map_finCongr_Ioi — Mathlib

English

Let h : n = m and i ∈ Fin n. The image of Ioi(i) under Fin.cast h is Ioi(i.cast h).

Русский

Пусть h : n = m и i ∈ Fin n. Образ Ioi(i) при приведении Fin.cast h равен Ioi(i.cast h).

LaTeX

$$$$ \operatorname{Finset.image}(\operatorname{Fin.cast} h)(\operatorname{Finset.Ioi}(i)) = \operatorname{Finset.Ioi}(\operatorname{Fin.cast} h\, i) $$$$

Lean4

@[simp]
theorem map_finCongr_Ioi (h : n = m) (i : Fin n) : (Ioi i).map (finCongr h).toEmbedding = Ioi (i.cast h) := by
  simp [← coe_inj]

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