Theorems · Definition · group theory

FunLike.addMonoid

{F : Type u_1} →
  {α : Type u_2} →
    {β : Type u_3} →
      [inst : FunLike F α β] →
        [inst_1 : Add F] →
          [inst_2 : Zero F] →
            [inst_3 : SMul ℕ F] →
              [inst_4 : AddMonoid β] → [IsZeroApply F α β] → [IsAddApply F α β] → [IsSMulApply ℕ F α β] → AddMonoid F

A FunLike type that satisfies (f + g) x = f x + g x, 0 x = 0, and (n • f) x = n • f x is an additive monoid if β is an additive monoid.

Defined in

Mathlib.Data.FunLike.Group

Cited by

0 results in Mathlib

Foundations

Depth 13 from the axioms · uses propext, Quot.sound

Assumes

FunLikeAddZeroSMulAddMonoidIsZeroApplyIsAddApplyIsSMulApply