disjoint_iff — Mathlib

English

Disjoint for invariant-submodule elements p and q is equivalent to disjointness of their submodules.

Русский

Дисjoint для элементов инвариантной подрешетки эквивалентен для их подподмодулей.

LaTeX

$$${p}\in f.invtSubmodule, {q}\in f.invtSubmodule \Rightarrow (Disjoint\ p\ q) \iff (Disjoint\ (p:name)\ (q:name))$$$

Lean4

protected theorem disjoint_iff {p q : f.invtSubmodule} :
    Disjoint p q ↔ Disjoint (p : Submodule R M) (q : Submodule R M) :=
  by
  obtain ⟨p, hp⟩ := p
  obtain ⟨q, hq⟩ := q
  simp

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