disjoint_supported_supported — Mathlib

English

If s and t are disjoint, then the corresponding supports are disjoint as submodules.

Русский

Если множества s и t разложимы, их поддерживаемые подмодули взаимно непростые.

LaTeX

$$If $\mathrm{Disjoint}(s,t)$ then $\mathrm{Disjoint}(\mathrm{supported}(M,R,s), \mathrm{supported}(M,R,t))$$$

Lean4

theorem disjoint_supported_supported {s t : Set α} (h : Disjoint s t) : Disjoint (supported M R s) (supported M R t) :=
  disjoint_iff.2 <| by rw [← supported_inter, disjoint_iff_inter_eq_empty.1 h, supported_empty]

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