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Theorems · Theorem · combinatorics

SimpleGraph.ComponentCompl.nonempty

∀ {V : Type u} {G : SimpleGraph V} {K : Set V} (C : G.ComponentCompl K), (↑C).Nonempty
Defined in
Mathlib.Combinatorics.SimpleGraph.Ends.Defs
Cited by
2 results in Mathlib
Foundations
Depth 20 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.

SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges · cited by 2ComponentCompl.infinite_i…SimpleGraph.ComponentCompl.exists_eq_mk · cited by 0ComponentCompl.exists_eq_…Set · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeSimpleGraph · cited by 3072SimpleGraphSet.Nonempty · cited by 2627Set.NonemptySimpleGraph.ComponentCompl · cited by 29SimpleGraph.ComponentComplSimpleGraph.ComponentCompl.ind · cited by 4ComponentCompl.indComponentCompl.nonemptyCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.