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),i3 are_congruent_mod i5 iff i1, (i3 - i2) are_congruent_mod i5;
