theorem
  k in Seg n implies (z1 - z2).k = z1.k - z2.k
proof
  assume that
A1: k in Seg n;
  set c1 = z1.k, c2 = z2.k;
  k in dom(z1 - z2) by A1,Lm4;
  hence (z1 - z2).k = diffcomplex.(c1,c2) by FUNCOP_1:22
    .= c1 - c2 by BINOP_2:def 4;
end;
