%   ORIGINAL: 'h4/thm/rich_list/TAKE_APPEND1_'
% 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: !n l1. 'h4/const/arithmetic/<=' n ('h4/const/list/LENGTH' l1) ==> (!l2. 'h4/const/list/TAKE' n ('h4/const/list/APPEND' l1 l2) = 'h4/const/list/TAKE' n l1)
%   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: !n l1. 'h4/const/arithmetic/<=' n ('h4/const/list/LENGTH' l1) ==> (!l2. 'h4/const/list/TAKE' n ('h4/const/list/APPEND' l1 l2) = 'h4/const/list/TAKE' n l1)
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_3f55211,V_3f55207]: ![F, G]: (![X]: s(V_3f55207,happ(s(fun(V_3f55211,V_3f55207),F),s(V_3f55211,X))) = s(V_3f55207,happ(s(fun(V_3f55211,V_3f55207),G),s(V_3f55211,X))) => s(fun(V_3f55211,V_3f55207),F) = s(fun(V_3f55211,V_3f55207),G))).
fof('h4/thm/rich_list/TAKE_APPEND1_', conjecture, ![A]: ![N, L1]: (p(s(bool,'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)))))) => ![L2]: 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/TAKE'(s('h4/type/num/num',N),s('h4/type/list/list'(A),L1))))).
