mul_right — Mathlib

English

If the supports of f_i are locally finite, then the supports of s_i · f_i are locally finite.

Русский

Если опоры функций f_i локально конечны, то опоры произведения f_i · s_i тоже локально конечны.

LaTeX

$$$\operatorname{LocallyFinite}(i \mapsto \operatorname{support}(f_i)) \Rightarrow \operatorname{LocallyFinite}\bigl(i \mapsto \operatorname{support}(s_i \cdot f_i)\bigr).$$$

Lean4

/-- If `a` is topologically nilpotent, then `a * b` is topologically nilpotent. -/
theorem mul_right {a : R} (ha : IsTopologicallyNilpotent a) (b : R) : IsTopologicallyNilpotent (a * b) :=
  ha.mul_right_of_commute (Commute.all ..)

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