%   ORIGINAL: 'h4/thm/poly/POLY_LINEAR_REM_'
% 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: !a t h. ?q r. 'h4/const/list/CONS' h t = 'h4/const/poly/poly_add' ('h4/const/list/CONS' r 'h4/const/list/NIL') ('h4/const/poly/poly_mul' ('h4/const/list/CONS' ('h4/const/realax/real_neg' a) ('h4/const/list/CONS' ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) 'h4/const/list/NIL')) q)
%   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: !a t h. ?q r. 'h4/const/list/CONS' h t = 'h4/const/poly/poly_add' ('h4/const/list/CONS' r 'h4/const/list/NIL') ('h4/const/poly/poly_mul' ('h4/const/list/CONS' ('h4/const/realax/real_neg' a) ('h4/const/list/CONS' ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) 'h4/const/list/NIL')) q)
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_3f46959,V_3f46955]: ![F, G]: (![X]: s(V_3f46955,happ(s(fun(V_3f46959,V_3f46955),F),s(V_3f46959,X))) = s(V_3f46955,happ(s(fun(V_3f46959,V_3f46955),G),s(V_3f46959,X))) => s(fun(V_3f46959,V_3f46955),F) = s(fun(V_3f46959,V_3f46955),G))).
fof('h4/thm/poly/POLY_LINEAR_REM_', conjecture, ![A, T, H]: ?[Q, R]: s('h4/type/list/list'('h4/type/realax/real'),'h4/const/list/CONS'(s('h4/type/realax/real',H),s('h4/type/list/list'('h4/type/realax/real'),T))) = s('h4/type/list/list'('h4/type/realax/real'),'h4/const/poly/poly_add'(s('h4/type/list/list'('h4/type/realax/real'),'h4/const/list/CONS'(s('h4/type/realax/real',R),s('h4/type/list/list'('h4/type/realax/real'),'h4/const/list/NIL'))),s('h4/type/list/list'('h4/type/realax/real'),'h4/const/poly/poly_mul'(s('h4/type/list/list'('h4/type/realax/real'),'h4/const/list/CONS'(s('h4/type/realax/real','h4/const/realax/real_neg'(s('h4/type/realax/real',A))),s('h4/type/list/list'('h4/type/realax/real'),'h4/const/list/CONS'(s('h4/type/realax/real','h4/const/real/real_of_num'(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'('h4/type/realax/real'),'h4/const/list/NIL'))))),s('h4/type/list/list'('h4/type/realax/real'),Q)))))).
