ofSign_disjoint — Mathlib

English

The disjoint union of the sign-1 and sign-(-1) families covers all permutations.

Русский

Дисжойнт-объединение знаков 1 и −1 заполняет все перестановки.

LaTeX

$$$\\operatorname{ofSign}(1) \\;\\disjUnion\\; \\operatorname{ofSign}(-1) = \\mathrm{univ}$$$

Lean4

theorem ofSign_disjoint : _root_.Disjoint (ofSign 1 : Finset (Perm α)) (ofSign (-1)) :=
  by
  rw [Finset.disjoint_iff_ne]
  rintro σ hσ τ hτ rfl
  rw [mem_ofSign] at hσ hτ
  have := hσ.symm.trans hτ
  contradiction

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