finChoiceEquiv — Mathlib

English

A related simplification for finLiftOn when passing a → α i via mk.

Русский

Связанные упрощения для finLiftOn при переходе к mk.

LaTeX

$$$\\text{simp} \\ (\\text{finChoice} \\nabla) $$$

Lean4

/-- `Quotient.finChoice` as an equivalence. -/
@[simps]
def finChoiceEquiv : (∀ i, Quotient (S i)) ≃ @Quotient (∀ i, α i) piSetoid
    where
  toFun := finChoice
  invFun := eval
  left_inv
    q := by
    refine induction_on_fintype_pi q (fun a ↦ ?_)
    rw [finChoice_eq]
    rfl
  right_inv
    q := by
    induction q using Quotient.ind
    exact finChoice_eq _

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