
theorem
  for I being non empty set for A being ManySortedSet of I for i,S be
  set holds {A}+*(i,S) is Segre-like
proof
  let I be non empty set;
  let A be ManySortedSet of I;
  let i,S be set;
  per cases;
  suppose
    not i in I;
    then not i in dom {A} by PARTFUN1:def 2;
    hence thesis by FUNCT_7:def 3;
  end;
  suppose
    i in I;
    then reconsider i as Element of I;
    take i;
    let j be Element of I such that
A1: i<>j;
    {A}.j = {A.j} by PZFMISC1:def 1;
    hence thesis by A1,FUNCT_7:32;
  end;
end;
