Theorems · Theorem · combinatorics
SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equiv
∀ {V : Type u_1} {G : SimpleGraph V} {s t : Set V},
Disjoint s t → ∀ (f : ↑s ≃ ↑t), (∀ (v : ↑s), G.Adj ↑v ↑(f v)) → ∃ M, M.verts = s ∪ t ∧ M.IsMatching- Cited by
- 2 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement and proof · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- Equiv.symmproof · cited by 3,681
- SimpleGraphstatement and proof · cited by 3,072
- Disjointstatement and proof · cited by 2,201
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Equiv.apply_symm_applyproof · cited by 346
- SimpleGraph.Subgraphstatement · cited by 326
- Equiv.symm_apply_applyproof · cited by 320
- ExistsUniqueproof · cited by 268
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.IsClique.even_iff_exists_isMatchingproof · cited by 1
- SimpleGraph.Subgraph.IsMatching.exists_of_universalVertsproof · cited by 0