zpowersEquivSupport_symm_apply — Mathlib

English

The inverse of the z-powers support map sends ⟨(σ^n)(choose hσ), mem⟩ back to ⟨σ^n, n, rfl⟩ for a cycle σ.

Русский

Обратное z-поковому отображению опоры переводит обратно к ⟨σ^n, n, rfl⟩ для цикла σ.

LaTeX

$$$ hσ.zpowersEquivSupport.symm ⟨(σ^n)(Classical.choose hσ), pow\_apply\_mem\_support.2 (mem\_support.2 (Classical.choose\_spec hσ).1)⟩ = ⟨σ^n, n, rfl⟩ $$$

Lean4

@[simp]
theorem zpowersEquivSupport_symm_apply {σ : Perm α} (hσ : IsCycle σ) (n : ℕ) :
    hσ.zpowersEquivSupport.symm
        ⟨(σ ^ n) (Classical.choose hσ), pow_apply_mem_support.2 (mem_support.2 (Classical.choose_spec hσ).1)⟩ =
      ⟨σ ^ n, n, rfl⟩ :=
  (Equiv.symm_apply_eq _).2 hσ.zpowersEquivSupport_apply

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