%   ORIGINAL: 'h4/thm/poly/RSQUAREFREE_ROOTS_'
% 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. 'h4/const/poly/rsquarefree' p <=> (!a. ~('h4/const/poly/poly' p a = 'h4/const/real/real_of_num' 'h4/const/num/0' /\ 'h4/const/poly/poly' ('h4/const/poly/diff' p) a = 'h4/const/real/real_of_num' 'h4/const/num/0'))
%   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. 'h4/const/poly/rsquarefree' p <=> (!a. ~('h4/const/poly/poly' p a = 'h4/const/real/real_of_num' 'h4/const/num/0' /\ 'h4/const/poly/poly' ('h4/const/poly/diff' p) a = 'h4/const/real/real_of_num' 'h4/const/num/0'))
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_3f47985,V_3f47981]: ![F, G]: (![X]: s(V_3f47981,happ(s(fun(V_3f47985,V_3f47981),F),s(V_3f47985,X))) = s(V_3f47981,happ(s(fun(V_3f47985,V_3f47981),G),s(V_3f47985,X))) => s(fun(V_3f47985,V_3f47981),F) = s(fun(V_3f47985,V_3f47981),G))).
fof('h4/thm/poly/RSQUAREFREE_ROOTS_', conjecture, ![P]: (p(s(bool,'h4/const/poly/rsquarefree'(s('h4/type/list/list'('h4/type/realax/real'),P)))) <=> ![A]: ~ ((s('h4/type/realax/real','h4/const/poly/poly'(s('h4/type/list/list'('h4/type/realax/real'),P),s('h4/type/realax/real',A))) = s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0'))) & s('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('h4/type/realax/real',A))) = s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0'))))))).
