reserve k,j,n for Nat,
  r for Real;
reserve x,x1,x2,y for Element of REAL n;
reserve f for real-valued FinSequence;
reserve p,p1,p2,p3 for Point of TOP-REAL n,
  x,x1,x2,y,y1,y2 for Real;
reserve p,p1,p2 for Point of TOP-REAL 2;

theorem Th45:
  |.1*n.| = sqrt n
proof
  reconsider j=1^2 as Element of REAL by XREAL_0:def 1;
  reconsider f= n |-> j as FinSequence of REAL;
  thus |.1*n .| = sqrt Sum f by RVSUM_1:56
    .= sqrt (n*1) by RVSUM_1:80
    .= sqrt n;
end;
