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 n>0 & 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 & A*x=y
proof
  let A be Matrix of n,REAL;
  assume that
A1: n>0 and
A2: A is invertible;
  let y be FinSequence of REAL;
  assume
A3: len y=n;
  reconsider x0=(Inv A)*y as FinSequence of REAL;
  len Inv(A)=n & width Inv(A) =n by MATRIX_0:24;
  then
A4: len x0=n by A1,A3,MATRIXR1:61;
  then A*x0=y by A1,A2,A3,Th87;
  hence thesis by A4;
end;
