Theorems · Theorem · logic and foundations
Set.Pairwise.eq
∀ {α : Type u_1} {r : α → α → Prop} {s : Set α} {a b : α}, s.Pairwise r → a ∈ s → b ∈ s → ¬r a b → a = b- Defined in
- Mathlib.Logic.Pairwise
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 15 from the axioms · 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.
- Setstatement and proof · cited by 53,352
- Set.Pairwisestatement and proof · cited by 321
- of_not_notproof · cited by 51
Cited by12
Results whose statement or proof uses this declaration.
- IsAntichain.eqproof · cited by 13
- Set.PairwiseDisjoint.elimproof · cited by 12
- Finset.card_dvd_card_image₂_rightproof · cited by 6
- Set.pairwise_bot_iffproof · cited by 2
- Metric.packingNumber_two_mul_le_externalCoveringNumberproof · cited by 2
- Equiv.Perm.Basis.injectiveproof · cited by 1
- IsStrongAntichain.eqproof · cited by 1
- StrictConvex.eqproof · cited by 1
- Set.intersecting_iff_pairwise_not_disjointproof · cited by 1
- SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingletonproof · cited by 1
- Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnionproof · cited by 1
- Besicovitch.exists_disjoint_closedBall_covering_aeproof · cited by 1