disjoint_union_right — Mathlib

English

Disjoint x (y ∪ z) ↔ Disjoint x y ∧ Disjoint x z.

Русский

Дисjoint x (y ∪ z) эквивалентно Disjoint x y и Disjoint x z.

LaTeX

$$$ \operatorname{Disjoint}(x, y \cup z) \iff \operatorname{Disjoint}(x,y) \land \operatorname{Disjoint}(x,z) $$$

Lean4

theorem disjoint_union_right (x y z : Finmap β) : Disjoint x (y ∪ z) ↔ Disjoint x y ∧ Disjoint x z := by
  rw [Disjoint.symm_iff, disjoint_union_left, Disjoint.symm_iff _ x, Disjoint.symm_iff _ x]

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