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,i2 are_congruent_mod 1
proof
  i1 - i2 = 1 * (i1 - i2);
  hence thesis;
end;
