Theorems · Definition · group theory

FunLike.leftCancelMonoid

{F : Type u_1} →
  {α : Type u_2} →
    {β : Type u_3} →
      [inst : FunLike F α β] →
        [inst_1 : Mul F] →
          [inst_2 : One F] →
            [inst_3 : Pow F ℕ] →
              [inst_4 : LeftCancelMonoid β] →
                [IsOneApply F α β] → [IsMulApply F α β] → [IsPowApply ℕ F α β] → LeftCancelMonoid F

A FunLike type that satisfies (f * g) x = f x * g x, 1 x = 1, and (f ^ n) x = f x ^ n is a left cancel monoid if β is a left cancel monoid.

Defined in

Mathlib.Data.FunLike.Group

Cited by

0 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Quot.sound

Assumes

FunLikeMulOnePowLeftCancelMonoidIsOneApplyIsMulApplyIsPowApply