Theorems · Theorem · logic and foundations
Set.isEmpty_coe_sort
∀ {α : Type u} {s : Set α}, IsEmpty ↑s ↔ s = ∅- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- IsEmptystatement · cited by 759
- not_iff_notproof · cited by 159
- Set.nonempty_iff_ne_emptyproof · cited by 96
Cited by6
Results whose statement or proof uses this declaration.
- IsEvenlyCovered.of_preimage_eq_emptyproof · cited by 4
- Set.Finite.ecard_lt_ecardproof · cited by 2
- Cardinal.mk_set_eq_zero_iffproof · cited by 1
- hasSmallInductiveDimensionLT_one_iffproof · cited by 1
- Finset.isEmpty_coe_sortproof · cited by 0
- linearIndepOn_zero_iffproof · cited by 0