Theorems · Theorem · linear algebra
Module.Basis.eval_injective
∀ {R : Type uR} {M : Type uM} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type u_1}
(b : Module.Basis ι R M), Function.Injective ⇑(Module.Dual.eval R M)- Defined in
- Mathlib.LinearAlgebra.Dual.Basis
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Module.Basisstatement and proof · cited by 1,477
- Module.Dualstatement · cited by 583
- Module.Basis.coordproof · cited by 64
- Module.Dual.evalstatement and proof · cited by 52
- Module.Basis.ext_elemproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- Module.eval_apply_injectiveproof · cited by 5
- Module.Basis.eval_kerproof · cited by 0