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 Th15:
  |.x1 - x2.| = |.x2 - x1.|
proof
  reconsider R1=x1,R2=x2 as Element of n-tuples_on REAL;
  thus |.x1 - x2.| = |.-(R2 - R1).| by RVSUM_1:35
    .= |.x2 - x1.| by Th7;
end;
