instNonUnitalNonAssocSemiring — Mathlib

English

Product of two NonUnitalNonAssocSemirings is a NonUnitalNonAssocSemiring.

Русский

Произведение двух нехолесных полукольц без единицы образует NonUnitalNonAssocSemiring.

LaTeX

$$$\text{NonUnitalNonAssocSemiring}(R \times S)$$$

Lean4

/-- Product of two `NonUnitalNonAssocSemiring`s is a `NonUnitalNonAssocSemiring`. -/
instance instNonUnitalNonAssocSemiring [NonUnitalNonAssocSemiring R] [NonUnitalNonAssocSemiring S] :
    NonUnitalNonAssocSemiring (R × S) :=
  { inferInstanceAs (AddCommMonoid (R × S)), inferInstanceAs (Distrib (R × S)),
    inferInstanceAs (MulZeroClass (R × S)) with }

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