   ORIGINAL: 'h4/thm/list/LAST_APPEND_CONS_'
% 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: !h l1 l2. 'h4/const/list/LAST' ('h4/const/list/APPEND' l1 ('h4/const/list/CONS' h l2)) = 'h4/const/list/LAST' ('h4/const/list/CONS' h l2)
%   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: !h l1 l2. 'h4/const/list/LAST' ('h4/const/list/APPEND' l1 ('h4/const/list/CONS' h l2)) = 'h4/const/list/LAST' ('h4/const/list/CONS' h l2)
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_3f7065,V_3f7061]: ![F, G]: (![X]: s(V_3f7061,happ(s(fun(V_3f7065,V_3f7061),F),s(V_3f7065,X))) = s(V_3f7061,happ(s(fun(V_3f7065,V_3f7061),G),s(V_3f7065,X))) => s(fun(V_3f7065,V_3f7061),F) = s(fun(V_3f7065,V_3f7061),G))).
fof('h4/thm/list/LAST_APPEND_CONS_', conjecture, ![A]: ![H, L1, L2]: s(A,'h4/const/list/LAST'(s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H),s('h4/type/list/list'(A),L2))))))) = s(A,'h4/const/list/LAST'(s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H),s('h4/type/list/list'(A),L2)))))).
