infinite_mul_of_not_infinitesimal_infinite

English

If x is infinite and y is not infinitesimal, then xy is infinite. (mirror of previous form)

Русский

Если x бесконечно велико, а y не бес infinitesimal, то xy бесконечно велико. (вариант формулировки)

LaTeX

$$$\mathrm{Infinite}(x) \land \lnot \mathrm{Infinitesimal}(y) \Rightarrow \mathrm{Infinite}(xy)$$$

Lean4

theorem infinite_mul_of_not_infinitesimal_infinite {x y : ℝ*} : ¬Infinitesimal x → Infinite y → Infinite (x * y) :=
  fun hx hy => by rw [mul_comm]; exact infinite_mul_of_infinite_not_infinitesimal hy hx

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