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 z = 0 implies z*' = -z
proof
  assume A1: Rea z = 0;
  -z = -Rea z + (-Im1 z)*<i> + (-Im2 z)*<j> + (-Im3 z)*<k> by Lm24;
  hence thesis by A1;
end;
