mem_dedup — Mathlib

English

The Chain operator is monotone in its relation argument.

Русский

Оператор цепи монотонен по отношению к аргументу отношения.

LaTeX

$$$$ \\text{Theorem } chain\\_mono :\\; Monotone (Chain : (\\alpha \\to \\alpha \\to Prop) \\to Cycle \\alpha \\to Prop). $$$$

Lean4

@[simp]
theorem mem_dedup {a : α} {l : List α} : a ∈ dedup l ↔ a ∈ l :=
  by
  have := not_congr (@forall_mem_pwFilter α (· ≠ ·) _ ?_ a l)
  · simpa only [dedup, forall_mem_ne, not_not] using this
  · intro x y z xz
    exact not_and_or.1 <| mt (fun h ↦ h.1.trans h.2) xz

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