Theorems · Theorem · linear algebra
Module.End.pow_apply_mem_of_forall_mem
∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {f' : M →ₗ[R] M}
{p : Submodule R M} (n : ℕ), (∀ x ∈ p, f' x ∈ p) → ∀ x ∈ p, (f' ^ n) x ∈ p- Cited by
- 7 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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 and proof · cited by 62,936
- 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
- pow_zeroproof · cited by 1,094
Cited by7
Results whose statement or proof uses this declaration.
- Module.End.pow_restrictstatement · cited by 6
- Module.End.isNilpotent_restrict_genEigenspace_natproof · cited by 4
- Module.End.isNilpotent_restrict_of_leproof · cited by 3
- Module.End.genEigenspace_restrictproof · cited by 2
- Module.End.isNilpotent.restrictproof · cited by 2
- LieModule.isNilpotent_toEnd_sub_algebraMapproof · cited by 2
- Module.End.mapsTo_restrict_maxGenEigenspace_restrict_of_mapsToproof · cited by 1