Theorems · Theorem · combinatorics
Fin.prod_univ_eq_prod_range
∀ {α : Type u_1} [inst : CommMonoid α] (f : ℕ → α) (n : ℕ), ∏ i, f ↑i = ∏ i ∈ Finset.range n, f iIt is equivalent to compute the product of a function over Fin n or Finset.range n.
- Defined in
- Mathlib.Data.Fintype.BigOperators
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 78 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetproof · cited by 13,712
- Finset.univstatement · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.rangestatement and proof · cited by 1,341
- Equiv.transproof · cited by 337
- Finset.prod_attachproof · cited by 22
- Fintype.prod_equivproof · cited by 18
- Equiv.subtypeEquivRightproof · cited by 17
- Finset.attach_eq_univproof · cited by 9
- Fin.equivSubtypeproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- Finset.prod_fin_eq_prod_rangeproof · cited by 2
- Finset.prod_rangeproof · cited by 1
- LinearMap.normDet_eq_prod_singularValuesproof · cited by 0
- Matrix.superFactorial_dvd_vandermonde_detproof · cited by 0
- Matrix.det_vandermonde_id_eq_superFactorialproof · cited by 0