toIsOrderedMonoid — Mathlib

English

A submonoid S of a canonical ordered monoid M inherits IsOrderedMonoid on its subtype.

Русский

Подмножество S под упорядоченного моноида M наследует IsOrderedMonoid на своем подвиде.

LaTeX

$$IsOrderedMonoid (Subtype (x ∈ S))$$

Lean4

/-- A submonoid of an ordered monoid is an ordered monoid. -/
@[to_additive /-- An `AddSubmonoid` of an ordered additive monoid is an ordered additive monoid. -/
    ]
instance toIsOrderedMonoid [CommMonoid M] [PartialOrder M] [IsOrderedMonoid M] (S : Submonoid M) : IsOrderedMonoid S :=
  Function.Injective.isOrderedMonoid Subtype.val (fun _ _ => rfl) .rfl

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