Theorems · Theorem · linear algebra
Submodule.dualAnnihilator_top
∀ {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
- 6 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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 and proof · cited by 583
- Submodule.dualAnnihilatorstatement · cited by 77
Cited by6
Results whose statement or proof uses this declaration.
- RootPairing.eq_zero_iff_forall_coroot'_eq_zeroproof · cited by 2
- LinearMap.IsPerfectCompl.left_top_iffproof · cited by 1
- Subspace.dualAnnihilator_iInf_eqproof · cited by 1
- Subspace.isCompl_dualAnnihilatorproof · cited by 0
- RootPairing.eq_top_of_mem_invtSubmodule_of_forall_eq_univproof · cited by 0
- Submodule.dualCoannihilator_topproof · cited by 0