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
  1q*' = 1q
proof
  [*jj,zz*] = [*1,0,0,0*] by Lm3; then
A1: 1q= [*1,0,0,0*] by ARYTM_0:def 5;
A2: Rea [*jj,zz,zz,zz*] = 1 by Th16;
A3: Im1 [*jj,zz,zz,zz*] = 0 by Th16;
A4: Im2 [*jj,zz,zz,zz*] = 0 by Th16;
  Im3 [*jj,zz,zz,zz*] = 0 by Th16;
  hence thesis by A1,A2,A3,A4,Th36;
end;
