(* A tactic to normalize one specific bracket *)
Ltac normb a b c :=
generalize (bracket_norm a b c);
intros (Hn1, (Hn2, (Hn3, (Hn4, Hn5))));
rewrite ?Hn1, ?Hn2, ?Hn3, ?Hn4, ?Hn5;
clear Hn1 Hn2 Hn3 Hn4 Hn5.
Definition fbracket a b c:= '[a, b, c].

Lemma fbracket_norm (a b c: point) :
('[a,b,c] =  fbracket a b c /\
'[a,c,b] =  (-(1)) *  (fbracket a b c) /\
'[b,a,c] = (-(1))%f * (fbracket a b c) /\
'[b,c,a] = (fbracket a b c) /\
'[c,a,b] = (fbracket a b c) /\
'[c,b,a] = (-(1))%f * (fbracket a b c))%f.