Mathlib Map

Theorems · Theorem

nonempty_subtype

∀ {α : Sort u_3} {p : α → Prop}, Nonempty (Subtype p) ↔ ∃ a, p a
Defined in
Mathlib.Logic.Nonempty
Cited by
22 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.Nonempty.to_subtype · cited by 55Nonempty.to_subtypeSet.nonempty_coe_sort · cited by 23Set.nonempty_coe_sortisConnected_iff_connectedSpace · cited by 7isConnected_iff_connected…Finset.nonempty_coe_sort · cited by 6Finset.nonempty_coe_sortDynamics.coverMincard_finite_iff · cited by 6Dynamics.coverMincard_fin…Set.Nonempty.of_subtype · cited by 5Nonempty.of_subtypeAlgebra.FormallySmooth.iff_split_surjection · cited by 5FormallySmooth.iff_split_…ciSup_subtype · cited by 4ciSup_subtypeENNReal.add_biSup' · cited by 3ENNReal.add_biSup'ENat.add_biSup' · cited by 3ENat.add_biSup'SimpleGraph.vertexCoverNum_exists · cited by 3SimpleGraph.vertexCoverNu…EuclideanGeometry.inter_eq_singleton_orthogonalProjection · cited by 2EuclideanGeometry.inter_e…Set.not_nonempty_iff_eq_empty' · cited by 2Set.not_nonempty_iff_eq_e…acc_iff_isEmpty_descending_chain · cited by 1acc_iff_isEmpty_descendin…lowerBounds_prod · cited by 1lowerBounds_prodnonempty_subtypeCITED BYCITES

Cites0

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Nothing in Mathlib beyond the foundations.

Cited by22

Results whose statement or proof uses this declaration.