Theorems · Theorem · linear algebra

Module.subsingleton_dual_iff

∀ (K : Type uK) {V : Type uV} [inst : CommSemiring K] [inst_1 : AddCommMonoid V] [inst_2 : Module K V]
  [Module.Projective K V], Subsingleton (Module.Dual K V) ↔ Subsingleton V

Defined in: Mathlib.LinearAlgebra.Dual.Lemmas
Cited by: 2 results in Mathlib
Foundations: Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid Module Module.Projective

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Cites8

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
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
Module.Dualstatement and proof · cited by 583
Module.Projectivestatement and proof · cited by 82
Module.Dual.evalproof · cited by 52
Module.eval_apply_injectiveproof · cited by 5

Cited by2

Results whose statement or proof uses this declaration.

Module.nontrivial_dual_iffproof · cited by 1
Submodule.dualAnnihilator_eq_bot_iffproof · cited by 0