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 be Matrix of n,REAL st A is invertible holds Inv Inv A = A
proof
  let A be Matrix of n,REAL;
  assume A is invertible;
  then
A1: Inv(A)*A=1_Rmatrix(n) & A*(Inv(A))=1_Rmatrix(n) by Def6;
  then Inv(A) is invertible;
  hence thesis by A1,Def6;
end;
