Theorems · Theorem · linear algebra
Submodule.flip_quotDualCoannihilatorToDual_injective
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
(W : Submodule R (Module.Dual R M)), Function.Injective ⇑W.quotDualCoannihilatorToDual.flip- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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 · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- HasQuotient.Quotientstatement · cited by 2,301
- LinearMap.extproof · cited by 844
- Module.Dualstatement and proof · cited by 583
- DFunLike.congr_funproof · cited by 288
- LinearMap.flipstatement and proof · cited by 193
Cited by3
Results whose statement or proof uses this declaration.
- Subspace.quotDualCoannihilatorToDual_bijectiveproof · cited by 1
- Submodule.quotDualCoannihilatorToDual_nondegenerateproof · cited by 0
- Subspace.finiteDimensional_quot_dualCoannihilator_iffproof · cited by 0