
theorem INVMN2:
  for n being Nat, M being Matrix of n, F_Real
  st M is Matrix of n, F_Rat & M is invertible
  holds M~ is Matrix of n, F_Rat
  proof
    let n be Nat, M be Matrix of n, F_Real;
    assume that
    A1: M is Matrix of n, F_Rat and
    A2: M is invertible;
    reconsider H = M as Matrix of n, F_Rat by A1;
    M ~ = H ~ by A2,INVMN1;
    hence M ~ is Matrix of n, F_Rat;
  end;
