Theorems · Theorem · linear algebra
Submodule.quotDualCoannihilatorToDual_apply
∀ {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)) (m : M) (w : ↥W),
(W.quotDualCoannihilatorToDual (Submodule.Quotient.mk m)) w = ↑w m- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- Module.Dualstatement and proof · cited by 583
- Submodule.Quotient.mkstatement · cited by 184
- Submodule.dualCoannihilatorstatement · cited by 41
- Submodule.quotDualCoannihilatorToDualstatement · cited by 8
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