proposition: Lemma set_to_T1_inj x y: inc x T1 -> inc y T1 -> set_to_T1 x = set_to_T1 y -> x = y.
proof: Proof. move => ha hb. by rewrite !set_to_T1_pr - {2} (B_eq ha) - {2} (B_eq hb) => ->. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)