
theorem
for p being non constant Element of the carrier of Polynom-Ring F_Rat
holds F_Rat, (Polynom-Ring F_Rat)/({p}-Ideal) are_disjoint
proof
let p be non constant Element of the carrier of Polynom-Ring F_Rat;
set F = F_Rat, KR = (Polynom-Ring F_Rat)/({p}-Ideal);
X: [#] F = the carrier of F & [#] KR = the carrier of KR;
(the carrier of F_Rat) /\
      (the carrier of (Polynom-Ring F_Rat)/({p}-Ideal)) = {} by Disj2;
hence thesis by X,FIELD_2:def 1;
end;
