Theorem: Matrix.cols_linearIndependent_iff_of_rowSpaces_eq (Matroid/ForMathlib/LinearAlgebra/Matrix/Rowspace.lean)

State before:
l : Type u_1
m✝ : Type u_2
m' : Type u_3
n✝ : Type u_4
n' : Type u_5
n₁ : Type u_6
n₂ : Type u_7
o : Type u_8
α : Type u_9
R✝ : Type u_10
A✝¹ B✝ : Matrix m✝ n✝ R✝
s✝ : Set m✝
t✝¹ : Set n✝
m : Type u_11
n : Type u_12
R : Type u_13
s : Set m
t✝ : Set n
A✝ B : Matrix m n R
K : Type u_14
inst✝ : Field K
A : Matrix m n K
m₁ : Type u_15
m₂ : Type u_16
A₁ : Matrix m₁ n K
A₂ : Matrix m₂ n K
h : A₁.rowSpace = A₂.rowSpace
t : Set n
⊢ LinearIndependent (ι := ↑t) K (A₁.colSubmatrix t).colFun ↔ LinearIndependent (ι := ↑t) K (A₂.colSubmatrix t).colFun
Tactic:
exact ⟨fun h' ↦ cols_linearIndependent_of_rowSpace_le_rowSpace h.le h',
  fun h' ↦ cols_linearIndependent_of_rowSpace_le_rowSpace h.symm.le h'⟩
State after:
no goals