Theorems · Theorem · order theory
AddSubmonoid.toNatSubmodule_toAddSubmonoid
∀ {M : Type u_3} [inst : AddCommMonoid M] (S : AddSubmonoid M), (AddSubmonoid.toNatSubmodule S).toAddSubmonoid = S- Defined in
- Mathlib.Algebra.Module.Submodule.Lattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement · cited by 7,192
- AddSubmonoidstatement and proof · cited by 1,178
- OrderIsostatement · cited by 874
- Submodule.toAddSubmonoidstatement · cited by 162
- OrderIso.symm_apply_applyproof · cited by 41
- AddSubmonoid.toNatSubmodulestatement and proof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- AddSubmonoid.fg_iff_exists_fin_addMonoidHomproof · cited by 4
- Nat.addSubmonoid_fgproof · cited by 0