Theorems · Theorem · group theory
Finset.prod_range_succ
∀ {M : Type u_4} [inst : CommMonoid M] (f : ℕ → M) (n : ℕ),
∏ x ∈ Finset.range (n + 1), f x = (∏ x ∈ Finset.range n, f x) * f n- Cited by
- 21 results in Mathlib
- Foundations
- Depth 68 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- mul_commproof · cited by 2,262
- Finset.rangestatement and proof · cited by 1,341
- Finset.prod_range_succ_commproof · cited by 3
Cited by21
Results whose statement or proof uses this declaration.
- Finset.prod_range_inductionproof · cited by 4
- Polynomial.cyclotomic_prime_pow_eq_geom_sumproof · cited by 3
- iter_deriv_zpow'proof · cited by 2
- int_prod_range_nonnegproof · cited by 1
- Finset.eventually_constant_prodproof · cited by 1
- Finset.prod_pow_choose_succproof · cited by 1
- Complex.GammaSeq_add_one_leftproof · cited by 1
- Complex.GammaSeq_mulproof · cited by 1
- pow_two_pow_sub_pow_two_powproof · cited by 1
- Real.Wallis.W_eq_factorial_ratioproof · cited by 1
- Real.Wallis.W_succproof · cited by 1
- Finset.prod_range_addproof · cited by 1