Theorems · Theorem · linear algebra

DFinsupp.lsum_single

∀ {ι : Type u_1} {R : Type u_3} (S : Type u_4) {M : ι → Type u_5} {N : Type u_6} [inst : Semiring R]
  [inst_1 : (i : ι) → AddCommMonoid (M i)] [inst_2 : (i : ι) → Module R (M i)] [inst_3 : AddCommMonoid N]
  [inst_4 : Module R N] [inst_5 : DecidableEq ι] [inst_6 : Semiring S] [inst_7 : Module S N]
  [inst_8 : SMulCommClass R S N] (F : (i : ι) → M i →ₗ[R] N) (i : ι) (x : M i),
  (((DFinsupp.lsum S) F) fun₀ | i => x) = (F i) x

While simp can prove this, it is often convenient to avoid unfolding lsum into sumAddHom with DFinsupp.lsum_apply_apply.

Defined in

Mathlib.LinearAlgebra.DFinsupp

Cited by

5 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleAddCommMonoidModuleDecidableEqSemiringModuleSMulCommClass