reserve x for set;
reserve i,j for Integer;
reserve n,n1,n2,n3 for Nat;
reserve K,K1,K2,K3 for Field;
reserve SK1,SK2 for Subfield of K;
reserve ek,ek1,ek2 for Element of K;
reserve p for Prime;
reserve a,b,c for Element of GF(p);
reserve F for FinSequence of GF(p);
reserve Px,Py,Pz for Element of GF(p);

theorem Th42:
  [0,1,0] is Element of EC_SetProjCo(a,b,p)
  proof
    [0,1,0] is Element of ProjCo(GF(p))
    & EC_WEqProjCo(a,b,p).([0,1,0]) = 0.GF(p) by Lm5;
    then [0,1,0] in {P where P is Element of ProjCo(GF(p)) :
    EC_WEqProjCo(a,b,p).P = 0.GF(p)};
    hence thesis;
  end;
