instClosedUnderRestrictionAnalyticGroupoid

English

If p and q are primes and p ≠ q, then q ≠ 0 in ZMod p (q mod p ≠ 0).

Русский

Если p и q — простые числа и p ≠ q, то q не равно нулю по модулю p.

LaTeX

$$$(q : \\mathbb{Z}/p\\mathbb{Z}) \\neq 0$$$

Lean4

/-- The analytic groupoid is closed under restriction. -/
instance : ClosedUnderRestriction (analyticGroupoid I) :=
  (closedUnderRestriction_iff_id_le _).mpr
    (by
      rw [StructureGroupoid.le_iff]
      rintro e ⟨s, hs, hes⟩
      exact (analyticGroupoid I).mem_of_eqOnSource' _ _ (ofSet_mem_analyticGroupoid hs) hes)

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