%   ORIGINAL: 'h4/thm/list/TAKE_compute_3'
% 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 h t. 'h4/const/list/TAKE' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' n)) ('h4/const/list/CONS' h t) = 'h4/const/list/CONS' h ('h4/const/list/TAKE' ('h4/const/arithmetic/-' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' n)) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) t)
%   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 h t. 'h4/const/list/TAKE' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' n)) ('h4/const/list/CONS' h t) = 'h4/const/list/CONS' h ('h4/const/list/TAKE' ('h4/const/arithmetic/-' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' n)) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) t)
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_3f12994,V_3f12990]: ![F, G]: (![X]: s(V_3f12990,happ(s(fun(V_3f12994,V_3f12990),F),s(V_3f12994,X))) = s(V_3f12990,happ(s(fun(V_3f12994,V_3f12990),G),s(V_3f12994,X))) => s(fun(V_3f12994,V_3f12990),F) = s(fun(V_3f12994,V_3f12990),G))).
fof('h4/thm/list/TAKE_compute_3', conjecture, ![C]: ![N, H, T]: s('h4/type/list/list'(C),'h4/const/list/TAKE'(s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num',N))))),s('h4/type/list/list'(C),'h4/const/list/CONS'(s(C,H),s('h4/type/list/list'(C),T))))) = s('h4/type/list/list'(C),'h4/const/list/CONS'(s(C,H),s('h4/type/list/list'(C),'h4/const/list/TAKE'(s('h4/type/num/num','h4/const/arithmetic/-'(s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num',N))))),s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num','h4/const/arithmetic/ZERO'))))))),s('h4/type/list/list'(C),T)))))).
