ofSubtype_support_disjoint — Mathlib

English

Let g be a permutation and x a permutation of the fixed points of g. Then the extension x of the fixed-point permutation is disjoint from g.

Русский

Пусть g — перестановка и x — перестановка зафиксированных точек g; тогда продолжение x неизменно дисjoint с g.

LaTeX

$$$\\text{Disjoint}(x.{\\text{ofSubtype}}, g).$$$

Lean4

theorem ofSubtype_support_disjoint {σ : Perm α} (x : Perm (Function.fixedPoints σ)) :
    _root_.Disjoint x.ofSubtype.support σ.support :=
  by
  rw [Finset.disjoint_iff_ne]
  rintro a ha b hb rfl
  rw [mem_support] at ha hb
  exact ha (ofSubtype_apply_of_not_mem x (mt Function.mem_fixedPoints_iff.mp hb))

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