inr_mono — Mathlib

English

The embedding inl is strictly monotone if the embedding is injective.

Русский

Встраивание inl строго монотонно, если оно инъективно.

LaTeX

$$$\text{inl}$ строго монотонно.$$

Lean4

theorem inr_mono [GroupWithZero M₀] [Preorder M₀] [LinearOrderedCommGroupWithZero N₀]
    [DecidablePred fun x : N₀ ↦ x = 0] : Monotone (inr M₀ N₀) :=
  by
  refine (WithZero.map'_mono MonoidHom.inr_mono).comp ?_
  intro x y
  obtain rfl | ⟨x, rfl⟩ := GroupWithZero.eq_zero_or_unit x <;>
      obtain rfl | ⟨y, rfl⟩ := GroupWithZero.eq_zero_or_unit y <;>
    · simp [WithZero.withZeroUnitsEquiv]

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