%   ORIGINAL: 'h4/thm/list/TAKE_APPEND2_'
% 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 n. 'h4/const/prim_rec/<' ('h4/const/list/LENGTH' l1) n ==> 'h4/const/list/TAKE' n ('h4/const/list/APPEND' l1 l2) = 'h4/const/list/APPEND' l1 ('h4/const/list/TAKE' ('h4/const/arithmetic/-' n ('h4/const/list/LENGTH' l1)) 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: !l2 l1 n. 'h4/const/prim_rec/<' ('h4/const/list/LENGTH' l1) n ==> 'h4/const/list/TAKE' n ('h4/const/list/APPEND' l1 l2) = 'h4/const/list/APPEND' l1 ('h4/const/list/TAKE' ('h4/const/arithmetic/-' n ('h4/const/list/LENGTH' l1)) 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_3f7190,V_3f7186]: ![F, G]: (![X]: s(V_3f7186,happ(s(fun(V_3f7190,V_3f7186),F),s(V_3f7190,X))) = s(V_3f7186,happ(s(fun(V_3f7190,V_3f7186),G),s(V_3f7190,X))) => s(fun(V_3f7190,V_3f7186),F) = s(fun(V_3f7190,V_3f7186),G))).
fof('h4/thm/list/TAKE_APPEND2_', conjecture, ![A]: ![L2, L1, N]: (p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L1))),s('h4/type/num/num',N)))) => s('h4/type/list/list'(A),'h4/const/list/TAKE'(s('h4/type/num/num',N),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),L1),s('h4/type/list/list'(A),'h4/const/list/TAKE'(s('h4/type/num/num','h4/const/arithmetic/-'(s('h4/type/num/num',N),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L1))))),s('h4/type/list/list'(A),L2))))))).
