theorem :: EC_PF_3:31

for p being 5 _or_greater Prime
for z being Element of EC_WParam p
for P, O being Element of EC_SetProjCo ((z `1),(z `2),p) st O = [0,1,0] & not P _EQ_ O holds
( P `2_3 = 0. (GF p) iff (addell_ProjCo (z,p)) . (P,P) _EQ_ O )