Theorems · Theorem · logic and foundations
Cardinal.mk_emptyCollection_iff
Deprecated since 2026-01-31Use Cardinal.mk_set_eq_zero_iff instead.
∀ {α : Type u} {s : Set α}, Cardinal.mk ↑s = 0 ↔ s = ∅Alias of Cardinal.mk_set_eq_zero_iff.
- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Cardinal.mk_set_eq_zero_iffproof · cited by 1
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