(*
assert (cnti = Htid) by apply proof_irr; subst Htid).
assert (ctn = cnti) by apply proof_irr; subst cnt).
destruct (cntAdd' _ _ _ cnti) as [(cnti', ne) | Ei].
*)

Ltac join_sub_tac :=
  try
    match goal with
      c : mem_compatible_with ?tp ?m ?Phi |- _ =>
      match goal with
      | cnt1 : containsThread tp _,
        cnt2 : containsThread tp _,
        cnt3 : containsThread tp _,
        cnt4 : containsThread tp _ |- _ =>
        assert (join_sub (getThreadR cnt1) Phi) by (apply compatible_threadRes_sub, c);
        assert (join_sub (getThreadR cnt2) Phi) by (apply compatible_threadRes_sub, c);
        assert (join_sub (getThreadR cnt3) Phi) by (apply compatible_threadRes_sub, c);
        assert (join_sub (getThreadR cnt4) Phi) by (apply compatible_threadRes_sub, c)
      | cnt1 : containsThread tp _,
        cnt2 : containsThread tp _,
        cnt3 : containsThread tp _ |- _ =>
        assert (join_sub (getThreadR cnt1) Phi) by (apply compatible_threadRes_sub, c);
        assert (join_sub (getThreadR cnt2) Phi) by (apply compatible_threadRes_sub, c);
        assert (join_sub (getThreadR cnt3) Phi) by (apply compatible_threadRes_sub, c)
      | cnt1 : containsThread tp _,
        cnt2 : containsThread tp _ |- _ =>
        assert (join_sub (getThreadR cnt1) Phi) by (apply compatible_threadRes_sub, c);
        assert (join_sub (getThreadR cnt2) Phi) by (apply compatible_threadRes_sub, c)
      | cnt1 : containsThread tp _ |- _ =>
        assert (join_sub (getThreadR cnt1) Phi) by (apply compatible_threadRes_sub, c)
      end
    end;
  try
    match goal with
    | F : AMap.find (elt:=option rmap) ?loc (lset ?tp) = Some (Some ?phi),
          c : mem_compatible_with ?tp _ ?Phi |- _
      => assert (join_sub phi Phi) by eapply (@compatible_lockRes_sub tp loc phi F), c
    end;
  eauto using join_sub_trans.

(* Specifications: *)
Lemma FF_orp: forall A (ND: NatDed A) (P: A), seplog.orp seplog.FF P = P.
Lemma TT_andp: forall A (ND: NatDed A) (P: A), seplog.andp seplog.TT P = P.