%   ORIGINAL: 'h4/thm/list/APPEND_11_LENGTH_0'
% 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: !l1 l2 'l1\'' 'l2\''. 'h4/const/list/LENGTH' l1 = 'h4/const/list/LENGTH' 'l1\'' ==> ('h4/const/list/APPEND' l1 l2 = 'h4/const/list/APPEND' 'l1\'' 'l2\'' <=> l1 = 'l1\'' /\ l2 = '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: !l1 l2 'l1\'' 'l2\''. 'h4/const/list/LENGTH' l1 = 'h4/const/list/LENGTH' 'l1\'' ==> ('h4/const/list/APPEND' l1 l2 = 'h4/const/list/APPEND' 'l1\'' 'l2\'' <=> l1 = 'l1\'' /\ l2 = '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_3f4563,V_3f4559]: ![F, G]: (![X]: s(V_3f4559,happ(s(fun(V_3f4563,V_3f4559),F),s(V_3f4563,X))) = s(V_3f4559,happ(s(fun(V_3f4563,V_3f4559),G),s(V_3f4563,X))) => s(fun(V_3f4563,V_3f4559),F) = s(fun(V_3f4563,V_3f4559),G))).
fof('h4/thm/list/APPEND_11_LENGTH_0', conjecture, ![A]: ![L1, L2, V_27l1_5c_27_27, V_27l2_5c_27_27]: (s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L1))) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),V_27l1_5c_27_27))) => (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),V_27l1_5c_27_27),s('h4/type/list/list'(A),V_27l2_5c_27_27))) <=> (s('h4/type/list/list'(A),L1) = s('h4/type/list/list'(A),V_27l1_5c_27_27) & s('h4/type/list/list'(A),L2) = s('h4/type/list/list'(A),V_27l2_5c_27_27))))).
