 reserve i,n for Nat;
 reserve r for Real;
 reserve ra for Element of F_Real;
 reserve a,b,c for non zero Element of F_Real;
 reserve u,v for Element of TOP-REAL 3;
 reserve p1 for FinSequence of (1-tuples_on REAL);
 reserve pf,uf for FinSequence of F_Real;
 reserve N for Matrix of 3,F_Real;
 reserve K for Field;
 reserve k for Element of K;

theorem Th02:
  ra * N = (ra * 1.(F_Real,3)) * N
  proof
    width 1.(F_Real,3) = 3 by MATRIX_0:24; then
A1: width 1.(F_Real,3) = len N by MATRIX_0:24;
    ra * N = ra * (1.(F_Real,3) * N) by MATRIX_3:18;
    hence thesis by A1,MATRIX15:1;
  end;
