Theorems · Theorem · ring theory

DirectSum.IsInternal.collectedBasis_mem

∀ {R : Type u} [inst : Semiring R] {ι : Type v} [dec_ι : DecidableEq ι] {M : Type u_1} [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] {A : ι → Submodule R M} (h : DirectSum.IsInternal A) {α : ι → Type u_2}
  (v : (i : ι) → Module.Basis (α i) R ↥(A i)) (a : (i : ι) × α i), (h.collectedBasis v) a ∈ A a.fst

Defined in

Mathlib.Algebra.DirectSum.Module

Cited by

0 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringDecidableEqAddCommMonoidModule