Theorems · Theorem · sequences and series
hasProd_subtype_iff_of_mulSupport_subset
∀ {α : Type u_1} {β : Type u_2} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] {f : β → α} {a : α} {s : Set β},
Function.mulSupport f ⊆ s → (HasProd (f ∘ Subtype.val) a ↔ HasProd f a)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 82 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- CommMonoidstatement and proof · cited by 2,264
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Function.mulSupportstatement and proof · cited by 240
- HasProdstatement and proof · cited by 157
- Function.Embedding.subtypeproof · cited by 128
- SummationFilter.comap_unconditionalproof · cited by 4
- hasProd_subtype_comap_iff_of_mulSupport_subsetproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- hasProd_subtype_iff_mulIndicatorproof · cited by 7
- hasProd_prod_of_ne_finset_oneproof · cited by 1
- hasProd_subtype_mulSupportproof · cited by 1