%   ORIGINAL: 'h4/thm/list/APPEND_EQ_SING_'
% 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: !l2 l1 e. 'h4/const/list/APPEND' l1 l2 = 'h4/const/list/CONS' e 'h4/const/list/NIL' <=> l1 = 'h4/const/list/CONS' e 'h4/const/list/NIL' /\ l2 = 'h4/const/list/NIL' \/ l1 = 'h4/const/list/NIL' /\ l2 = 'h4/const/list/CONS' e 'h4/const/list/NIL'
%   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: !l2 l1 e. 'h4/const/list/APPEND' l1 l2 = 'h4/const/list/CONS' e 'h4/const/list/NIL' <=> l1 = 'h4/const/list/CONS' e 'h4/const/list/NIL' /\ l2 = 'h4/const/list/NIL' \/ l1 = 'h4/const/list/NIL' /\ l2 = 'h4/const/list/CONS' e 'h4/const/list/NIL'
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_3f4463,V_3f4459]: ![F, G]: (![X]: s(V_3f4459,happ(s(fun(V_3f4463,V_3f4459),F),s(V_3f4463,X))) = s(V_3f4459,happ(s(fun(V_3f4463,V_3f4459),G),s(V_3f4463,X))) => s(fun(V_3f4463,V_3f4459),F) = s(fun(V_3f4463,V_3f4459),G))).
fof('h4/thm/list/APPEND_EQ_SING_', conjecture, ![A]: ![L2, L1, E]: (s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(A),L2))) = s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,E),s('h4/type/list/list'(A),'h4/const/list/NIL'))) <=> ((s('h4/type/list/list'(A),L1) = s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,E),s('h4/type/list/list'(A),'h4/const/list/NIL'))) & s('h4/type/list/list'(A),L2) = s('h4/type/list/list'(A),'h4/const/list/NIL')) | (s('h4/type/list/list'(A),L1) = s('h4/type/list/list'(A),'h4/const/list/NIL') & s('h4/type/list/list'(A),L2) = s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,E),s('h4/type/list/list'(A),'h4/const/list/NIL'))))))).
