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;

theorem Th16:
  |.x1 - x2.| <= |.x1 - x .| + |.x - x2.|
proof
  reconsider R1=x1,R2=x2,R=x as Element of n-tuples_on REAL;
  |.x1 - x2.| = |.R1 - R + R - R2.| by RVSUM_1:43
    .= |.(x1 - x) + (x - x2).| by RVSUM_1:40;
  hence thesis by Th9;
end;
