%   ORIGINAL: 'h4/thm/poly/POLY_DIFF_AUX_ISZERO_'
% 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: !p n. 'h4/const/list/EVERY' (\c. c = 'h4/const/real/real_of_num' 'h4/const/num/0') ('h4/const/poly/poly_diff_aux' ('h4/const/num/SUC' n) p) <=> 'h4/const/list/EVERY' (\c. c = 'h4/const/real/real_of_num' 'h4/const/num/0') p
%   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: !_0. (!c. happ _0 c <=> c = 'h4/const/real/real_of_num' 'h4/const/num/0') ==> (!p n. 'h4/const/list/EVERY' _0 ('h4/const/poly/poly_diff_aux' ('h4/const/num/SUC' n) p) <=> 'h4/const/list/EVERY' _0 p)
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_3f47359,V_3f47355]: ![F, G]: (![X]: s(V_3f47355,happ(s(fun(V_3f47359,V_3f47355),F),s(V_3f47359,X))) = s(V_3f47355,happ(s(fun(V_3f47359,V_3f47355),G),s(V_3f47359,X))) => s(fun(V_3f47359,V_3f47355),F) = s(fun(V_3f47359,V_3f47355),G))).
fof('h4/thm/poly/POLY_DIFF_AUX_ISZERO_', conjecture, ![V__0]: (![C]: (p(s(bool,happ(s(fun('h4/type/realax/real',bool),V__0),s('h4/type/realax/real',C)))) <=> s('h4/type/realax/real',C) = s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0')))) => ![P, N]: s(bool,'h4/const/list/EVERY'(s(fun('h4/type/realax/real',bool),V__0),s('h4/type/list/list'('h4/type/realax/real'),'h4/const/poly/poly_diff_aux'(s('h4/type/num/num','h4/const/num/SUC'(s('h4/type/num/num',N))),s('h4/type/list/list'('h4/type/realax/real'),P))))) = s(bool,'h4/const/list/EVERY'(s(fun('h4/type/realax/real',bool),V__0),s('h4/type/list/list'('h4/type/realax/real'),P))))).
