nontrivial_of_nontrivial_coe — Mathlib

English

If the set s has a nontrivial coe_sort, then α is nontrivial.

Русский

Если множество s имеет неtrивиальный коe-сорт, тогда α не тривиален.

LaTeX

$$Nontrivial (s)_Helper \Rightarrow Nontrivial α$$

Lean4

/-- A type with a set `s` whose `coe_sort` is a nontrivial type is nontrivial.
For the corresponding result for `Subtype`, see `Subtype.nontrivial_iff_exists_ne`. -/
theorem nontrivial_of_nontrivial_coe (hs : Nontrivial s) : Nontrivial α :=
  nontrivial_of_nontrivial <| nontrivial_coe_sort.1 hs

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