%   ORIGINAL: 'h4/thm/list/TAKE_SUM_'
% 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 m l. 'h4/const/arithmetic/<=' ('h4/const/arithmetic/+' n m) ('h4/const/list/LENGTH' l) ==> 'h4/const/list/TAKE' ('h4/const/arithmetic/+' n m) l = 'h4/const/list/APPEND' ('h4/const/list/TAKE' n l) ('h4/const/list/TAKE' m ('h4/const/list/DROP' n l))
%   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 m l. 'h4/const/arithmetic/<=' ('h4/const/arithmetic/+' n m) ('h4/const/list/LENGTH' l) ==> 'h4/const/list/TAKE' ('h4/const/arithmetic/+' n m) l = 'h4/const/list/APPEND' ('h4/const/list/TAKE' n l) ('h4/const/list/TAKE' m ('h4/const/list/DROP' n l))
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_3f12094,V_3f12090]: ![F, G]: (![X]: s(V_3f12090,happ(s(fun(V_3f12094,V_3f12090),F),s(V_3f12094,X))) = s(V_3f12090,happ(s(fun(V_3f12094,V_3f12090),G),s(V_3f12094,X))) => s(fun(V_3f12094,V_3f12090),F) = s(fun(V_3f12094,V_3f12090),G))).
fof('h4/thm/list/TAKE_SUM_', conjecture, ![A]: ![N, M, L]: (p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',N),s('h4/type/num/num',M))),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L)))))) => 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',M))),s('h4/type/list/list'(A),L))) = s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),'h4/const/list/TAKE'(s('h4/type/num/num',N),s('h4/type/list/list'(A),L))),s('h4/type/list/list'(A),'h4/const/list/TAKE'(s('h4/type/num/num',M),s('h4/type/list/list'(A),'h4/const/list/DROP'(s('h4/type/num/num',N),s('h4/type/list/list'(A),L))))))))).
