isBoundedSMul — Mathlib

English

For a NonUnitalSeminormedRing α, left multiplication is a bounded scalar action on α, i.e., IsBoundedSMul α α.

Русский

Для Нелокального полносла α ограничено действие слева умножения на α, т.е. IsBoundedSMul α α.

LaTeX

$$$IsBoundedSMul\\;\\alpha\\;\\alpha$$$

Lean4

/-- Left multiplication is bounded. -/
instance isBoundedSMul [NonUnitalSeminormedRing α] : IsBoundedSMul α α
    where
  dist_smul_pair' x y₁ y₂ := by simpa [mul_sub, dist_eq_norm] using norm_mul_le x (y₁ - y₂)
  dist_pair_smul' x₁ x₂ y := by simpa [sub_mul, dist_eq_norm] using norm_mul_le (x₁ - x₂) y

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