AffineSubspace.mem_map_iff_mem_of_injective
∀ {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} {x : P₁} {s : AffineSubspace k P₁},
Function.Injective ⇑f → (f x ∈ AffineSubspace.map f s ↔ x ∈ s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, 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.
- 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
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement and proof · cited by 871
- AffineMapstatement and proof · cited by 674
- AffineSubspace.mapstatement · cited by 78
- Function.Injective.mem_set_imageproof · cited by 53
Cited by2
Results whose statement or proof uses this declaration.
- Function.Injective.sOppSide_map_iffproof · cited by 1
- Function.Injective.sSameSide_map_iffproof · cited by 1