fact: Definition orthonormal_family_axiom := forall S U1' U1 U2 U3 U4, ~ (S <> U1' /\ Bet U1 S U1' /\ Cong S U1 S U1' /\ Cong S U2 S U1' /\ Cong S U3 S U1' /\ Cong S U4 S U1' /\ Cong U1 U2 U1' U2 /\ Cong U1 U3 U1' U2 /\ Cong U1 U4 U1' U2 /\ Cong U2 U3 U1' U2 /\ Cong U2 U4 U1' U2 /\ Cong U3 U4 U1' U2).
imports: GeoCoq.Tarski_dev.Ch11_angles GeoCoq.Utils.all_equiv