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
  Rea (<k>*') = 0 & Im1 (<k>*') = 0 & Im2 (<k>*') = 0 & Im3 (<k>*') = -1
proof
  <k>*' = [*zz,zz,zz,-jj*] by Th24,Th36;
  hence thesis by Th16;
end;
