nonneg — Mathlib

English

The set of nonnegative elements in an ordered semiring forms a subsemiring.

Русский

Множество неотрицательных элементов упорядоченного полукольца формирует подпол semiring.

LaTeX

$$$\\text{nonneg}(R) = \\{ x \\in R \\;|\\; 0 \\le x \\}$ defines a Subsemiring of R$$

Lean4

/-- The set of nonnegative elements in an ordered semiring, as a subsemiring. -/
@[simps]
def nonneg : Subsemiring R where
  carrier := Set.Ici 0
  mul_mem' := mul_nonneg
  one_mem' := zero_le_one
  add_mem' := add_nonneg
  zero_mem' := le_rfl

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