Theorems · Theorem · linear algebra

coe_basisOfTopLeSpanOfCardEqFinrank

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : OrzechProperty R] [inst_2 : AddCommMonoid M]
  [inst_3 : Module R M] {ι : Type u_3} [inst_4 : Fintype ι] (b : ι → M) (le_span : ⊤ ≤ Submodule.span R (Set.range b))
  (card_eq : Fintype.card ι = Module.finrank R M), ⇑(basisOfTopLeSpanOfCardEqFinrank b le_span card_eq) = b

Defined in

Mathlib.LinearAlgebra.Dimension.OrzechProperty

Cited by

2 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringOrzechPropertyAddCommMonoidModuleFintype