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 Th4: :: search in MML
  for a,b,m being Integer st a,b are_congruent_mod m holds
  not m divides a or m divides b
  proof
    let a,b,m be Integer;
    assume a,b are_congruent_mod m & m divides a;
    then m divides a-(a-b) by INT_5:1;
    hence thesis;
  end;
