Ico_union_Ico_eq_Ico — Mathlib

English

If the two left and right endpoints satisfy compatibility conditions, the union of Ico(a,b) and Ico(c,d) equals Ico(min(a,c), max(b,d)).

Русский

Если крайние точки интервальных отрезков совместимы, то объединение Ico(a,b) и Ico(c,d) равно Ico(min(a,c), max(b,d)).

LaTeX

$$$ Ico(a,b) \cup Ico(c,d) = Ico(\min(a,c), \max(b,d)) $ under suitable compatibility conditions.$$

Lean4

theorem Ico_union_Ico_eq_Ico {a b c : α} (hab : a ≤ b) (hbc : b ≤ c) : Ico a b ∪ Ico b c = Ico a c := by
  rw [← coe_inj, coe_union, coe_Ico, coe_Ico, coe_Ico, Set.Ico_union_Ico_eq_Ico hab hbc]

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