Theorems · Theorem · combinatorics

Finset.prod_prod_bipartiteAbove_eq_prod_prod_bipartiteBelow

∀ {R : Type u_1} {α : Type u_2} {β : Type u_3} (r : α → β → Prop) {s : Finset α} {t : Finset β} [inst : CommMonoid R]
  (f : α → β → R) [inst_1 : (a : α) → (b : β) → Decidable (r a b)],
  ∏ a ∈ s, ∏ b ∈ Finset.bipartiteAbove r t a, f a b = ∏ b ∈ t, ∏ a ∈ Finset.bipartiteBelow r s b, f a b

Defined in

Mathlib.Combinatorics.Enumerative.DoubleCounting

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidDecidable