Theorems · Theorem · linear algebra

Module.Basis.mk_range_eq_rank

∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type w}
  [StrongRankCondition R] (v : Module.Basis ι R M), Cardinal.mk ↑(Set.range ⇑v) = Module.rank R M

Defined in

Mathlib.LinearAlgebra.Dimension.StrongRankCondition

Cited by

2 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleStrongRankCondition