Theorems · Definition · linear algebra

Module.Basis.empty

{ι : Type u_1} →
  {R : Type u_3} →
    (M : Type u_5) →
      [inst : Semiring R] →
        [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → [Subsingleton M] → [IsEmpty ι] → Module.Basis ι R M

If M is a subsingleton and ι is empty, this is the unique ι-indexed basis for M.

Defined in

Mathlib.LinearAlgebra.Basis.Basic

Cited by

6 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleSubsingletonIsEmpty