Theorems · Theorem · group theory
Finset.prod_comm
∀ {α : Type u_3} {β : Type u_4} {γ : Type u_5} [inst : CommMonoid β] {s : Finset γ} {t : Finset α} {f : γ → α → β},
∏ x ∈ s, ∏ y ∈ t, f x y = ∏ y ∈ t, ∏ x ∈ s, f x y- Cited by
- 8 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.prod_comm'proof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- finprod_prod_commproof · cited by 3
- NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_powproof · cited by 1
- Finset.prod_prod_bipartiteAbove_eq_prod_prod_bipartiteBelowproof · cited by 0
- Finsupp.prod_finsetProd_commproof · cited by 0
- Finset.prod_comm_cycleproof · cited by 0
- DFinsupp.prod_commproof · cited by 0
- finprod_mem_commproof · cited by 0
- Finsupp.prod_commproof · cited by 0