sigmaUnique — Mathlib

English

Any family of Unique types is a right identity for dependent type product up to equivalence: (a: α) × β a ≃ β default.

Русский

Любая familie уникальных типов является правым тождеством для зависимого произведения: (a: α) × β a ≃ β default.

LaTeX

$$$$ (\\alpha) \\times (\\beta(\\cdot)) \\simeq \\beta(\\mathrm{default}). $$$$

Lean4

/-- Any family of `Unique` types is a right identity for dependent type product up to
equivalence. -/
def sigmaUnique (α) (β : α → Type*) [∀ a, Unique (β a)] : (a : α) × (β a) ≃ α :=
  (Equiv.sigmaCongrRight fun a ↦ equivPUnit.{_, 1} (β a)).trans <| sigmaPUnit α

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