append_left — Mathlib

English

Left append behavior aligns with a canonical choice of enumeration of s.

Русский

Лево-приключение согласуется с выборами перечисления s.

LaTeX

$$$\mathrm{append\_left}: \mathrm{Fin}(n) \hookrightarrow \mathrm{FixSubgroup}(M,s) \Rightarrow \mathrm{...}$$$

Lean4

@[to_additive]
theorem append_left {n : ℕ} [Finite s] (x : Fin n ↪ ofFixingSubgroup M s) (i : Fin s.ncard) :
    let Hs : Nonempty (Fin (s.ncard) ≃ s) := Finite.card_eq.mp (by simp [Nat.card_coe_set_eq])
    ofFixingSubgroup.append x (Fin.castAdd n i) = (Classical.choice Hs) i :=
  by simp [ofFixingSubgroup.append]

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