Theorems · Theorem · sequences and series
Equiv.hasProd_iff
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] {f : β → α} {a : α}
(e : γ ≃ β), HasProd (f ∘ ⇑e) a ↔ HasProd f a- Cited by
- 8 results in Mathlib
- Foundations
- Depth 83 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Equivstatement and proof · cited by 8,337
- CommMonoidstatement and proof · cited by 2,264
- SummationFilter.unconditionalstatement · cited by 2,068
- Equiv.injectiveproof · cited by 464
- HasProdstatement · cited by 157
- EquivLike.range_eq_univproof · cited by 27
- Function.Injective.hasProd_iffproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- Equiv.multipliable_iffproof · cited by 3
- HasProd.prod_range_mulproof · cited by 3
- Equiv.hasProd_iff_of_mulSupportproof · cited by 2
- HasProd.prod_fiberwiseproof · cited by 2
- Function.Injective.hasProd_range_iffproof · cited by 2
- hasProd_nat_add_iffproof · cited by 1
- hasProd_pnat_iff_hasProd_succproof · cited by 0
- HasProd.tprod_fiberwiseproof · cited by 0