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 Th34:
  Rea(-z) = -(Rea z) & Im1(-z) = -(Im1 z) & Im2(-z) = -(Im2 z) &
  Im3(-z) = -(Im3 z)
proof
  -z = -Rea z + (-Im1 z)*<i> + (-Im2 z)*<j> + (-Im3 z)*<k> by Lm24; then
  -z = [*-Rea z,-Im1 z,-Im2 z,-Im3 z*] by Lm19;
  hence thesis by Th16;
end;
