import Mathlib.Data.Set.Basic
import Mathlib.Tactic
open Set
variable {α : Type}
variable (s t u : Set α)

example :
  s ∩ (t ∪ u) ⊆ (s ∩ t) ∪ (s ∩ u) :=
by sorry

theory Propiedad_semidistributiva_de_la_interseccion_sobre_la_union
imports Main
begin

lemma "s ∩ (t ∪ u) ⊆ (s ∩ t) ∪ (s ∩ u)"
oops

end

import Mathlib.Data.Set.Basic
import Mathlib.Tactic
open Set
variable {α : Type}
variable (s t u : Set α)

example
  (h : s ⊆ t)
  : s ∩ u ⊆ t ∩ u :=
by sorry

theory Propiedad_de_monotonia_de_la_interseccion
imports Main
begin

lemma
  assumes "s ⊆ t"
  shows   "s ∩ u ⊆ t ∩ u"
oops

end