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Theorems · Theorem · combinatorics

Finset.singleton_nonempty

∀ {α : Type u_1} (a : α), {a}.Nonempty
Defined in
Mathlib.Data.Finset.Insert
Cited by
15 results in Mathlib
Foundations
Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Finset.Nonempty.cons_induction · cited by 35Nonempty.cons_inductionmap_finset_sup' · cited by 12map_finset_sup'Finset.apply_sup'_eq_sup'_comp · cited by 11Finset.apply_sup'_eq_sup'…Finset.apply_inf'_eq_inf'_comp · cited by 6Finset.apply_inf'_eq_inf'…Finset.singleton_ne_empty · cited by 6Finset.singleton_ne_emptyFinset.min'_singleton · cited by 4Finset.min'_singletonmap_finset_inf' · cited by 3map_finset_inf'Geometry.SimplicialComplex.vertices_eq · cited by 1SimplicialComplex.vertice…Finset.max'_singleton · cited by 1Finset.max'_singletonMeasureTheory.setToFun_finsetSum_measure · cited by 0MeasureTheory.setToFun_fi…Finset.sup'_singleton · cited by 0Finset.sup'_singletonFinset.empty_ssubset_singleton · cited by 0Finset.empty_ssubset_sing…Finset.Nonempty.strong_induction · cited by 0Nonempty.strong_inductionFinset.inf'_singleton · cited by 0Finset.inf'_singletonGeometry.SimplicialComplex.face_subset_face_iff · cited by 0SimplicialComplex.face_su…Finset · cited by 13712FinsetFinset.Nonempty · cited by 1001Finset.NonemptyFinset.mem_singleton_self · cited by 44Finset.mem_singleton_selfFinset.singleton_nonemptyCITED BYCITES

Cites3

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Cited by15

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