Theorems · Theorem
isEmpty_or_nonempty
∀ (α : Sort u_1), IsEmpty α ∨ Nonempty α
- Defined in
- Mathlib.Logic.IsEmpty.Basic
- Cited by
- 269 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 56 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsEmptystatement and proof · cited by 759
- emproof · cited by 115
- not_isEmpty_iffproof · cited by 19
Cited by270
Results whose statement or proof uses this declaration.
- MeasurableSet.iUnionproof · cited by 81
- Filter.prod_atTop_atTop_eqproof · cited by 20
- Measurable.iSupproof · cited by 14
- Monotone.measure_iUnionproof · cited by 10
- ciSup_monoproof · cited by 9
- SimpleGraph.minDegree_of_subsingletonproof · cited by 6
- Matrix.GeneralLinearGroup.center_eq_range_scalarproof · cited by 6
- lp.norm_nonneg'proof · cited by 6
- Field.exists_primitive_elementproof · cited by 6
- Matrix.center_eq_scalar_imageproof · cited by 6
- MeasureTheory.analyticSet_range_of_polishSpaceproof · cited by 6
- SupClosed.iSup_memproof · cited by 5
Showing the 200 most cited of 270.