Theorems · Theorem · order theory
Set.image_congr
∀ {α : Type u_1} {β : Type u_2} {f g : α → β} {s : Set α}, (∀ a ∈ s, f a = g a) → f '' s = g '' s- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 533 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 20 definitions · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by533
Results whose statement or proof uses this declaration.
- Set.image_compproof · cited by 142
- Filter.comap_comapproof · cited by 69
- Set.image_idproof · cited by 60
- AlgebraicGeometry.Scheme.Hom.preimage_image_eqproof · cited by 37
- Set.zero_smul_setproof · cited by 20
- Submodule.map_compproof · cited by 19
- AlgebraicGeometry.Scheme.Hom.image_top_eq_opensRangeproof · cited by 17
- AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_infproof · cited by 15
- IsAddQuotientCoveringMap.toMultiplicativeproof · cited by 12
- SpectrumRestricts.imageproof · cited by 11
- segment_eq_image_lineMapproof · cited by 11
- Algebra.adjoin_union_eq_adjoin_adjoinproof · cited by 8
Showing the 200 most cited of 533.