Theorems · Theorem · combinatorics
SimpleGraph.DeleteFar.mono
∀ {V : Type u_1} {G : SimpleGraph V} {𝕜 : Type u_2} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜]
[inst_2 : Fintype ↑G.edgeSet] {p : SimpleGraph V → Prop} {r₁ r₂ : 𝕜}, G.DeleteFar p r₂ → r₁ ≤ r₂ → G.DeleteFar p r₁- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingPartialOrderFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Ringstatement and proof · cited by 7,463
- Set.Elemstatement and proof · cited by 7,166
- PartialOrderstatement and proof · cited by 6,410
- LE.le.transproof · cited by 3,151
- SimpleGraphstatement and proof · cited by 3,072
- Sym2statement and proof · cited by 737
- SimpleGraph.edgeSetstatement and proof · cited by 199
- SimpleGraph.edgeFinsetproof · cited by 116
- SimpleGraph.deleteEdgesproof · cited by 64
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.FarFromTriangleFree.monoproof · cited by 0