Theorems · Theorem · sequences and series
tprod_subtype_eq_of_mulSupport_subset
∀ {α : Type u_1} {β : Type u_2} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] {f : β → α} {s : Set β},
Function.mulSupport f ⊆ s → ∏' (x : ↑s), f ↑x = ∏' (x : β), f x- Cited by
- 5 results in Mathlib
- Foundations
- Depth 84 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 · cited by 2,068
- Function.mulSupportstatement and proof · cited by 240
- Subtype.val_injectiveproof · cited by 232
- tprodstatement · cited by 230
- Subtype.range_coe_subtypeproof · cited by 170
- Function.Injective.tprod_eqproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- tprod_mulIndicator_of_disjoint_on_mulSupport_of_memproof · cited by 2
- tprod_subtypeproof · cited by 2
- tprod_univproof · cited by 2
- tprod_subtype_mulSupportproof · cited by 1
- tprod_eq_tprod_primes_of_mulSupport_subset_prime_powersproof · cited by 1