disjoint_coe_of_mem — Mathlib

English

If two subboxes J1 and J2 belong to the same partition, and are distinct, then their sets are disjoint.

Русский

Если J1 и J2 принадлежат одной части разбиения и различны, то их множества взаимно дисjointны.

LaTeX

$$$\text{Disjoint}(J_1, J_2)$$$

Lean4

theorem disjoint_coe_of_mem (h₁ : J₁ ∈ π) (h₂ : J₂ ∈ π) (h : J₁ ≠ J₂) : Disjoint (J₁ : Set (ι → ℝ)) J₂ :=
  π.pairwiseDisjoint h₁ h₂ h

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