Theorems · Theorem · ring theory
LinearMap.mulLeft_inj
∀ {R : Type u_6} {A : Type u_7} [inst : Semiring R] [inst_1 : NonAssocSemiring A] [inst_2 : Module R A]
[inst_3 : SMulCommClass R A A] {a b : A}, LinearMap.mulLeft R a = LinearMap.mulLeft R b ↔ a = b- Defined in
- Mathlib.Algebra.Module.LinearMap.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- mul_oneproof · cited by 3,885
- SMulCommClassstatement and proof · cited by 1,927
- NonAssocSemiringstatement and proof · cited by 805
- LinearMap.mulLeftstatement and proof · cited by 34
- LinearMap.ext_iffproof · cited by 32
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.mulLeft_eq_zero_iffproof · cited by 0