Theorems · Theorem · order theory
Disjoint.ne_of_mem
∀ {α : Type u} {s t : Set α}, Disjoint s t → ∀ ⦃a : α⦄, a ∈ s → ∀ ⦃b : α⦄, b ∈ t → a ≠ bAlias of the forward direction of Set.disjoint_iff_forall_ne.
- Defined in
- Mathlib.Data.Set.Disjoint
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 24 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
- Disjointstatement · cited by 2,201
- Set.disjoint_iff_forall_neproof · cited by 22
Cited by11
Results whose statement or proof uses this declaration.
- Circle.disjoint_path_image_Iocproof · cited by 2
- MeasureTheory.tendsto_measure_biUnion_Ici_zero_of_pairwise_disjointproof · cited by 2
- SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equivproof · cited by 2
- IndexedPartition.piecewise_injproof · cited by 1
- Set.biUnion_compl_eq_of_pairwise_disjoint_of_iUnion_eq_univproof · cited by 1
- SimpleGraph.IsClique.even_iff_exists_isMatchingproof · cited by 1
- isEmbedding_sumElimproof · cited by 1
- Set.offDiag_unionproof · cited by 1
- Ideal.isPrime_of_maximally_disjointproof · cited by 1
- SimpleGraph.Subgraph.IsMatching.exists_of_universalVertsproof · cited by 0