reserve n for Nat,
  a, b, r, w for Real,
  x, y, z for Point of TOP-REAL n,
  e for Point of Euclid n;
reserve V for RealLinearSpace,
        p,q,x for Element of V;
reserve p, q, x for Point of TOP-REAL n;
reserve s, t for Point of TOP-REAL 2;

theorem
  s in Sphere(0.TOP-REAL 2,r) implies s`1^2 + s`2^2 = r^2
proof
  assume s in Sphere(0.TOP-REAL 2,r);
  then |. s-0.TOP-REAL 2 .| = r by Th7;
  then |. s .| = r by RLVECT_1:13;
  hence thesis by JGRAPH_1:29;
end;
