sInf_toSubsemiring — Mathlib

English

The subsemiring corresponding to the infimum of a set S of Subalgebras equals the infimum of the subsemirings: (sInf S).toSubsemiring = sInf (Subalgebra.toSubsemiring '' S).

Русский

Подсемиринг, соответствующийInf, равен инфимума сигнатуры S: (sInf S).toSubsemiring = sInf (toSubsemiring '' S).

LaTeX

$$$(sInf S).toSubsemiring = sInf( Subalgebra.toSubsemiring '' S )$$

Lean4

@[simp]
theorem sInf_toSubsemiring (S : Set (Subalgebra R A)) : (sInf S).toSubsemiring = sInf (Subalgebra.toSubsemiring '' S) :=
  SetLike.coe_injective <| by simp

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