reserve a,b,c,d,e,f for Real,
        g           for positive Real,
        x,y         for Complex,
        S,T         for Element of REAL 2,
        u,v,w       for Element of TOP-REAL 3;
reserve a,b,c for Element of F_Real,
          M,N for Matrix of 3,F_Real;
reserve D        for non empty set;
reserve d1,d2,d3 for Element of D;
reserve A        for Matrix of 1,3,D;
reserve B        for Matrix of 3,1,D;
reserve u,v for non zero Element of TOP-REAL 3;

theorem Th43:
  symmetric_3(1,1,-1,0,0,0) * symmetric_3(1,1,-1,0,0,0) = 1.(F_Real,3)
  proof
    reconsider a = 1 as non zero Real;
    -1 / a = -1;
    hence thesis by Th41;
  end;
