inf_toSubalgebra — Mathlib

English

The infimum of two star subalgebras, as a subalgebra, is the infimum of their underlying subalgebras.

Русский

Infimum двух звездных подпалебр как подпалебра равен infimum их оснований.

LaTeX

$$$(S \sqcap T).toSubalgebra = S.toSubalgebra \sqcap T.toSubalgebra$$$

Lean4

@[simp]
theorem inf_toSubalgebra (S T : StarSubalgebra R A) : (S ⊓ T).toSubalgebra = S.toSubalgebra ⊓ T.toSubalgebra := by ext;
  simp
    -- Porting note: Lean can no longer prove this by `rfl`, it times out

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