(* simplification *)

Theorem PEsimp_ok e : (PEsimp e === e)%poly.
Inductive FExpr : Type :=
| FEO : FExpr
| FEI : FExpr
| FEc: C ->  FExpr
| FEX: positive ->  FExpr
| FEadd: FExpr -> FExpr ->  FExpr
| FEsub: FExpr -> FExpr ->  FExpr
| FEmul: FExpr -> FExpr ->  FExpr
| FEopp: FExpr ->  FExpr
| FEinv: FExpr ->  FExpr
| FEdiv: FExpr -> FExpr ->  FExpr
| FEpow: FExpr -> N -> FExpr .