proposition: Lemma ℚlt_realizer : forall e, ℚlt↓e ⊩ ∀₂p,q∈ℚ×ℚ, ∀A B, (p < q ↦ A) → (q <= p ↦ B) → (p < q ↦ A) ∩ (q <= p ↦ B).
proof: Proof. intro e. start. destruct (Qclt_le_dec p q) as [Hlt |?]; destruct Hπ; try apply Qclt_not_le in Hlt; Ksolve; try contradiction || now elim (Qle_not_lt q p). Qed.
imports: QArith ClassicalRealizability.Qcabs ClassicalRealizability.Qcminmax ClassicalRealizability.Kbase