theorem
  X is p-Semisimple iff for x,z holds (x\z)`` = x\z
proof
  thus X is p-Semisimple implies for x,z holds (x\z)`` = x\z;
  assume
A1: for x,z holds (x\z)`` = x\z;
  now
    let x;
    (x\0.X)``=x\0.X by A1;
    then (x`)`=x\0.X by Th2;
    hence x``=x by Th2;
  end;
  hence thesis by Th54;
end;
