reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i for Integer;
reserve r for Real;
reserve p for Prime;

theorem Th6:
  for a,b being Integer holds
  k <> 0 & a,b are_congruent_mod n|^k implies a,b are_congruent_mod n
  proof
    let a,b be Integer;
    assume k <> 0;
    then n divides n|^k by NAT_3:3;
    hence thesis by INT_2:9;
  end;
