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 Th7:
  |.-f.| = |.f.|
proof
  thus |.-f.| = sqrt Sum sqr abs -f by Lm2
    .= sqrt Sum sqr abs f by Th2
    .= |.f.| by Lm2;
end;
