Theorems · Theorem · order theory
Set.preimage_mono
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {s t : Set β}, s ⊆ t → f ⁻¹' s ⊆ f ⁻¹' t- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 95 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 12 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.preimagestatement and proof · cited by 4,946
Cited by95
Results whose statement or proof uses this declaration.
- Filter.comap_principalproof · cited by 47
- Ideal.comap_monoproof · cited by 25
- UniformSpace.ball_monoproof · cited by 20
- Submodule.comap_monoproof · cited by 18
- preimage_interior_subset_interior_preimageproof · cited by 14
- Continuous.closure_preimage_subsetproof · cited by 12
- AddSubgroup.comap_monoproof · cited by 11
- Subgroup.comap_monoproof · cited by 11
- MDifferentiableWithinAt.monoproof · cited by 10
- HasMFDerivWithinAt.monoproof · cited by 9
- Metric.cthickening_monoproof · cited by 6
- Metric.thickening_monoproof · cited by 6