reserve x for set;
reserve i,j for Integer;
reserve n,n1,n2,n3 for Nat;
reserve p for Prime;
reserve a,b,c,d for Element of GF(p);
reserve K for Ring;
reserve a1,a2,a3,a4,a5,a6 for Element of K;
reserve px,py,pz for object;
reserve Px,Py,Pz for Element of GF(p);
reserve P for Element of ProjCo(GF(p));
reserve O for Element of EC_SetProjCo(a,b,p);

theorem
  for p be Prime, a, b, Px, Py, Pz be Element of GF(p),
  P be Element of EC_SetProjCo(a,b,p) st P = [Px, Py, Pz]
  holds P`1_3 = Px & P`2_3 = Py & P`3_3 = Pz by Def3,Def4,Def5;
