AffineMap.linear_injective_iff
∀ {k : Type u_1} {V1 : Type u_2} {P1 : Type u_3} {V2 : Type u_4} {P2 : Type u_5} [inst : Ring k]
[inst_1 : AddCommGroup V1] [inst_2 : Module k V1] [inst_3 : AddTorsor V1 P1] [inst_4 : AddCommGroup V2]
[inst_5 : Module k V2] [inst_6 : AddTorsor V2 P2] (f : P1 →ᵃ[k] P2),
Function.Injective ⇑f.linear ↔ Function.Injective ⇑f- Cited by
- 5 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Equiv.symmproof · cited by 3,681
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubproof · cited by 817
- AffineMapstatement and proof · cited by 674
- AffineMap.linearstatement and proof · cited by 105
- vadd_vsubproof · cited by 58
Cited by5
Results whose statement or proof uses this declaration.
- Function.Injective.wSameSide_map_iffproof · cited by 2
- Function.Injective.wOppSide_map_iffproof · cited by 2
- AffineIndependent.map'proof · cited by 1
- AffineMap.antilipschitzWith_of_finiteDimensionalproof · cited by 0
- AffineMap.linear_bijective_iffproof · cited by 0