instNontrivial — Mathlib

English

If X is nontrivial, there exists a nontrivial BlockMem G a for any a ∈ X.

Русский

Если пространство не тривиально, существует ненулевой блок BlockMem для любого a ∈ X.

LaTeX

$$instance (G) [Nontrivial X] (a : X) : Nontrivial (BlockMem G a)$$

Lean4

@[to_additive]
instance [Nontrivial X] (a : X) : Nontrivial (BlockMem G a) :=
  by
  rw [nontrivial_iff]
  use ⊥, ⊤
  intro h
  rw [← Subtype.coe_inj] at h
  simp only [coe_top, coe_bot] at h
  obtain ⟨b, hb⟩ := exists_ne a
  apply hb
  rw [← Set.mem_singleton_iff, h]
  apply Set.mem_univ

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