Theorems · Theorem · linear algebra

basisOfLinearIndependentOfCardEqFinrank.congr_simp

∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {ι : Type u_1}
  [inst_3 : Fintype ι] [inst_4 : Nonempty ι] {b b_1 : ι → V} (e_b : b = b_1) (lin_ind : LinearIndependent K b)
  (card_eq : Fintype.card ι = Module.finrank K V),
  basisOfLinearIndependentOfCardEqFinrank lin_ind card_eq = basisOfLinearIndependentOfCardEqFinrank ⋯ card_eq

Defined in

Mathlib.LinearAlgebra.FiniteDimensional.Lemmas

Cited by

0 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleFintypeNonempty