(* 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.
Tactic Notation "REWR" :=
first
[ unshelve erewrite <-gtc_age |
unshelve erewrite gLockSetCode |
unshelve erewrite gRemLockSetCode |
rewrite gssThreadCode |
rewrite gssThreadCC |
unshelve erewrite gsoThreadCode |
unshelve erewrite <-gsoThreadCC |
unshelve erewrite gsoAddCode |
rewrite gssAddCode |
unshelve erewrite <-getThreadR_age |
unshelve erewrite gssThreadRes |
unshelve erewrite gsoThreadRes |
unshelve erewrite gThreadCR |
unshelve erewrite gssAddRes |
unshelve erewrite gsoAddRes |
unshelve erewrite gLockSetRes |
unshelve erewrite perm_of_age |
unshelve erewrite gRemLockSetRes |
unshelve erewrite m_phi_age_to
]; auto.
Tactic Notation "REWR" "in" hyp(H) :=
first
[ unshelve erewrite <-gtc_age in H |
unshelve erewrite gLockSetCode in H |
unshelve erewrite gRemLockSetCode in H |
rewrite gssThreadCode in H |
rewrite gssThreadCC in H |
unshelve erewrite gsoThreadCode in H |
unshelve erewrite <-gsoThreadCC in H |
unshelve erewrite gsoAddCode in H |
rewrite gssAddCode in H |
unshelve erewrite <-getThreadR_age in H |
unshelve erewrite gssThreadRes in H |
unshelve erewrite gsoThreadRes in H |
unshelve erewrite gThreadCR in H |
unshelve erewrite gssAddRes in H |
unshelve erewrite gsoAddRes in H |
unshelve erewrite gLockSetRes in H |
unshelve erewrite perm_of_age in H |
unshelve erewrite gRemLockSetRes in H |
unshelve erewrite m_phi_age_to in H
]; auto.
Tactic Notation "REWR" "in" "*" :=
first
[ unshelve erewrite <-gtc_age in * |
unshelve erewrite gLockSetCode in * |
unshelve erewrite gRemLockSetCode in * |
rewrite gssThreadCode in * |
rewrite gssThreadCC in * |
unshelve erewrite gsoThreadCode in * |
unshelve erewrite <-gsoThreadCC in * |
unshelve erewrite gsoAddCode in * |
rewrite gssAddCode in * |
unshelve erewrite <-getThreadR_age in * |
unshelve erewrite gssThreadRes in * |
unshelve erewrite gsoThreadRes in * |
unshelve erewrite gThreadCR in * |
unshelve erewrite gssAddRes in * |
unshelve erewrite gsoAddRes in * |
unshelve erewrite gLockSetRes in * |
unshelve erewrite perm_of_age in * |
unshelve erewrite gRemLockSetRes in * |
unshelve erewrite m_phi_age_to in *
]; auto.

Lemma FF_orp:
forall A (ND: NatDed A) (P: A), seplog.orp seplog.FF P = P.