Theorems · Theorem · logic and foundations
Cardinal.mk_set_ne_zero_iff
∀ {α : Type u} {s : Set α}, Cardinal.mk ↑s ≠ 0 ↔ s.Nonempty- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Nonemptystatement and proof · cited by 2,627
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Set.nonempty_coe_sortproof · cited by 23
- Cardinal.mk_ne_zero_iffproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.sdiff_nonempty_of_mk_lt_mkproof · cited by 2