Theorems · Theorem · linear algebra
Submodule.dualAnnihilator_bot
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
⊥.dualAnnihilator = ⊤- Defined in
- Mathlib.LinearAlgebra.Dual.Defs
- Cited by
- 5 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.
Cites11
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- Bot.botstatement · cited by 4,720
- Module.Dualstatement · cited by 583
- Submodule.dualAnnihilatorstatement · cited by 77
- GaloisConnection.l_botproof · cited by 63
- Submodule.dualAnnihilator_gcproof · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- LinearMap.dualMap_surjective_iffproof · cited by 2
- LieAlgebra.IsKilling.span_weight_eq_topproof · cited by 2
- LieAlgebra.IsKilling.iInf_ker_weight_eq_botproof · cited by 2
- Submodule.dualAnnihilator_eq_top_iffproof · cited by 1
- Subspace.isCompl_dualAnnihilatorproof · cited by 0