/-
Port of `Analysis/Utils.agda`. The `≼ᴼ-trans` module parameter lifts into the
`Preorder` instance.
-/
import Spa.Lattice

namespace Spa

/-- Agda: `eval-combine₂`. -/
theorem eval_combine₂ {O : Type*} [Preorder O] {combine : O → O → O}
    (hmono : Monotone₂ combine) {o₁ o₂ o₃ o₄ : O}
    (h₁ : o₁ ≤ o₃) (h₂ : o₂ ≤ o₄) : combine o₁ o₂ ≤ combine o₃ o₄ :=
  le_trans (hmono.1 o₂ h₁) (hmono.2 o₃ h₂)

end Spa