Theorems · Theorem · linear algebra

linearIndependent_of_top_le_span_of_card_eq_finrank

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [OrzechProperty R] [inst_2 : AddCommMonoid M] [inst_3 : Module R M]
  {ι : Type u_3} [inst_4 : Fintype ι] {b : ι → M},
  ⊤ ≤ Submodule.span R (Set.range b) → Fintype.card ι = Module.finrank R M → LinearIndependent R b

Defined in

Mathlib.LinearAlgebra.Dimension.OrzechProperty

Cited by

4 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringOrzechPropertyAddCommMonoidModuleFintype