toCommSemiring — Mathlib

English

A subsemiring of a commutative semiring is itself a commutative semiring under the inherited operations.

Русский

Подпол semiring под коммутативным полусистемом образует коммутативный полусемиринг при наследовании операций.

LaTeX

$$$S \subseteq R,\ (R\text{ commutative semiring}) \Rightarrow S \text{ is a CommSemiring with induced operations.}$$$

Lean4

/-- A subsemiring of a `CommSemiring` is a `CommSemiring`. -/
instance toCommSemiring {R} [CommSemiring R] [SetLike S R] [SubsemiringClass S R] : CommSemiring s :=
  fast_instance%Subtype.coe_injective.commSemiring Subtype.val rfl rfl (fun _ _ => rfl) (fun _ _ => rfl)
      (fun _ _ => rfl) (fun _ _ => rfl) fun _ => rfl

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