| impw: Proof \to Proof (* weakening *)
| impr: Proof \to Proof (* right introduction *)
| impi: Proof \to Proof \to Proof \to Proof (* left introduction *)
| impw: Proof \to Proof (* weakening *)
| impr: Proof \to Proof (* right introduction *)
| impi: Proof \to Proof \to Proof \to Proof (* left introduction *)