biUnion — Mathlib

English

Folding with a binary operation over a disjiUnion equals folding over the base set and then folding inside each fibre.

Русский

Свёртка по дисjoint‑объединению равна свёртке по базовому множеству с затем свёрткой внутри каждой волокны.

LaTeX

$$$\\text{fold}_op (s.disjiUnion t h) (b) f = \\text{fold}_op b_0 (\\lambda i => (t i).fold_op (b i) f) s$$$

Lean4

/-- `Finset.biUnion s t` is the union of `t a` over `a ∈ s`.

(This was formerly `bind` due to the monad structure on types with `DecidableEq`.) -/
protected def biUnion (s : Finset α) (t : α → Finset β) : Finset β :=
  (s.1.bind fun a ↦ (t a).1).toFinset

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