reserve a,b,c,x,y,z for object,X,Y,Z for set,
  n for Nat,
  i,j for Integer,
  r,r1,r2,r3,s for Real,
  c1,c2 for Complex,
  p for Point of TOP-REAL n;

theorem Th13:
  -(0*n) = 0*n
  proof
    set f = 0*n, g = -f;
    thus len f = len g by COMPLSP2:5;
    let k be Nat such that 1 <= k & k <= len g;
A1: f.k = 0;
    thus f.k = -Q
    .= g.k by A1,VALUED_1:8;
  end;
