Theorems · Definition · logic and foundations
Equiv.Set.imageOfInjOn
{α : Type u_3} → {β : Type u_4} → (f : α → β) → (s : Set α) → Set.InjOn f s → ↑s ≃ ↑(f '' s)If a function f is injective on a set s, then s is equivalent to f '' s.
- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by12
Results whose statement or proof uses this declaration.
- Equiv.Set.imageproof · cited by 15
- Cardinal.mk_image_eq_of_injOnproof · cited by 7
- Cardinal.mk_image_eq_of_injOn_liftproof · cited by 4
- linearIndepOn_iff_imageproof · cited by 3
- tprod_imageproof · cited by 3
- tsum_imageproof · cited by 3
- LinearIndepOn.image_of_compproof · cited by 2
- ENat.card_image_of_injOnproof · cited by 2
- algebraicIndependent_imageproof · cited by 1
- AlgebraicIndependent.image_of_compproof · cited by 1
- LinearIndepOn.comp_of_imageproof · cited by 0
- isTranscendenceBasis_imageproof · cited by 0