mul_right — Mathlib

English

If f =^l g, then f^c =^l g^c for any exponent c when β is a Pow object.

Русский

Если f =^l g, то f^c =^l g^c для любого показателя мощности c.

LaTeX

$$$\\\\forall f,g : \\\\alpha \\\\to \\\\beta \\\\forall l \\\\ (l : Filter \\\\alpha), \\\\forall c \\\\in \\\\gamma, \\\\ (f =^l g) \\\\Rightarrow \\\\bigl((f)^c =^l (g)^c\\\\bigr)$$$

Lean4

@[to_additive]
theorem mul_right [Mul β] {f₁ f₂ f₃ : α → β} (h : f₁ =ᶠ[l] f₂) : f₁ * f₃ =ᶠ[l] f₂ * f₃ :=
  EventuallyEq.mul h (by rfl)

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