Definition pcmp (c: comparison) (p1 p2: aptr) : abool :=
match p1, p2 with
| Pbot, _ | _, Pbot => Bnone
| Gl id1 ofs1, Gl id2 ofs2 =>
if peq id1 id2 then Maybe (Ptrofs.cmpu c ofs1 ofs2)
else cmp_different_blocks c
| Gl id1 ofs1, Glo id2 =>
if peq id1 id2 then Btop else cmp_different_blocks c
| Glo id1, Gl id2 ofs2 =>
if peq id1 id2 then Btop else cmp_different_blocks c
| Glo id1, Glo id2 =>
if peq id1 id2 then Btop else cmp_different_blocks c
| Stk ofs1, Stk ofs2 => Maybe (Ptrofs.cmpu c ofs1 ofs2)
| (Gl _ _ | Glo _ | Glob | Nonstack), (Stk _ | Stack) => cmp_different_blocks c
| (Stk _ | Stack), (Gl _ _ | Glo _ | Glob | Nonstack) => cmp_different_blocks c
| _, _ => Btop
end.

Lemma pcmp_none:
forall c p1 p2, cmatch None (pcmp c p1 p2).