Theorems · Theorem · combinatorics
Fin.prod_univ_castSucc
∀ {M : Type u_2} [inst : CommMonoid M] {n : ℕ} (f : Fin (n + 1) → M), ∏ i, f i = (∏ i, f i.castSucc) * f (Fin.last n)A product of a function f : Fin (n + 1) → M over all Fin (n + 1)
is the product of f (Fin.last n) times the remaining product
- Defined in
- Mathlib.Algebra.BigOperators.Fin
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 79 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- mul_commproof · cited by 2,262
- Finset.prod_congrproof · cited by 646
- Fin.succAbove_lastproof · cited by 14
- Fin.prod_univ_succAboveproof · cited by 9
Cited by10
Results whose statement or proof uses this declaration.
- Fin.prod_univ_threeproof · cited by 4
- Fin.prod_univ_sevenproof · cited by 1
- Fin.prod_univ_sixproof · cited by 1
- Fin.prod_univ_fiveproof · cited by 1
- Fin.prod_univ_fourproof · cited by 1
- ContinuousMultilinearMap.norm_map_init_leproof · cited by 0
- ContinuousMultilinearMap.norm_map_snoc_leproof · cited by 0
- Fin.prod_prod_eq_prod_triangle_mulproof · cited by 0
- Fin.prod_snocproof · cited by 0
- Fin.prod_univ_eightproof · cited by 0