Theorems · Theorem · combinatorics
Fin.prod_univ_succ
∀ {M : Type u_2} [inst : CommMonoid M] {n : ℕ} (f : Fin (n + 1) → M), ∏ i, f i = f 0 * ∏ i, f i.succA product of a function f : Fin (n + 1) → M over all Fin (n + 1)
is the product of f 0 times the remaining product
- Defined in
- Mathlib.Algebra.BigOperators.Fin
- Cited by
- 17 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.univstatement · cited by 3,473
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Fin.prod_univ_succAboveproof · cited by 9
Cited by17
Results whose statement or proof uses this declaration.
- Fin.prod_univ_twoproof · cited by 16
- MvPolynomial.finSuccEquiv_coeff_coeffproof · cited by 5
- VectorFourier.fourierIntegral_iteratedFDerivproof · cited by 2
- MeasureTheory.integral_fin_nat_prod_eq_prodproof · cited by 2
- NNReal.geom_mean_le_arith_mean2_weightedproof · cited by 1
- NNReal.geom_mean_le_arith_mean3_weightedproof · cited by 1
- NNReal.geom_mean_le_arith_mean4_weightedproof · cited by 1
- DihedralGroup.commProb_consproof · cited by 1
- VectorFourier.hasFTaylorSeriesUpTo_fourierIntegralproof · cited by 1
- Matrix.det_succ_column_zeroproof · cited by 1
- MeasureTheory.Integrable.fin_nat_prodproof · cited by 1
- ContinuousMultilinearMap.norm_map_cons_leproof · cited by 0