%   ORIGINAL: 'h4/thm/list/APPEND_EQ_APPEND_'
% 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: !m2 m1 l2 l1. 'h4/const/list/APPEND' l1 l2 = 'h4/const/list/APPEND' m1 m2 <=> (?l. l1 = 'h4/const/list/APPEND' m1 l /\ m2 = 'h4/const/list/APPEND' l l2) \/ (?l. m1 = 'h4/const/list/APPEND' l1 l /\ l2 = 'h4/const/list/APPEND' l m2)
%   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: !m2 m1 l2 l1. 'h4/const/list/APPEND' l1 l2 = 'h4/const/list/APPEND' m1 m2 <=> (?l. l1 = 'h4/const/list/APPEND' m1 l /\ m2 = 'h4/const/list/APPEND' l l2) \/ (?l. m1 = 'h4/const/list/APPEND' l1 l /\ l2 = 'h4/const/list/APPEND' l m2)
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_3f10216,V_3f10212]: ![F, G]: (![X]: s(V_3f10212,happ(s(fun(V_3f10216,V_3f10212),F),s(V_3f10216,X))) = s(V_3f10212,happ(s(fun(V_3f10216,V_3f10212),G),s(V_3f10216,X))) => s(fun(V_3f10216,V_3f10212),F) = s(fun(V_3f10216,V_3f10212),G))).
fof('h4/thm/list/APPEND_EQ_APPEND_', conjecture, ![A]: ![M2, M1, L2, L1]: (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/APPEND'(s('h4/type/list/list'(A),M1),s('h4/type/list/list'(A),M2))) <=> (?[L]: (s('h4/type/list/list'(A),L1) = s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),M1),s('h4/type/list/list'(A),L))) & s('h4/type/list/list'(A),M2) = s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L),s('h4/type/list/list'(A),L2)))) | ?[L]: (s('h4/type/list/list'(A),M1) = s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(A),L))) & s('h4/type/list/list'(A),L2) = s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L),s('h4/type/list/list'(A),M2))))))).
