Theorems · Theorem · linear algebra

Module.Basis.repr_support_subset_of_mem_span

∀ {ι : Type u_1} {R : Type u_3} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (b : Module.Basis ι R M) (s : Set ι) {m : M}, m ∈ Submodule.span R (⇑b '' s) → ↑(b.repr m).support ⊆ s

Defined in

Mathlib.LinearAlgebra.Basis.Basic

Cited by

2 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule