fact: Fixpoint Pmul (P P'' : Pol) {struct P''} : Pol := match P'' with | Pc c => PmulC P c | Pinj j' Q' => PmulI Pmul Q' j' P | PX P' i' Q' => match P with | Pc c => PmulC P'' c | Pinj j Q => let QQ' := match j with | xH => Pmul Q Q' | xO j => Pmul (Pinj (Pos.pred_double j) Q) Q' | xI j => Pmul (Pinj (xO j) Q) Q' end in mkPX (Pmul P P') i' QQ' | PX P i Q=> let QQ' := Pmul Q Q' in let PQ' := PmulI Pmul Q' xH P in let QP' := Pmul (mkPinj xH Q) P' in let PP' := Pmul P P' in (mkPX (mkPX PP' i P0 ++ QP') i' P0) ++ mkPX PQ' i QQ' end end.
imports: Setoid Morphisms BinList BinPos BinNat BinInt Ring_theory