Theorems · Theorem · general topology
RestrictedProduct.mulSingle_ne_one_iff
∀ {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) → One (G i)] [inst_3 : ∀ (i : ι), OneMemClass (S i) (G i)] (i : ι)
{x : G i}, RestrictedProduct.mulSingle A i x ≠ 1 ↔ x ≠ 1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- SetLikestatement and proof · cited by 1,084
- Filter.cofinitestatement · cited by 251
- RestrictedProductstatement · cited by 117
- Subtype.coe_ne_coeproof · cited by 27
- OneMemClassstatement and proof · cited by 21
- RestrictedProduct.mulSinglestatement · cited by 16
- Pi.mulSingle_ne_one_iffproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.