Theorems · Definition · group theory

FunLike.addCommGroup

{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 : Neg F] →
                [inst_5 : Sub F] →
                  [inst_6 : SMul ℤ F] →
                    [inst_7 : AddCommGroup β] →
                      [IsZeroApply F α β] →
                        [IsAddApply F α β] →
                          [IsNegApply F α β] →
                            [IsSubApply F α β] → [IsSMulApply ℕ F α β] → [IsSMulApply ℤ F α β] → AddCommGroup F

A FunLike type is an additive commutative group if β is an additive 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

FunLikeAddZeroSMulNegSubSMulAddCommGroupIsZeroApplyIsAddApplyIsNegApplyIsSubApplyIsSMulApplyIsSMulApply