reserve m,n,i,i2,j for Nat,
  r,r1,r2,s,t for Real,
  x,y,z for object;
reserve p,p1,p2,p3,q,q1,q2,q3,q4 for Point of TOP-REAL n;
reserve u for Point of Euclid n;
reserve R for Subset of TOP-REAL n;
reserve P,Q for Subset of TOP-REAL n;
reserve D for non vertical non horizontal non empty compact Subset of TOP-REAL
  2;
reserve f for clockwise_oriented non constant standard
  special_circular_sequence;
reserve p for Point of TOP-REAL 2;

theorem
 for n being Nat, r,s being Real st r > 0
 for x being Element of Euclid n st x = 0*n
 for A being Subset of TOP-REAL n st A = Ball(x,s)
  holds r*A = Ball(x,r*s) by Lm2;
