reserve i,j for Nat;

theorem Th29:
  for a being Real, A being (Matrix of REAL), i2,j2 being Nat st
  [i2,j2] in Indices A holds (a*A)*(i2,j2)=a*(A*(i2,j2))
proof
  let a be Real,A be Matrix of REAL;
  let i2,j2 be Nat;
  reconsider ea=a as Element of F_Real by XREAL_0:def 1;
  assume [i2,j2] in Indices A;
  then (MXF2MXR (ea*(MXR2MXF A)))*(i2,j2) = ea*((MXR2MXF A)*(i2,j2))
    by MATRIX_3:def 5
    .=a*(A*(i2,j2));
  hence thesis by Def7;
end;
