antisymm_iff — Mathlib

English

If a ≠ 0 and a < b in the nimber order, then invAux(a) belongs to the invSet of b.

Русский

Если a ≠ 0 и a < b по порядку Nimber, тогда invAux(a) ∈ invSet(b).

LaTeX

$$$ invAux(a) \in invSet(b) $$$

Lean4

theorem antisymm_iff {l₁ l₂ : Lists' α true} : of' l₁ ~ of' l₂ ↔ l₁ ⊆ l₂ ∧ l₂ ⊆ l₁ :=
  by
  refine ⟨fun h => ?_, fun ⟨h₁, h₂⟩ => Equiv.antisymm h₁ h₂⟩
  obtain - | ⟨h₁, h₂⟩ := h
  · simp [Lists'.Subset.refl]
  · exact ⟨h₁, h₂⟩

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