Definition sourceN (n:block) (j:meminj) (m:mem)
                   (b2:block) (ofs2:Z): option(block * Z) :=
Pos.peano_rect
            (fun p => option(block * Z))
            (match isSource j m b2 ofs2 1%positive
             with Some ofs1 => Some(1%positive, ofs1)
                | None => None
             end)
            (fun p Hp => match isSource j m b2 ofs2 (Pos.succ p)
             with Some ofs1 => Some (Pos.succ p, ofs1)
                | None => Hp
             end)
            n.

(* Specifications: *)
Lemma sourceN_SomeE: forall j m b2 ofs2 n b1 ofs1, sourceN n j m b2 ofs2 = Some(b1,ofs1) -> exists delta, (b1 <= n)%positive /\ j b1 = Some(b2,delta) /\ Mem.perm m b1 ofs1 Max Nonempty /\ ofs2=ofs1+delta.
Lemma sourceN_NoneE: forall j m b2 ofs2 n, sourceN n j m b2 ofs2 = None -> forall b1 delta, (b1 <= n)%positive -> j b1 = Some(b2,delta) -> ~ Mem.perm m b1 (ofs2-delta) Max Nonempty.
Lemma sourceN_SomeI: forall n j m b2 b1 ofs1 delta (OV:Mem.meminj_no_overlap j m), j b1 = Some(b2,delta) -> Mem.perm m b1 ofs1 Max Nonempty -> (b1 <= n)%positive -> sourceN n j m b2 (ofs1+delta) = Some(b1,ofs1).
Lemma sourceN_SomeE: forall j m b2 ofs2 n b1 ofs1, sourceN n j m b2 ofs2 = Some(b1,ofs1) -> exists delta, (b1 <= n)%positive /\ j b1 = Some(b2,delta) /\ Mem.perm m b1 ofs1 Max Nonempty /\ ofs2=ofs1+delta.
Lemma sourceN_NoneE: forall j m b2 ofs2 n, sourceN n j m b2 ofs2 = None -> forall b1 delta, (b1 <= n)%positive -> j b1 = Some(b2,delta) -> ~ Mem.perm m b1 (ofs2-delta) Max Nonempty.
Lemma sourceN_SomeI: forall n j m b2 b1 ofs1 delta (OV:Mem.meminj_no_overlap j m), j b1 = Some(b2,delta) -> Mem.perm m b1 ofs1 Max Nonempty -> (b1 <= n)%positive -> sourceN n j m b2 (ofs1+delta) = Some(b1,ofs1).