directSumGRing — Mathlib

English

The divisibility relation is transitive: if a|b and b|c then a|c.

Русский

Отношение делимости транзитивно: если a|b и b|c, то a|c.

LaTeX

$$$$\text{If }a|b\text{ and }b|c\text{ then }a|c.$$$$

Lean4

/-- A direct sum of copies of a `Ring` inherits the multiplication structure. -/
instance directSumGRing {R : Type*} [AddMonoid ι] [Ring R] : DirectSum.GRing fun _ : ι => R
    where
  __ := Semiring.directSumGSemiring ι
  intCast z := z
  intCast_ofNat := Int.cast_natCast
  intCast_negSucc_ofNat := Int.cast_negSucc

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