
theorem Th27:
  for I being non empty set for A being Segre-like non
trivial-yielding ManySortedSet of I for N being non trivial set holds A+*(indx(
  A),N) is Segre-like non trivial-yielding
proof
  let I be non empty set;
  let A be Segre-like non trivial-yielding ManySortedSet of I;
  let N be non trivial set;
  thus A+*(indx(A),N) is Segre-like
  proof
    take indx(A);
    let i be Element of I;
    assume
A1: i <> indx(A);
    then A+*(indx(A),N).i = A.i by FUNCT_7:32;
    hence thesis by A1,Th12;
  end;
  thus A+*(indx(A),N) is non trivial-yielding
  proof
    take A+*(indx(A),N).indx(A);
    dom (A+*(indx(A),N)) = I by PARTFUN1:def 2;
    hence A+*(indx(A),N).indx(A) in rng (A+*(indx(A),N)) by FUNCT_1:def 3;
    I = dom A by PARTFUN1:def 2;
    hence thesis by FUNCT_7:31;
  end;
end;
