proposition: Lemma mult_le_compat x₁ y₁ x₂ y₂ : 0 ≤ x₁ → 0 ≤ x₂ → x₁ ≤ y₁ → x₂ ≤ y₂ → x₁ * x₂ ≤ y₁ * y₂.
proof: Proof. intros Ex₁ Ey₁ E1 E2. transitivity (y₁ * x₂). now apply (order_preserving_flip_nonneg (.*.) x₂). apply (order_preserving_nonneg (.*.) y₁); [| easy]. now transitivity x₁. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.orders MathClasses.orders.maps