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 Th15:
  sqr <*r1,r2,r3*> = <* r1^2, r2^2, r3^2 *>
  proof
    <* r1,r2*> is FinSequence of REAL &
    <* r3 *> is FinSequence of REAL by TOPREALC:19;
    hence sqr <*r1,r2,r3*> = sqr <* r1,r2*> ^ sqr <*r3*> by TOPREAL7:10
    .= <* r1^2, r2^2 *> ^ sqr <*r3*> by TOPREAL6:11
    .= <* r1^2, r2^2, r3^2 *> by RVSUM_1:55;
  end;
