Theorems · Definition · general algebraic systems
Pi.mulSingle
{ι : Type u_1} → {M : ι → Type u_6} → [(i : ι) → One (M i)] → [DecidableEq ι] → (i : ι) → M i → (j : ι) → M jThe function supported at i, with value x there, and 1 elsewhere.
- Defined in
- Mathlib.Algebra.Notation.Pi.Basic
- Cited by
- 111 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 18 definitions · uses no axioms
- Assumes
- OneDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Function.updateproof · cited by 502
Cited by113
Results whose statement or proof uses this declaration.
- Pi.mulSingle_eq_samestatement · cited by 18
- RestrictedProduct.mulSingleproof · cited by 16
- Pi.mulSingle_eq_of_nestatement · cited by 14
- Pi.mulSingle_applystatement · cited by 6
- Pi.mulSingle_onestatement · cited by 4
- MonoidHom.noncommPiCoprod_mulSinglestatement and proof · cited by 3
- Pi.mulSingle_apply_commutestatement and proof · cited by 3
- Pi.mulSingle_injectivestatement · cited by 3
- MonoidHom.noncommPiCoprod_rangeproof · cited by 2
- Finset.noncommProd_mulSinglestatement and proof · cited by 2
- Finset.univ_prod_mulSinglestatement and proof · cited by 2
- OneHom.mulSingleproof · cited by 2