Theorems · Theorem · combinatorics

SimpleGraph.DeleteFar.le_card_sub_card

∀ {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} {r : 𝕜} [inst_3 : Fintype (Sym2 V)],
  G.DeleteFar p r →
    ∀ ⦃H : SimpleGraph V⦄ [inst_4 : DecidableRel H.Adj], H ≤ G → p H → r ≤ ↑G.edgeFinset.card - ↑H.edgeFinset.card

Alias of the forward direction of SimpleGraph.deleteFar_iff.

Defined in

Mathlib.Combinatorics.SimpleGraph.DeleteEdges

Cited by

1 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingPartialOrderFintypeFintypeDecidableRel