Theorems · Theorem · linear algebra
Submodule.le_dualAnnihilator_dualCoannihilator
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(U : Submodule R M), U ≤ U.dualAnnihilator.dualCoannihilator- Defined in
- Mathlib.LinearAlgebra.Dual.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- 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
- Submodule.dualAnnihilatorstatement · cited by 77
- GaloisConnection.le_u_lproof · cited by 52
- Submodule.dualCoannihilatorstatement · cited by 41
- Submodule.dualAnnihilator_gcproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- Subspace.dualAnnihilator_dualCoannihilator_eqproof · cited by 2
- Submodule.sup_dualAnnihilator_le_infproof · cited by 1
- Submodule.iSup_dualAnnihilator_le_iInfproof · cited by 0