proposition: Lemma ℚle_realizer : forall e, ℚle↓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 q p) as [Hlt |?]; destruct Hπ; try apply Qclt_not_le in Hlt; Ksolve; contradiction || now elim (Qle_not_lt p q). Qed.
imports: QArith ClassicalRealizability.Qcabs ClassicalRealizability.Qcminmax ClassicalRealizability.Kbase