deffunc H₁( Element of EC_SetAffCo (z,p), Element of EC_SetAffCo (z,p)) -> Element of ProjCo (GF p) = rep_pt ((addell_ProjCo (z,p)) . ($1,$2));
for o1, o2 being BinOp of (EC_SetAffCo (z,p)) st ( for P, Q being Element of EC_SetAffCo (z,p) holds o1 . (P,Q) = H₁(P,Q) ) & ( for P, Q being Element of EC_SetAffCo (z,p) holds o2 . (P,Q) = H₁(P,Q) ) holds
o1 = o2 from BINOP_2:sch 2();
hence for b₁, b₂ being BinOp of (EC_SetAffCo (z,p)) st ( for P, Q being Element of EC_SetAffCo (z,p) holds b₁ . (P,Q) = rep_pt ((addell_ProjCo (z,p)) . (P,Q)) ) & ( for P, Q being Element of EC_SetAffCo (z,p) holds b₂ . (P,Q) = rep_pt ((addell_ProjCo (z,p)) . (P,Q)) ) holds
b₁ = b₂ ; :: thesis: verum