cycleOf_inv — Mathlib

English

As with cycleOf_inv, we have cycleOf f x inverted equals cycleOf f^{-1} x.

Русский

Как и в cycleOf_inv, цикл f x обращается к инверсии: (cycleOf f x)^{-1} = cycleOf f^{-1} x.

LaTeX

$$$ (cycleOf f x)^{-1} = cycleOf f^{-1} x $$$

Lean4

theorem cycleOf_inv (f : Perm α) [DecidableRel f.SameCycle] (x : α) : (cycleOf f x)⁻¹ = cycleOf f⁻¹ x :=
  Equiv.ext fun y => by
    rw [inv_eq_iff_eq, cycleOf_apply, cycleOf_apply]
    split_ifs <;> simp_all [sameCycle_inv, sameCycle_inv_apply_right]

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