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Theorems · Theorem · logic and foundations

Set.pairwise_empty

∀ {α : Type u_1} (r : α → α → Prop), ∅.Pairwise r
Defined in
Mathlib.Data.Set.Pairwise.Basic
Cited by
7 results in Mathlib
Foundations
Depth 6 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.pairwiseDisjoint_empty · cited by 4Set.pairwiseDisjoint_emptyDynamics.isDynNetIn_empty · cited by 1Dynamics.isDynNetIn_emptystrictConvex_empty · cited by 1strictConvex_emptySetRel.IsSeparated.empty · cited by 0IsSeparated.emptyIsChain.empty · cited by 0IsChain.emptyMetric.IsSeparated.empty · cited by 0IsSeparated.emptyIsAntichain.empty · cited by 0IsAntichain.emptySet · cited by 53352SetSet.Pairwise · cited by 321Set.PairwiseSet.subsingleton_empty · cited by 16Set.subsingleton_emptySet.Subsingleton.pairwise · cited by 13Subsingleton.pairwiseSet.pairwise_emptyCITED BYCITES

Cites4

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

Cited by7

Results whose statement or proof uses this declaration.