AffineEquiv.image_symm
∀ {k : Type u_1} {P₁ : Type u_2} {P₂ : Type u_3} {V₁ : Type u_6} {V₂ : Type u_7} [inst : Ring k]
[inst_1 : AddCommGroup V₁] [inst_2 : AddCommGroup V₂] [inst_3 : Module k V₁] [inst_4 : Module k V₂]
[inst_5 : AddTorsor V₁ P₁] [inst_6 : AddTorsor V₂ P₂] (f : P₁ ≃ᵃ[k] P₂) (s : Set P₂), ⇑f.symm '' s = ⇑f ⁻¹' s- Cited by
- 4 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Set.imagestatement · cited by 5,609
- Set.preimagestatement · cited by 4,946
- AddTorsorstatement and proof · cited by 1,657
- AffineEquivstatement and proof · cited by 191
- Equiv.image_eq_preimage_symmproof · cited by 64
- AffineEquiv.symmstatement and proof · cited by 53
- AffineEquiv.toEquivproof · cited by 38
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.hausdorffMeasure_homothety_preimageproof · cited by 2
- AffineSubspace.comap_spanproof · cited by 1
- AffineSubspace.map_symmproof · cited by 1
- AffineEquiv.preimage_symmproof · cited by 1