%   ORIGINAL: 'h4/thm/list/APPEND_FRONT_LAST_'
% 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: !l. ~(l = 'h4/const/list/NIL') ==> 'h4/const/list/APPEND' ('h4/const/list/FRONT' l) ('h4/const/list/CONS' ('h4/const/list/LAST' l) 'h4/const/list/NIL') = l
%   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: !l. ~(l = 'h4/const/list/NIL') ==> 'h4/const/list/APPEND' ('h4/const/list/FRONT' l) ('h4/const/list/CONS' ('h4/const/list/LAST' l) 'h4/const/list/NIL') = l
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_3f7014,V_3f7010]: ![F, G]: (![X]: s(V_3f7010,happ(s(fun(V_3f7014,V_3f7010),F),s(V_3f7014,X))) = s(V_3f7010,happ(s(fun(V_3f7014,V_3f7010),G),s(V_3f7014,X))) => s(fun(V_3f7014,V_3f7010),F) = s(fun(V_3f7014,V_3f7010),G))).
fof('h4/thm/list/APPEND_FRONT_LAST_', conjecture, ![A]: ![L]: (~ (s('h4/type/list/list'(A),L) = s('h4/type/list/list'(A),'h4/const/list/NIL')) => s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),'h4/const/list/FRONT'(s('h4/type/list/list'(A),L))),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,'h4/const/list/LAST'(s('h4/type/list/list'(A),L))),s('h4/type/list/list'(A),'h4/const/list/NIL'))))) = s('h4/type/list/list'(A),L))).
