reserve a,b,c,d,x,y,w,z,x1,x2,x3,x4 , X for set;
reserve A for non empty set;
reserve i,j,k for Element of NAT;
reserve a,b,c,d for Real;
reserve y,r,s,x,t,w for Element of RAT+;
reserve z,z1,z2,z3,z4 for Quaternion;
 reserve x for Real;

theorem Th60:
  0 <= |.z.|
proof
A1: 0 <= (Rea z)^2 by XREAL_1:63;
A2: 0 <= (Im1 z)^2 by XREAL_1:63;
A3: 0 <= (Im2 z)^2 by XREAL_1:63;
  0 <= (Im3 z)^2 by XREAL_1:63;
  hence thesis by A1,A2,A3,SQUARE_1:def 2;
end;
