 reserve m,n for Nat;
 reserve i,j for Integer;
 reserve S for non empty multMagma;
 reserve r,r1,r2,s,s1,s2,t for Element of S;
 reserve G for Group-like non empty multMagma;
 reserve e,h for Element of G;
 reserve G for Group;
 reserve f,g,h for Element of G;
 reserve u for UnOp of G;

theorem
  multMagma (# REAL, addreal #) is commutative Group
proof
  reconsider G = multMagma (# REAL, addreal #) as Group by Th3;
  G is commutative
  proof
    let h,g be Element of G;
    reconsider A = h, B = g as Real;
    thus h * g = B + A by BINOP_2:def 9
      .= g * h by BINOP_2:def 9;
  end;
  hence thesis;
end;
