reserve x for set,
  D for non empty set,
  k,n,m,i,j,l for Nat,
  K for Field;

theorem Th5:
  for a being Real,A being Matrix of REAL holds 
  len (a*A) = len A & width (a*A) = width A
proof
  let a be Real,A be Matrix of REAL;
  reconsider ea=a as Element of F_Real by XREAL_0:def 1;
A1: width (a*A)= width MXR2MXF MXF2MXR (ea*(MXR2MXF A)) by MATRIXR1:def 7
    .= width A by MATRIX_3:def 5;
  len (a*A)= len MXR2MXF MXF2MXR (ea*(MXR2MXF A)) by MATRIXR1:def 7
    .= len A by MATRIX_3:def 5;
  hence thesis by A1;
end;
