instSuccOrderShrink — Mathlib

English

PredOrder on Shrink(α) is induced by the order isomorphism from α: a ≤ b in Shrink(α) iff (orderIsoShrink(α)).symm(a) ≤ (orderIsoShrink(α)).symm(b) in α.

Русский

PredOrder на Shrink(α) индуцирован через порядковый изоморфизм: a ≤ b в Shrink(α) эквивалентно (orderIsoShrink(α)).symm(a) ≤ (orderIsoShrink(α)).symm(b) в α.

LaTeX

$$$a \le b \text{ in } \operatorname{Shrink}(\alpha) \iff ((\operatorname{orderIsoShrink}(\alpha)).\mathrm{symm}}(a) \le ((\operatorname{orderIsoShrink}(\alpha)).\mathrm{symm}}(b))$$$

Lean4

noncomputable instance [SuccOrder α] : SuccOrder (Shrink.{u} α) :=
  SuccOrder.ofOrderIso (orderIsoShrink.{u} α)

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