reserve i,j for Nat;

theorem Th27:
  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;
  thus len (a*A)=len(MXF2MXR (ea*(MXR2MXF A))) by Def7
    .=len A by MATRIX_3:def 5;
  thus width (a*A)=width(MXF2MXR (ea*(MXR2MXF A))) by Def7
    .=width A by MATRIX_3:def 5;
end;
