reserve x,y for set,
  i,j,k,l,m,n for Nat,
  K for Field,
  N for without_zero finite Subset of NAT,
  a,b for Element of K,
  A,B,B1,B2,X,X1,X2 for (Matrix of K),
  A9 for (Matrix of m,n,K),
  B9 for (Matrix of m,k,K);
reserve D for non empty set,
  bD for FinSequence of D,
  b,f,g for FinSequence of K,
  MD for Matrix of D;

theorem
  a * LineVec2Mx f =LineVec2Mx (a*f)
proof
A1: len (a*LineVec2Mx f)=len (LineVec2Mx f) by MATRIX_3:def 5;
A2: len (LineVec2Mx f)=1 by MATRIX_0:def 2;
  then Line(a * LineVec2Mx f,1) = a*Line(LineVec2Mx f,1) by MATRIXR1:20
    .= a*f by Th25;
  hence thesis by A2,A1,Th25;
end;
