sInf_toAddSubmonoid — Mathlib

English

The AddSubmonoid generated by the Infimum of a set s equals the infimum of the toAddSubmonoid of each t ∈ s.

Русский

АддПодподмножество, порождаемое sInf s, равно.infimum для toAddSubmonoid каждого t ∈ s.

LaTeX

$$$ (sInf s).toAddSubmonoid = \bigwedge_{t \in s} t.toAddSubmonoid $$$

Lean4

@[simp]
theorem sInf_toAddSubmonoid (s : Set (NonUnitalSubsemiring R)) :
    (sInf s).toAddSubmonoid = ⨅ t ∈ s, NonUnitalSubsemiring.toAddSubmonoid t :=
  mk'_toAddSubmonoid _ _

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