Theorems · Theorem · linear algebra

MultilinearMap.dfinsuppFamily_apply_toFun

∀ {ι : Type uι} {κ : ι → Type uκ} {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)]
  (f : (p : (i : ι) → κ i) → MultilinearMap R (fun i => M i (p i)) (N p)) (x : (i : ι) → Π₀ (j : κ i), M i j)
  (p : (i : ι) → κ i), ((MultilinearMap.dfinsuppFamily f) x) p = (f p) fun i => (x i) (p i)

Defined in

Mathlib.LinearAlgebra.Multilinear.DFinsupp

Cited by

7 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqFintypeSemiringAddCommMonoidAddCommMonoidModuleModule