Theorems · Theorem · combinatorics
SimpleGraph.addCayley_le_iff
∀ {M : Type u_1} (s : Set M) [inst : Add M] (G : SimpleGraph M),
SimpleGraph.addCayley s ≤ G ↔ ∀ g ∈ s, ∀ (a : M), a + g ≠ a → G.Adj (a + g) a- Defined in
- Mathlib.Combinatorics.SimpleGraph.Cayley
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.Adj.symmproof · cited by 66
- SimpleGraph.addCayleystatement · cited by 15
- SimpleGraph.addCayley_adj'proof · cited by 4
- SimpleGraph.le_iff_adjproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.addCayley_gcproof · cited by 3