reserve a,b,c,x,y,z for object,X,Y,Z for set,
  n for Nat,
  i,j for Integer,
  r,r1,r2,r3,s for Real,
  c1,c2 for Complex,
  p for Point of TOP-REAL n;

theorem Th18:
  for c being Complex
  for f being complex-valued FinSequence holds (f(/)c)^2 = (f^2) (/) (c^2)
  proof
    let c be Complex;
    let f be complex-valued FinSequence;
    thus (f(/)c)^2 = (1/c)^2 (#) (f^2) by Th17
    .= (1*1)/(c*c) (#) (f^2) by XCMPLX_1:76
    .= (f^2) (/) (c^2);
  end;
