Theorems · Theorem · logic and foundations
Cardinal.mk_image_eq_of_injOn
∀ {α β : Type u} (f : α → β) (s : Set α), Set.InjOn f s → Cardinal.mk ↑(f '' s) = Cardinal.mk ↑s- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses 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.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Set.imagestatement · cited by 5,609
- Equiv.symmproof · cited by 3,681
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Set.InjOnstatement and proof · cited by 543
- Cardinal.mk_congrproof · cited by 55
- Equiv.Set.imageOfInjOnproof · cited by 11
Cited by7
Results whose statement or proof uses this declaration.
- Cardinal.mk_image_eqproof · cited by 5
- Cardinal.mk_vadd_setproof · cited by 2
- IsLocalRing.rank_cotangentSpace_eq_spanrank_maximalIdeal_of_fgproof · cited by 1
- Cardinal.mk_negproof · cited by 1
- Cardinal.mk_invproof · cited by 1
- Cardinal.mk_smul_setproof · cited by 1
- Cardinal.mk_smul_set₀proof · cited by 0