mem_nonUnitalSubalgebraOfNonUnitalSubring

English

For S a NonUnitalSubring R, the membership in nonUnitalSubalgebraOfNonUnitalSubring S matches membership in S.

Русский

Для S — NonUnitalSubring R, принадлежность в nonUnitalSubalgebraOfNonUnitalSubring S совпадает с принадлежностью к S.

LaTeX

$$$x \\in \\operatorname{nonUnitalSubalgebraOfNonUnitalSubring}(S) \\iff x \\in S$$$

Lean4

@[simp]
theorem mem_nonUnitalSubalgebraOfNonUnitalSubring {x : R} {S : NonUnitalSubring R} :
    x ∈ nonUnitalSubalgebraOfNonUnitalSubring S ↔ x ∈ S :=
  Iff.rfl

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