proposition: Lemma ℕle_realizer : forall e, ℤle↓e ⊩ ∀₂n,m∈ℕ×ℕ, ∀A B, (n <= m ↦ A) → (~n <= m ↦ B) → (n <= m ↦ A) ∩ (~n <= m ↦ B).
proof: Proof. intro e. start. destruct Hπ; destruct (Z_le_dec (Z.of_nat n) (Z.of_nat m)); rewrite <- Nat2Z.inj_le in *; Ksolve; contradiction. Qed.
imports: ZArith ClassicalRealizability.Kbase