theorem
  1,2,3,4 are_mutually_distinct &
  not ex n being positive Nat st 1+n,2+n,3+n,4+n are_mutually_coprime
  proof
    thus 1,2,3,4 are_mutually_distinct;
    given n being positive Nat such that
A1: 1+n,2+n,3+n,4+n are_mutually_coprime;
    per cases;
    suppose n is odd;
      hence thesis by A1,NEWTON05:35,POLYFORM:6;
    end;
    suppose n is even;
      hence thesis by A1,NEWTON05:35,POLYFORM:7;
    end;
  end;
