Theorems · Theorem · linear algebra
Module.End.mem_invtSubmodule
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(f : Module.End R M) {p : Submodule R M}, p ∈ f.invtSubmodule ↔ p ≤ Submodule.comap f p- Cited by
- 9 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Module.Endstatement and proof · cited by 774
- Submodule.comapstatement · cited by 347
- Sublatticestatement · cited by 225
- Module.End.invtSubmodulestatement · cited by 93
Cited by9
Results whose statement or proof uses this declaration.
- LinearMap.IsIdempotentElem.ker_mem_invtSubmodule_iffproof · cited by 4
- RootPairing.span_root_image_eq_top_of_forall_orthogonalproof · cited by 1
- RootPairing.rootSpan_mem_invtSubmodule_reflectionproof · cited by 1
- RootPairing.invtSubmodule_reflection_of_invtSubmodule_coreflectionproof · cited by 1
- LinearEquiv.map_mem_invtSubmodule_conj_iffproof · cited by 1
- Module.End.span_orbit_mem_invtSubmoduleproof · cited by 1
- LieIdeal.rootSpan_mem_invtRootSubmoduleproof · cited by 1
- Submodule.mem_invtSubmodule_reflection_of_memproof · cited by 1
- RootPairing.Base.induction_on_cartanMatrixproof · cited by 0