trans — Mathlib

English

Equivalences relating the support of k•g and the action of k⁻¹ on elements.

Русский

Эквивалентности опоры k•g и действия k⁻¹ на элементы.

LaTeX

$$theorem mem_conj_support (k : ConjAct (Perm α)) (g : Perm α) (a : α) : a ∈ (k • g).support ↔ ConjAct.ofConjAct k⁻¹ a ∈ g.support$$

Lean4

@[trans]
theorem trans : SameCycle f x y → SameCycle f y z → SameCycle f x z := fun ⟨i, hi⟩ ⟨j, hj⟩ =>
  ⟨j + i, by rw [zpow_add, mul_apply, hi, hj]⟩

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