reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;

theorem
  m,n are_coprime implies a*n+m,n are_coprime
  proof
    a*n+m,m are_congruent_mod n;
    hence thesis by WSIERP_1:43;
  end;
