ofPermHomFun_apply_of_mem_fixedPoints

English

For any Basis a, τ, x, the application of a.ofPermHom τ x coincides with a.ofPermHomFun τ x.

Русский

Для любого a, τ и x применение a.ofPermHom τ x совпадает с a.ofPermHomFun τ x.

LaTeX

$$$a.ofPermHom τ x = a.ofPermHomFun τ x$$$

Lean4

theorem ofPermHomFun_apply_of_mem_fixedPoints {x : α} (hx : x ∈ Function.fixedPoints g) : ofPermHomFun a τ x = x :=
  by
  rw [ofPermHomFun, dif_neg]
  rw [cycleOf_mem_cycleFactorsFinset_iff, notMem_support]
  exact hx

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