Remark in_inj_value:
  forall mv v q, In mv (inj_value q v) -> exists n, mv = Fragment v q n.

(* Specifications: *)
Lemma proj_inj_value_mismatch: forall q1 q2 v, q1 <> q2 -> proj_value q1 (inj_value q2 v) = Vundef.