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;

theorem Th4:
  |.|[r]|.|=|.r.|
proof
  set p=|[r]|;
  reconsider w=|[r]| as Element of REAL 1 by EUCLID:22;
  reconsider r2=r^2 as Element of REAL by XREAL_0:def 1;
  sqr w=<*r2*> by RVSUM_1:55;
  then |.p.| =sqrt r2 by FINSOP_1:11
    .=|.r.| by COMPLEX1:72;
  hence thesis;
end;
