%   ORIGINAL: 'h4/thm/poly/POLY_SQUAREFREE_DECOMP_ORDER_'
% 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 q d e r s. ~('h4/const/poly/poly' ('h4/const/poly/diff' p) = 'h4/const/poly/poly' 'h4/const/list/NIL') /\ 'h4/const/poly/poly' p = 'h4/const/poly/poly' ('h4/const/poly/poly_mul' q d) /\ 'h4/const/poly/poly' ('h4/const/poly/diff' p) = 'h4/const/poly/poly' ('h4/const/poly/poly_mul' e d) /\ 'h4/const/poly/poly' d = 'h4/const/poly/poly' ('h4/const/poly/poly_add' ('h4/const/poly/poly_mul' r p) ('h4/const/poly/poly_mul' s ('h4/const/poly/diff' p))) ==> (!a. 'h4/const/poly/poly_order' a q = 'h4/const/bool/COND' ('h4/const/poly/poly_order' a p = 'h4/const/num/0') 'h4/const/num/0' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')))
%   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 q d e r s. ~('h4/const/poly/poly' ('h4/const/poly/diff' p) = 'h4/const/poly/poly' 'h4/const/list/NIL') /\ 'h4/const/poly/poly' p = 'h4/const/poly/poly' ('h4/const/poly/poly_mul' q d) /\ 'h4/const/poly/poly' ('h4/const/poly/diff' p) = 'h4/const/poly/poly' ('h4/const/poly/poly_mul' e d) /\ 'h4/const/poly/poly' d = 'h4/const/poly/poly' ('h4/const/poly/poly_add' ('h4/const/poly/poly_mul' r p) ('h4/const/poly/poly_mul' s ('h4/const/poly/diff' p))) ==> (!a. ?v. (v <=> 'h4/const/poly/poly_order' a p = 'h4/const/num/0') /\ 'h4/const/poly/poly_order' a q = 'h4/const/bool/COND' v 'h4/const/num/0' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')))
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_3f47959,V_3f47955]: ![F, G]: (![X]: s(V_3f47955,happ(s(fun(V_3f47959,V_3f47955),F),s(V_3f47959,X))) = s(V_3f47955,happ(s(fun(V_3f47959,V_3f47955),G),s(V_3f47959,X))) => s(fun(V_3f47959,V_3f47955),F) = s(fun(V_3f47959,V_3f47955),G))).
fof('h4/thm/poly/POLY_SQUAREFREE_DECOMP_ORDER_', conjecture, ![P, Q, D, E, R, S]: ((~ (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/diff'(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')))) & (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'),Q),s('h4/type/list/list'('h4/type/realax/real'),D))))) & (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/diff'(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'),E),s('h4/type/list/list'('h4/type/realax/real'),D))))) & s(fun('h4/type/realax/real','h4/type/realax/real'),'h4/const/poly/poly'(s('h4/type/list/list'('h4/type/realax/real'),D))) = 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_add'(s('h4/type/list/list'('h4/type/realax/real'),'h4/const/poly/poly_mul'(s('h4/type/list/list'('h4/type/realax/real'),R),s('h4/type/list/list'('h4/type/realax/real'),P))),s('h4/type/list/list'('h4/type/realax/real'),'h4/const/poly/poly_mul'(s('h4/type/list/list'('h4/type/realax/real'),S),s('h4/type/list/list'('h4/type/realax/real'),'h4/const/poly/diff'(s('h4/type/list/list'('h4/type/realax/real'),P)))))))))))) => ![A]: ?[V]: ((p(s(bool,V)) <=> 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/num/num','h4/const/num/0')) & 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'),Q))) = s('h4/type/num/num','h4/const/bool/COND'(s(bool,V),s('h4/type/num/num','h4/const/num/0'),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')))))))))).
