Theorems · Theorem · commutative algebra
Submodule.torsionBySet_le_torsionBySet_of_subset
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {s t : Set R},
s ⊆ t → Submodule.torsionBySet R M t ≤ Submodule.torsionBySet R M s- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- Set.imageproof · cited by 5,609
- Submodule.torsionBySetstatement · cited by 34
- Submodule.torsionByproof · cited by 31
- sInf_le_sInfproof · cited by 23
Cited by5
Results whose statement or proof uses this declaration.
- Submodule.iSup_torsionBySet_ideal_eq_torsionBySet_iInfproof · cited by 5
- Submodule.torsionBySet_eq_torsionBySet_spanproof · cited by 2
- Submodule.torsionBySet_univproof · cited by 2
- Submodule.torsionBySet_le_torsionBySet_powproof · cited by 1
- Submodule.torsionBy_le_torsionBy_of_dvdproof · cited by 0