`| Ax of int` |

`| I_Arrow of proof` |

`| E_Arrow of int * int * proof` |

`| D_Arrow of int * proof * proof` |

`| E_False of int` |

`| I_And of proof * proof` |

`| E_And of int * proof` |

`| D_And of int * proof` |

`| I_Or_l of proof` |

`| I_Or_r of proof` |

`| E_Or of int * proof * proof` |

`| D_Or of int * proof` |

`| Pop of int * proof` |