Inductive ReduStarConfluent (Q : list (poly A0 eqA ltM))
(p : list (Term A n)) : Prop :=
    ReduStarConfluent0 :
      (forall r s : list (Term A n),
       reducestar A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q
         p r ->
       reducestar A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q
         p s -> eqP A eqA n r s) -> ReduStarConfluent Q p.Inductive ReduStarConfluent (Q : list (poly A0 eqA ltM))
(p : list (Term A n)) : Prop :=
    ReduStarConfluent0 :
      (forall r s : list (Term A n),
       reducestar A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q
         p r ->
       reducestar A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q
         p s -> eqP A eqA n r s) -> ReduStarConfluent Q p.

Theorem confl_under : forall (Q : list (poly A0 eqA ltM)) (a : Term A n) (p : list (Term A n)), canonical A0 eqA ltM (pX a p) -> (forall q : list (Term A n), canonical A0 eqA ltM q -> ltP (A:=A) (n:=n) ltM q (pX a p) -> ReduStarConfluent Q q) -> forall r s : list (Term A n), reduce A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q (pX a p) (pX a r) -> reduce A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q (pX a p) (pX a s) -> forall r1 s1 : list (Term A n), reducestar A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q (pX a r) r1 -> reducestar A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q (pX a s) s1 -> eqP A eqA n r1 s1.