Mathlib Map

Theorems · Definition · group theory

OneHom.mulSingle

{I : Type u} →
  (f : I → Type v) → [DecidableEq I] → [inst : (i : I) → One (f i)] → (i : I) → OneHom (f i) ((i : I) → f i)

The one-preserving homomorphism including a single value into a dependent family of values, as functions supported at a point. This is the OneHom version of Pi.mulSingle.

Defined in
Mathlib.Algebra.Group.Pi.Lemmas
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqOne
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MonoidHom.mulSingle · cited by 21MonoidHom.mulSingleOneHom.coe_mulSingle · cited by 0OneHom.coe_mulSingleOneHom.mulSingle_apply · cited by 0OneHom.mulSingle_applyPi.mulSingle · cited by 111Pi.mulSingleOneHom · cited by 55OneHomPi.mulSingle_one · cited by 4Pi.mulSingle_oneOneHom.mulSingleCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.