Theorems · Theorem · linear algebra
PiToModule.fromEnd_injective
∀ {ι : Type u_1} [inst : Fintype ι] {M : Type u_2} [inst_1 : AddCommGroup M] (R : Type u_3) [inst_2 : CommRing R]
[inst_3 : Module R M] (b : ι → M), Submodule.span R (Set.range b) = ⊤ → Function.Injective ⇑(PiToModule.fromEnd R b)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Top.topstatement and proof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- Submodulestatement and proof · cited by 7,192
- Set.rangestatement and proof · cited by 4,705
- Submodule.spanstatement and proof · cited by 1,504
- LinearMap.extproof · cited by 844
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.Represents.eqproof · cited by 1