Theorems · Theorem · linear algebra
Module.eval_ker
∀ (K : Type uK) (V : Type uV) [inst : CommSemiring K] [inst_1 : AddCommMonoid V] [inst_2 : Module K V] [Module.Projective K V], (Module.Dual.eval K V).ker = ⊥
- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Submodulestatement · cited by 7,192
- Bot.botstatement · cited by 4,720
- LinearMap.kerstatement · cited by 848
- Module.Dualstatement · cited by 583
- Module.Projectivestatement and proof · cited by 82
- Module.Dual.evalstatement · cited by 52
- LinearMap.ker_eq_bot_of_injectiveproof · cited by 20
- Module.eval_apply_injectiveproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Module.eval_apply_eq_zero_iffproof · cited by 0
- Submodule.dualCoannihilator_topproof · cited by 0