Theorems · Theorem · linear algebra
Submodule.le_comap_pow_of_le_comap
∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (p : Submodule R M)
{f : M →ₗ[R] M}, p ≤ Submodule.comap f p → ∀ (k : ℕ), p ≤ Submodule.comap (f ^ k) p- Defined in
- Mathlib.Algebra.Module.Submodule.Map
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- LE.le.transproof · cited by 3,151
- pow_zeroproof · cited by 1,094
- Submodule.comapstatement and proof · cited by 347
- Submodule.comap_monoproof · cited by 18
- Module.End.iterate_succproof · cited by 5
- Submodule.comap_idproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.mapQ_powstatement and proof · cited by 1
- Module.End.IsNilpotent.mapQproof · cited by 1