Theorems · Theorem · sequences and series
HasProd.of_nat_of_neg_add_one
∀ {M : Type u_1} [inst : CommMonoid M] [inst_1 : TopologicalSpace M] {m m' : M} [ContinuousMul M] {f : ℤ → M},
HasProd (fun n => f ↑n) m → HasProd (fun n => f (-(↑n + 1))) m' → HasProd f (m * m')- Cited by
- 5 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Set.rangeproof · cited by 4,705
- CommMonoidstatement and proof · cited by 2,264
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- IsComplproof · cited by 351
- ContinuousMulstatement and proof · cited by 343
- HasProdstatement and proof · cited by 157
- disjoint_iff_inf_leproof · cited by 64
- Nat.cast_injectiveproof · cited by 39
- codisjoint_iff_le_supproof · cited by 15
- HasProd.mul_isComplproof · cited by 4
- Function.Injective.hasProd_range_iffproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- HasProd.of_add_one_of_neg_add_oneproof · cited by 2
- HasProd.of_nat_of_negproof · cited by 2
- Multipliable.of_nat_of_neg_add_oneproof · cited by 2
- HasProd.int_recproof · cited by 1
- tprod_of_nat_of_neg_add_oneproof · cited by 0