reserve a,a1,a2,a3,b,b1,b2,b3,r,s,t,u for Real;
reserve n for Nat;
reserve x0,x,x1,x2,x3,y0,y,y1,y2,y3 for Element of REAL n;
reserve L,L0,L1,L2 for Element of line_of_REAL n;

theorem
  dist(x,L) >= 0
proof
  ex x0 being Element of REAL n st x0 in L & |.x-x0.| = dist(x,L) by Th57;
  hence thesis;
end;
