reserve X for set, x,y,z for object,
  k,l,n for Nat,
  r for Real;
reserve i,i0,i1,i2,i3,i4,i5,i8,i9,j for Integer;

theorem
  i1,0 are_congruent_mod i1 & 0,i1 are_congruent_mod i1
proof
A1: i1 * (- 1) = 0 - i1;
  thus thesis by A1;
end;
