Theorems · Theorem · logic and foundations
Cardinal.compl_nonempty_of_mk_lt_mk
∀ {α : Type u} {S : Set α}, Cardinal.mk ↑S < Cardinal.mk α → Sᶜ.Nonempty- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, 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 and proof · cited by 7,166
- Compl.complstatement · cited by 2,925
- Set.Nonemptystatement and proof · cited by 2,627
- Cardinalstatement and proof · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
- Set.compl_eq_univ_sdiffproof · cited by 43
- Cardinal.mk_univproof · cited by 12
- Cardinal.sdiff_nonempty_of_mk_lt_mkproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.