Theorems · Theorem · linear algebra
iSupIndep.dfinsuppSumAddHom_injective
∀ {ι : Type u_1} {N : Type u_6} [inst : DecidableEq ι] [inst_1 : AddCommGroup N] {p : ι → AddSubgroup N},
iSupIndep p → Function.Injective ⇑(DFinsupp.sumAddHom fun i => (p i).subtype)The canonical map out of a direct sum of a family of additive subgroups is injective when the
additive subgroups are iSupIndep.
- Defined in
- Mathlib.LinearAlgebra.DFinsupp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqAddCommGroup
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 · cited by 62,936
- AddCommGroupstatement and proof · cited by 12,871
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement · cited by 3,230
- DFinsuppstatement · cited by 694
- iSupIndepstatement and proof · cited by 100
- AddSubgroup.subtypestatement · cited by 82
- DFinsupp.sumAddHomstatement · cited by 38
- AddSubgroup.toIntSubmoduleproof · cited by 25
- iSupIndep_map_orderIso_iffproof · cited by 5
- iSupIndep.dfinsupp_lsum_injectiveproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- iSupIndep_iff_dfinsuppSumAddHom_injectiveproof · cited by 0