Theorems · Theorem · linear algebra
DFinsupp.injective_pi_lapply
∀ {ι : Type u_1} {R : Type u_3} {M : ι → Type u_5} [inst : Semiring R] [inst_1 : (i : ι) → AddCommMonoid (M i)]
[inst_2 : (i : ι) → Module R (M i)], Function.Injective ⇑(LinearMap.pi DFinsupp.lapply)- Defined in
- Mathlib.LinearAlgebra.DFinsupp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- DFinsuppstatement and proof · cited by 694
- DFinsupp.extproof · cited by 78
- LinearMap.pistatement and proof · cited by 31
- DFinsupp.lapplystatement and proof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- IsSemisimpleModule.jacobson_eq_botproof · cited by 4
- Pi.linearIndependent_singleproof · cited by 3