disjoint_ofSubtype_of_memFixedPoints_self

English

Let g be a permutation and u a permutation of its fixed points. Then the extension of u to the whole set is disjoint from g.

Русский

Пусть g — перестановка, u — перестановка её зафиксированных точек. Тогда продолжение u на всю множество дисjoint с g.

LaTeX

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

Lean4

theorem disjoint_ofSubtype_of_memFixedPoints_self {g : Perm α} (u : Perm (Function.fixedPoints g)) :
    Disjoint (ofSubtype u) g := by
  rw [disjoint_iff_eq_or_eq]
  intro x
  by_cases hx : x ∈ Function.fixedPoints g
  · right; exact hx
  · left; rw [ofSubtype_apply_of_not_mem u hx]

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