
theorem Th23: :: Central00:
  for R be Skew-Field, s be Element of R
  holds the carrier of centralizer s c= the carrier of R
proof
  let R be Skew-Field, s be Element of R;
  set cs = centralizer s;
  set ccs = the carrier of cs;
A1: ccs = {x where x is Element of R: x*s = s*x} by Def5;
  let x be object;
  assume x in the carrier of centralizer s;
  then ex a being Element of R st a=x & a*s=s*a by A1;
  hence thesis;
end;
