
theorem Th28: :: Central1:
  for R be finite Skew-Field, s be Element of R
  holds 1 < card (the carrier of centralizer s)
proof
  let R be finite Skew-Field, s be Element of R;
A1: card {0.R, 1.R} = 2 by CARD_2:57;
A2: 0.R is Element of centralizer s by Th27;
  1_R is Element of centralizer s by Th27;
  then {0.R, 1_R} c= the carrier of centralizer s by A2,ZFMISC_1:32;
  then 2 <= card the carrier of centralizer s by A1,NAT_1:43;
  hence thesis by XXREAL_0:2;
end;
