sInf_toSubsemigroup — Mathlib

English

The Infimum of a family of nonunital subrings, viewed as a subsemigroup, equals the infimum taken in the family of subsemigroups.

Русский

Infimum семейства подподкольц без единицы, воспринятый как подпол semigroup, равен инфимуму по семейству подполь semigroup.

LaTeX

$$$$ (sInf\, s).toSubsemigroup = \\big(\\bigwedge t \\in s, Subsemigroup t\\big). $$$$

Lean4

@[simp]
theorem sInf_toSubsemigroup (s : Set (NonUnitalSubring R)) :
    (sInf s).toSubsemigroup = ⨅ t ∈ s, NonUnitalSubring.toSubsemigroup t :=
  mk'_toSubsemigroup _ _

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