Theorems · Theorem · sequences and series
HasProd.of_add_one_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 + 1)) m → HasProd (fun n => f (-(↑n + 1))) m' → HasProd f (m * f 0 * m')- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- TopologicalSpacestatement and proof · cited by 24,529
- CommMonoidstatement and proof · cited by 2,264
- mul_commproof · cited by 2,262
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- ContinuousMulstatement and proof · cited by 343
- HasProdstatement and proof · cited by 157
- HasProd.of_nat_of_neg_add_oneproof · cited by 5
- HasProd.zero_mulproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Multipliable.of_add_one_of_neg_add_oneproof · cited by 0
- tprod_of_add_one_of_neg_add_oneproof · cited by 0