Theorems · Theorem · linear algebra

MultilinearMap.dfinsuppFamily_smul

∀ {ι : Type uι} {κ : ι → Type uκ} {S : Type uS} {R : Type uR} {M : (i : ι) → κ i → Type uM}
  {N : ((i : ι) → κ i) → Type uN} [inst : DecidableEq ι] [inst_1 : Fintype ι] [inst_2 : Semiring R]
  [inst_3 : (i : ι) → (k : κ i) → AddCommMonoid (M i k)] [inst_4 : (p : (i : ι) → κ i) → AddCommMonoid (N p)]
  [inst_5 : (i : ι) → (k : κ i) → Module R (M i k)] [inst_6 : (p : (i : ι) → κ i) → Module R (N p)] [inst_7 : Monoid S]
  [inst_8 : (p : (i : ι) → κ i) → DistribMulAction S (N p)] [inst_9 : ∀ (p : (i : ι) → κ i), SMulCommClass R S (N p)]
  (s : S) (f : (p : (i : ι) → κ i) → MultilinearMap R (fun i => M i (p i)) (N p)),
  MultilinearMap.dfinsuppFamily (s • f) = s • MultilinearMap.dfinsuppFamily f

Defined in

Mathlib.LinearAlgebra.Multilinear.DFinsupp

Cited by

0 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqFintypeSemiringAddCommMonoidAddCommMonoidModuleModuleMonoidDistribMulActionSMulCommClass