Theorems · Theorem · sequences and series
HasProd.nat_mul_neg_add_one
∀ {M : Type u_1} [inst : CommMonoid M] [inst_1 : TopologicalSpace M] {m : M} {f : ℤ → M},
HasProd f m → HasProd (fun n => f ↑n * f (-(↑n + 1))) m- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidTopologicalSpace
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.
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetproof · cited by 13,712
- Finset.prodproof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Finset.imageproof · cited by 910
- Function.Injective.injOnproof · cited by 280
- HasProdstatement and proof · cited by 157
- Finset.preimageproof · cited by 108
- Finset.prod_mul_distribproof · cited by 68
- Nat.cast_injectiveproof · cited by 39
- Finset.prod_unionproof · cited by 31
Cited by2
Results whose statement or proof uses this declaration.
- Multipliable.nat_mul_neg_add_oneproof · cited by 0
- tprod_nat_mul_neg_add_oneproof · cited by 0