Theorems · Theorem · group theory
Finset.prod_Ico_succ_top
∀ {M : Type u_3} [inst : CommMonoid M] {a b : ℕ},
a ≤ b → ∀ (f : ℕ → M), ∏ k ∈ Finset.Ico a (b + 1), f k = (∏ k ∈ Finset.Ico a b, f k) * f b- Defined in
- Mathlib.Algebra.BigOperators.Intervals
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 64 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- mul_commproof · cited by 2,262
- Finset.Icostatement and proof · cited by 450
- Finset.prod_insertproof · cited by 109
- Finset.right_notMem_Icoproof · cited by 13
- Finset.insert_Ico_right_eq_Ico_add_oneproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- gaussSum_pow_eq_prod_jacobiSum_auxproof · cited by 1
- discrete_gronwall_prod_generalproof · cited by 1
- Finset.prod_Ico_succ_div_topproof · cited by 0
- Finset.prod_Icc_succ_topproof · cited by 0