powers_le_zpowers — Mathlib

English

A simplification lemma about the relation between the fst-projections and the subgroup actions for units involved in the reduced word context.

Русский

Упрощенная лемма about связи между fst-проекциями и действиями подгрупп в контексте редуцированного слова.

LaTeX

$$Lemma about equalities of fst-projections under unit-involved multiplications in reduced words.$$

Lean4

@[to_additive]
theorem powers_le_zpowers {G : Type*} [Group G] (g : G) : Submonoid.powers g ≤ (Subgroup.zpowers g).toSubmonoid :=
  by
  rw [Subgroup.toSubmonoid_zpowers]
  exact le_sup_left

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