Theorems · Definition · commutative algebra

Function.Injective.nonAssocSemiring

{R : Type u_1} →
  {S : Type u_2} →
    (f : S → R) →
      Function.Injective f →
        [inst : Add S] →
          [inst_1 : Mul S] →
            [inst_2 : Zero S] →
              [inst_3 : One S] →
                [inst_4 : SMul ℕ S] →
                  [inst_5 : NatCast S] →
                    [inst_6 : NonAssocSemiring R] →
                      f 0 = 0 →
                        f 1 = 1 →
                          (∀ (x y : S), f (x + y) = f x + f y) →
                            (∀ (x y : S), f (x * y) = f x * f y) →
                              (∀ (n : ℕ) (x : S), f (n • x) = n • f x) → (∀ (n : ℕ), f ↑n = ↑n) → NonAssocSemiring S

Pullback a NonAssocSemiring instance along an injective function.

Defined in

Mathlib.Algebra.Ring.InjSurj

Cited by

0 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext

Assumes

AddMulZeroOneSMulNatCastNonAssocSemiring