Theorems · Theorem · linear algebra
iSupIndep_of_dfinsuppSumAddHom_injective
∀ {ι : Type u_1} {N : Type u_6} [inst : DecidableEq ι] [inst_1 : AddCommMonoid N] (p : ι → AddSubmonoid N),
Function.Injective ⇑(DFinsupp.sumAddHom fun i => (p i).subtype) → iSupIndep pIf DFinsupp.sumAddHom applied with AddSubmonoid.subtype is injective then the additive
submonoids are independent.
- Defined in
- Mathlib.LinearAlgebra.DFinsupp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement · cited by 3,230
- AddSubmonoidstatement and proof · cited by 1,178
- DFinsuppstatement · cited by 694
- iSupIndepstatement · cited by 100
- DFinsupp.sumAddHomstatement and proof · cited by 38
- AddSubmonoid.subtypestatement and proof · cited by 28
- AddSubmonoid.toNatSubmoduleproof · cited by 9
- iSupIndep_map_orderIso_iffproof · cited by 5
- iSupIndep_of_dfinsupp_lsum_injectiveproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- DirectSum.IsInternal.addSubmonoid_iSupIndepproof · cited by 0