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

theorem
  for A being Matrix of 2,REAL holds 
  Det A = (A*(1,1))*(A*(2,2))-(A*(1,2))*(A*(2,1))
proof
  let A be Matrix of 2,REAL;
  reconsider N=MXR2MXF A as Matrix of 2,F_Real;
  Det A = (N*(1,1))*(N*(2,2))-(N*(1,2))*(N*(2,1)) by MATRIX_7:12;
  hence thesis;
end;
