Theorems · Definition · group theory

FunLike.commGroup

{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 : Inv F] →
                [inst_5 : Div F] →
                  [inst_6 : Pow F ℤ] →
                    [inst_7 : CommGroup β] →
                      [IsOneApply F α β] →
                        [IsMulApply F α β] →
                          [IsInvApply F α β] →
                            [IsDivApply F α β] → [IsPowApply ℕ F α β] → [IsPowApply ℤ F α β] → CommGroup F

A FunLike type is a commutative group if β is a commutative group.

Defined in

Mathlib.Data.FunLike.Group

Cited by

0 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Quot.sound

Assumes

FunLikeMulOnePowInvDivPowCommGroupIsOneApplyIsMulApplyIsInvApplyIsDivApplyIsPowApplyIsPowApply