AffineMap.lineMap_eq_lineMap_iff
∀ {k : Type u_1} {V1 : Type u_2} {P1 : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V1] [inst_2 : Module k V1]
[inst_3 : AddTorsor V1 P1] [IsDomain k] [Module.IsTorsionFree k V1] {p₀ p₁ : P1} {c₁ c₂ : k},
(AffineMap.lineMap p₀ p₁) c₁ = (AffineMap.lineMap p₀ p₁) c₂ ↔ p₀ = p₁ ∨ c₁ = c₂- Cited by
- 3 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- IsDomainstatement and proof · cited by 2,196
- HVAdd.hVAddproof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubproof · cited by 817
- AffineMapstatement · cited by 674
- Module.IsTorsionFreestatement and proof · cited by 600
- sub_eq_zeroproof · cited by 407
- AffineMap.lineMapstatement and proof · cited by 254
Cited by3
Results whose statement or proof uses this declaration.
- AffineMap.lineMap_injectiveproof · cited by 5
- AffineMap.lineMap_eq_left_iffproof · cited by 0
- AffineMap.lineMap_eq_right_iffproof · cited by 0