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Structures · Lean core

Lean.Grind.Semiring

A semiring, i.e. a type equipped with addition, multiplication, and a map from the natural numbers, satisfying appropriate compatibilities. Use Ring instead if the type also has negation, CommSemiring if the multiplication is commutative, or CommRing if the type has negation and multiplication is commutative.

Defined in
Init.Grind.Ring.Basic
Shape
One type argument · adds natCast, ofNat, nsmul, npow, add_zero, add_comm, add_assoc, mul_assoc, mul_one, one_mul, left_distrib, right_distrib, zero_mul, mul_zero, pow_zero, pow_succ, ofNat_succ, ofNat_eq_natCast, nsmul_eq_natCast_mul

Extends2

Extended by3

Forgetful instances

Every Lean.Grind.Semiring is also a

Provided automatically by

Concrete types that are instances0

No instance on a concrete type; it is reached through other classes.

How is a type an instance?

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Assumed by0

No theorem or definition in Mathlib takes this class as a hypothesis.

Ancestors16