Theorems · Definition · commutative algebra

FunLike.distribSMul

{M : Type u_1} →
  {F : Type u_3} →
    {α : Type u_4} →
      {β : Type u_5} →
        [i : FunLike F α β] →
          [inst : AddZeroClass β] →
            [inst_1 : AddZeroClass F] →
              [inst_2 : DistribSMul M β] →
                [inst_3 : SMul M F] → [IsZeroApply F α β] → [IsAddApply F α β] → [IsSMulApply M F α β] → DistribSMul M F

A FunLike type with scalar multiplication that satisfies (m • f) x = m • f x and 0 x = 0, (f + g) x = f x + g x is a DistribSMul if β is a DistribSMul.

Defined in

Mathlib.Data.FunLike.Module

Cited by

0 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound

Assumes

FunLikeAddZeroClassAddZeroClassDistribSMulSMulIsZeroApplyIsAddApplyIsSMulApply