
theorem
  RNS_Real is finite-dimensional & dim RNS_Real = 1
  proof
    consider I be LinearOperator of RNS_Real,REAL-NS 1 such that
    A1: I is isomorphism by Th9;

    consider K be Lipschitzian LinearOperator of REAL-NS 1,RNS_Real
    such that
    A2: K = I " & K is isomorphism by A1,NORMSP_3:37;

      REAL-NS 1 is finite-dimensional
    & dim(REAL-NS 1) = 1 by REAL_NS2:62;
    hence thesis by A2,REAL_NS2:88;
  end;
