
theorem Th31: :: CardCenter1:
  for R being finite Skew-Field holds card the carrier of R =
  (card (the carrier of center R)) |^ (dim VectSp_over_center R)
proof
  let R be finite Skew-Field;
  set vR = VectSp_over_center R;
A1: the addLoopStr of vR = the addLoopStr of R by Def6;
  set B = the Basis of vR;
  B is finite by A1;
  then vR is finite-dimensional by MATRLIN:def 1;
  hence thesis by A1,Th15;
end;
