card_eq — Mathlib

English

If G and G' are isomorphic graphs and V, W are finite, then the vertex sets have equal cardinalities: |V| = |W|.

Русский

Если графы G и G' изоморфны и V, W конечны, то кардинальности множеств вершин равны: |V| = |W|.

LaTeX

$$$\#V = \#W \quad\text{under } G \cong G'$$$

Lean4

theorem card_eq [Fintype V] [Fintype W] : Fintype.card V = Fintype.card W :=
  by
  rw [← Fintype.ofEquiv_card f.toEquiv]
  convert rfl

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