Theorems · Theorem · sequences and series
HasProd.prod_range_mul
∀ {M : Type u_1} [inst : CommMonoid M] [inst_1 : TopologicalSpace M] {m : M} [ContinuousMul M] {f : ℕ → M} {k : ℕ},
HasProd (fun n => f (n + k)) m → HasProd f ((∏ i ∈ Finset.range k, f i) * m)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- Equiv.symmproof · cited by 3,681
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Finset.rangestatement and proof · cited by 1,341
- ContinuousMulstatement and proof · cited by 343
- HasProdstatement and proof · cited by 157
- Equiv.hasProd_iffproof · cited by 8
- notMemRangeEquivproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Multipliable.prod_mul_tprod_nat_mul'proof · cited by 2
- HasProd.zero_mulproof · cited by 1
- Multipliable.comp_nat_addproof · cited by 0