Theorems · Definition · order theory
AddSubmonoid.toNatSubmodule
{M : Type u_3} → [inst : AddCommMonoid M] → AddSubmonoid M ≃o Submodule ℕ MAn additive submonoid is equivalent to a ℕ-submodule.
- Defined in
- Mathlib.Algebra.Module.Submodule.Lattice
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoid
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.
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement · cited by 7,192
- AddSubmonoidstatement and proof · cited by 1,178
- OrderIsostatement · cited by 874
- Submodule.toAddSubmonoidproof · cited by 162
Cited by9
Results whose statement or proof uses this declaration.
- Submodule.span_nat_eq_addSubmonoidClosureproof · cited by 5
- AddSubmonoid.fg_iff_exists_fin_addMonoidHomproof · cited by 4
- AddSubmonoid.toNatSubmodule_toAddSubmonoidstatement and proof · cited by 2
- iSupIndep_of_dfinsuppSumAddHom_injectiveproof · cited by 1
- Nat.addSubmonoid_fgproof · cited by 0
- AddSubmonoid.coe_toNatSubmodulestatement · cited by 0
- Submodule.toAddSubmonoid_toNatSubmodulestatement and proof · cited by 0
- AddSubmonoid.toNatSubmodule_closurestatement · cited by 0
- AddSubmonoid.toNatSubmodule_symmstatement · cited by 0