Theorems · Theorem · ring theory

DirectSum.of_zero_smul

∀ {ι : Type u_1} [inst : DecidableEq ι] (A : ι → Type u_2) [inst_1 : AddZeroClass ι]
  [inst_2 : (i : ι) → AddCommMonoid (A i)] [inst_3 : DirectSum.GNonUnitalNonAssocSemiring A] {i : ι} (a : A 0)
  (b : A i), (DirectSum.of A i) (a • b) = (DirectSum.of A 0) a * (DirectSum.of A i) b

Defined in

Mathlib.Algebra.DirectSum.Ring

Cited by

1 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddZeroClassAddCommMonoidDirectSum.GNonUnitalNonAssocSemiring