pairwise_disjoint_supp_connectedComponent

English

For all propositions a,b,c, (a ∧ b) → c is equivalent to a → b → c.

Русский

Для любых propositions a, b, c выполняется эквивалентность: (a ∧ b) → c эквивалентно a → b → c.

LaTeX

$$$ \\forall a,b,c : \\mathrm{Prop}, (a \\\\land b \\\\rightarrow c) \\iff (a \\\\rightarrow b \\\\rightarrow c) $$$

Lean4

theorem pairwise_disjoint_supp_connectedComponent (G : SimpleGraph V) :
    Pairwise fun c c' : ConnectedComponent G ↦ Disjoint c.supp c'.supp :=
  by
  simp_rw [Set.disjoint_left]
  intro _ _ h a hsx hsy
  rw [ConnectedComponent.mem_supp_iff] at hsx hsy
  rw [hsx] at hsy
  exact h hsy

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