decidableMemRange — Mathlib

English

The range size of sigma-congrRightHom equals the product of the sizes of permutation groups across α.

Русский

Мощность образа sigmaCongrRightHom равна произведению мощностей групп перестановок по каждому элементу множества.

LaTeX

$$$\\mathrm{Fintype.card}(\\mathrm{range}(\\mathrm{sigmaCongrRightHom}(\\beta))) = \\mathrm{Fintype.card}\\left(\\prod_{a\\in\\alpha} \\mathrm{Perm}(\\beta(a))\\right)$$$

Lean4

instance decidableMemRange {α β : Type*} [DecidableEq α] [DecidableEq β] [Fintype α] [Fintype β] :
    DecidablePred (· ∈ (sumCongrHom α β).range) := fun _ => inferInstance

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