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Theorems · Theorem · general topology

RestrictedProduct.single_zero

∀ {ι : Type u_1} {S : ι → Type u_3} {G : ι → Type u_4} [inst : (i : ι) → SetLike (S i) (G i)] (A : (i : ι) → S i)
  [inst_1 : DecidableEq ι] [inst_2 : (i : ι) → Zero (G i)] [inst_3 : ∀ (i : ι), ZeroMemClass (S i) (G i)] (i : ι),
  RestrictedProduct.single A i 0 = 0
Defined in
Mathlib.Topology.Algebra.RestrictedProduct.Basic
Cited by
0 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SetLikeDecidableEqZeroZeroMemClass
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SetLike.coe · cited by 8199SetLike.coeSetLike · cited by 1084SetLikeFilter.cofinite · cited by 251Filter.cofiniteRestrictedProduct · cited by 117RestrictedProductZeroMemClass · cited by 25ZeroMemClassRestrictedProduct.single · cited by 18RestrictedProduct.singleRestrictedProduct.ext · cited by 15RestrictedProduct.extPi.single_zero · cited by 10Pi.single_zeroRestrictedProduct.single_zeroCITED BYCITES

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