theorem Th36:
  z*' = [*Rea z, -Im1 z, -Im2 z, -Im3 z*]
proof
 <i> = [*zz,jj,zz,zz*] by Lm2,Lm3;
  then z*'= Rea z + [*(-Im1 z)*0,(-Im1 z) *1,(-Im1 z) *0,(-Im1 z) *0 *]
  + (-Im2 z)*<j> + (-Im3 z)*<k> by Def20
    .= Rea z + [*0,-Im1 z,0,0 *] +
  [*(-Im2 z)*0,(-Im2 z)*0,(-Im2 z)*1,(-Im2 z)*0*] + (-Im3 z)*<k> by Def20
    .= Rea z + [*0,-Im1 z,0,0 *] + [*0,0,(-Im2 z),0*] +
  [*(-Im3 z)*0,(-Im3 z)*0,(-Im3 z)*0,(-Im3 z)*1*] by Def20
    .= [*Rea z+0,-Im1 z,0,0 *] + [*0,0,(-Im2 z),0*]
  + [*0,0,0,(-Im3 z)*] by Def18
    .= [*Rea z+0,-Im1 z+0,0+(-Im2 z),0+0*] + [*0,0,0,(-Im3 z)*] by Def6
    .= [*Rea z+0,-Im1 z+0,-Im2 z+0,0+(-Im3 z)*] by Def6;
  hence thesis;
end;
