proposition: Lemma balanced_inj w n1 n2 b1 b2 : gram_balanced n1 b1 w -> gram_balanced n2 b2 w -> n1 = n2 /\ b1 = b2.
proof: Proof. by elim: w n1 n2 b1 b2 => [|[|||] w IHw] [|n1] [|n2] [|] [|] //= bal1 bal2; case: (IHw _ _ _ _ bal1 bal2) => // /(congr1 succn)[<-]. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype) fourcolor(color)