Theorems · Definition · group theory
Finsupp.uniqueAddEquiv
{ι : Type u_1} → {M : Type u_3} → [inst : AddZeroClass M] → ι → [Subsingleton ι] → (ι →₀ M) ≃+ MIf M is the trivial monoid, then the monoid of finitely supported functions ι →₀ M is
is isomorphic to M.
- Defined in
- Mathlib.Algebra.Group.Finsupp
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClassSubsingleton
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- Finsuppstatement and proof · cited by 5,255
- AddZeroClassstatement and proof · cited by 1,237
- AddEquivstatement · cited by 1,087
- Finsupp.uniqueEquivproof · cited by 7
Cited by10
Results whose statement or proof uses this declaration.
- Finsupp.uniqueLinearEquivproof · cited by 16
- MonoidAlgebra.uniqueLinearEquivproof · cited by 11
- MonoidAlgebra.uniqueRingEquivproof · cited by 7
- AddMonoidAlgebra.uniqueRingEquivproof · cited by 5
- Finsupp.uniqueAddEquiv_symm_applystatement and proof · cited by 4
- AddMonoidAlgebra.uniqueLinearEquivproof · cited by 2
- PowerSeries.coeff_prodproof · cited by 2
- Finsupp.uniqueAddEquiv.congr_simpstatement and proof · cited by 0
- Finsupp.uniqueAddEquiv_applystatement and proof · cited by 0
- Finsupp.uniqueAddEquiv_symm_apply_applystatement · cited by 0