Record rsplit : Type := mk_rsplit {
   rsplit_left : PExpr C;
   rsplit_common : PExpr C;
   rsplit_right : PExpr C}.Record rsplit : Type := mk_rsplit {
   rsplit_left : PExpr C;
   rsplit_common : PExpr C;
   rsplit_right : PExpr C}.Record rsplit : Type := mk_rsplit {
   rsplit_left : PExpr C;
   rsplit_common : PExpr C;
   rsplit_right : PExpr C}.Record rsplit : Type := mk_rsplit {
   rsplit_left : PExpr C;
   rsplit_common : PExpr C;
   rsplit_right : PExpr C}.Record rsplit : Type := mk_rsplit {
   rsplit_left : PExpr C;
   rsplit_common : PExpr C;
   rsplit_right : PExpr C}.(* Stupid name clash *)
Notation left := rsplit_left.Notation right := rsplit_right.Notation common := rsplit_common.

Theorem split_aux_ok: forall e1 p e2, (e1 ^ Npos p === left (split_aux e1 p e2) * common (split_aux e1 p e2) /\ e2 === right (split_aux e1 p e2) * common (split_aux e1 p e2))%poly.