reserve i,j for Nat;

theorem
  for A being Matrix of REAL st len A>0 holds 0 * A = 0_Rmatrix (len A,
  width A)
proof
  let A be Matrix of REAL;
  assume
A1: len A>0;
  0 * A = MXF2MXR ((0.F_Real)*(MXR2MXF A)) by Def7
    .= 0_Rmatrix(len A,width A) by A1,MATRIX_5:24;
  hence thesis;
end;
