reserve x for set,
  D for non empty set,
  k,n,m,i,j,l for Nat,
  K for Field;
reserve n,i,j for Nat;
reserve n for Nat;

theorem
  for A being Matrix of n,REAL st A is invertible holds for y being
FinSequence of REAL st len y=n holds ex x being FinSequence of REAL st len x=n
  & x*A=y
proof
  let A be Matrix of n,REAL;
  assume
A1: A is invertible;
  let y be FinSequence of REAL;
  assume
A2: len y=n;
  reconsider x0=y*(Inv A) as FinSequence of REAL;
  len Inv(A)=n by MATRIX_0:24;
  then
A3: len x0=width Inv A by A2,MATRIXR1:62
    .=n by MATRIX_0:24;
  then x0*A=y by A1,A2,Th89;
  hence thesis by A3;
end;
