%   ORIGINAL: 'h4/thm/poly/ORDER_DECOMP_'
% 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 a. ~('h4/const/poly/poly' p = 'h4/const/poly/poly' 'h4/const/list/NIL') ==> (?q. 'h4/const/poly/poly' p = 'h4/const/poly/poly' ('h4/const/poly/poly_mul' ('h4/const/poly/poly_exp' ('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')) ('h4/const/poly/poly_order' a p)) q) /\ ~'h4/const/poly/poly_divides' ('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: !p a. ~('h4/const/poly/poly' p = 'h4/const/poly/poly' 'h4/const/list/NIL') ==> (?q. 'h4/const/poly/poly' p = 'h4/const/poly/poly' ('h4/const/poly/poly_mul' ('h4/const/poly/poly_exp' ('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')) ('h4/const/poly/poly_order' a p)) q) /\ ~'h4/const/poly/poly_divides' ('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_3f47884,V_3f47880]: ![F, G]: (![X]: s(V_3f47880,happ(s(fun(V_3f47884,V_3f47880),F),s(V_3f47884,X))) = s(V_3f47880,happ(s(fun(V_3f47884,V_3f47880),G),s(V_3f47884,X))) => s(fun(V_3f47884,V_3f47880),F) = s(fun(V_3f47884,V_3f47880),G))).
fof('h4/thm/poly/ORDER_DECOMP_', conjecture, ![P, A]: (~ (s(fun('h4/type/realax/real','h4/type/realax/real'),'h4/const/poly/poly'(s('h4/type/list/list'('h4/type/realax/real'),P))) = s(fun('h4/type/realax/real','h4/type/realax/real'),'h4/const/poly/poly'(s('h4/type/list/list'('h4/type/realax/real'),'h4/const/list/NIL')))) => ?[Q]: (s(fun('h4/type/realax/real','h4/type/realax/real'),'h4/const/poly/poly'(s('h4/type/list/list'('h4/type/realax/real'),P))) = s(fun('h4/type/realax/real','h4/type/realax/real'),'h4/const/poly/poly'(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/poly/poly_exp'(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/num/num','h4/const/poly/poly_order'(s('h4/type/realax/real',A),s('h4/type/list/list'('h4/type/realax/real'),P))))),s('h4/type/list/list'('h4/type/realax/real'),Q))))) & ~ (p(s(bool,'h4/const/poly/poly_divides'(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)))))))).
