DeleteFar — Mathlib

English

The sum of the cardinalities of the induced edgeFinsets on s and its complement relative to x equals the cardinal product |s||t| in the appropriate setting.

Русский

Сумма кардинальностей edgeFinset на s и его дополнении равна произведению кардиналностей соответствующих множеств.

LaTeX

$$$ #(G.induce s).edgeFinset + #(G.induce (s^c)).edgeFinset = #s \cdot #t $$$

Lean4

/-- A graph is `r`-*delete-far* from a property `p` if we must delete at least `r` edges from it to
get a graph with the property `p`. -/
def DeleteFar (p : SimpleGraph V → Prop) (r : 𝕜) : Prop :=
  ∀ ⦃s⦄, s ⊆ G.edgeFinset → p (G.deleteEdges s) → r ≤ #s

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