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 Th55:
  -z = [*-Rea z, -Im1 z, -Im2 z, -Im3 z*]
proof
A1: z = [*Rea z, Im1 z, Im2 z, Im3 z*] by Th17;
  set z9 = [*-Rea z, -Im1 z, -Im2 z, -Im3 z*];
  z + z9 = [*Rea z+ -Rea z, Im1 z+ -Im1 z, Im2 z+ -Im2 z, Im3 z+ -Im3 z*]
  by A1,Def6
    .= 0 by Lm6;
  hence thesis by Def7;
end;
