diff --git a/base_logic/derived.v b/base_logic/derived.v
index 7cb853696e2f78b00aee8cafee2f6c8afdcbb4ab..7f4efa6e25a760fc172de6ba5a00cb25374cf4d6 100644
--- a/base_logic/derived.v
+++ b/base_logic/derived.v
@@ -12,11 +12,11 @@ Arguments uPred_always_if _ !_ _/.
 Notation "â–¡? p P" := (uPred_always_if p P)
   (at level 20, p at level 0, P at level 20, format "â–¡? p  P").
 
-Definition uPred_except_last {M} (P : uPred M) : uPred M := ▷ False ∨ P.
-Notation "â—‡ P" := (uPred_except_last P)
+Definition uPred_except_0 {M} (P : uPred M) : uPred M := ▷ False ∨ P.
+Notation "â—‡ P" := (uPred_except_0 P)
   (at level 20, right associativity) : uPred_scope.
-Instance: Params (@uPred_except_last) 1.
-Typeclasses Opaque uPred_except_last.
+Instance: Params (@uPred_except_0) 1.
+Typeclasses Opaque uPred_except_0.
 
 Class TimelessP {M} (P : uPred M) := timelessP : ▷ P ⊢ ◇ P.
 Arguments timelessP {_} _ {_}.
@@ -547,50 +547,50 @@ Proof. destruct p; simpl; auto using always_later. Qed.
 
 
 (* True now *)
-Global Instance except_last_ne n : Proper (dist n ==> dist n) (@uPred_except_last M).
+Global Instance except_0_ne n : Proper (dist n ==> dist n) (@uPred_except_0 M).
 Proof. solve_proper. Qed.
-Global Instance except_last_proper : Proper ((⊣⊢) ==> (⊣⊢)) (@uPred_except_last M).
+Global Instance except_0_proper : Proper ((⊣⊢) ==> (⊣⊢)) (@uPred_except_0 M).
 Proof. solve_proper. Qed.
-Global Instance except_last_mono' : Proper ((⊢) ==> (⊢)) (@uPred_except_last M).
+Global Instance except_0_mono' : Proper ((⊢) ==> (⊢)) (@uPred_except_0 M).
 Proof. solve_proper. Qed.
-Global Instance except_last_flip_mono' :
-  Proper (flip (⊢) ==> flip (⊢)) (@uPred_except_last M).
+Global Instance except_0_flip_mono' :
+  Proper (flip (⊢) ==> flip (⊢)) (@uPred_except_0 M).
 Proof. solve_proper. Qed.
 
-Lemma except_last_intro P : P ⊢ ◇ P.
-Proof. rewrite /uPred_except_last; auto. Qed.
-Lemma except_last_mono P Q : (P ⊢ Q) → ◇ P ⊢ ◇ Q.
+Lemma except_0_intro P : P ⊢ ◇ P.
+Proof. rewrite /uPred_except_0; auto. Qed.
+Lemma except_0_mono P Q : (P ⊢ Q) → ◇ P ⊢ ◇ Q.
 Proof. by intros ->. Qed.
-Lemma except_last_idemp P : ◇ ◇ P ⊢ ◇ P.
-Proof. rewrite /uPred_except_last; auto. Qed.
-
-Lemma except_last_True : ◇ True ⊣⊢ True.
-Proof. rewrite /uPred_except_last. apply (anti_symm _); auto. Qed.
-Lemma except_last_or P Q : ◇ (P ∨ Q) ⊣⊢ ◇ P ∨ ◇ Q.
-Proof. rewrite /uPred_except_last. apply (anti_symm _); auto. Qed.
-Lemma except_last_and P Q : ◇ (P ∧ Q) ⊣⊢ ◇ P ∧ ◇ Q.
-Proof. by rewrite /uPred_except_last or_and_l. Qed.
-Lemma except_last_sep P Q : ◇ (P ★ Q) ⊣⊢ ◇ P ★ ◇ Q.
-Proof.
-  rewrite /uPred_except_last. apply (anti_symm _).
+Lemma except_0_idemp P : ◇ ◇ P ⊢ ◇ P.
+Proof. rewrite /uPred_except_0; auto. Qed.
+
+Lemma except_0_True : ◇ True ⊣⊢ True.
+Proof. rewrite /uPred_except_0. apply (anti_symm _); auto. Qed.
+Lemma except_0_or P Q : ◇ (P ∨ Q) ⊣⊢ ◇ P ∨ ◇ Q.
+Proof. rewrite /uPred_except_0. apply (anti_symm _); auto. Qed.
+Lemma except_0_and P Q : ◇ (P ∧ Q) ⊣⊢ ◇ P ∧ ◇ Q.
+Proof. by rewrite /uPred_except_0 or_and_l. Qed.
+Lemma except_0_sep P Q : ◇ (P ★ Q) ⊣⊢ ◇ P ★ ◇ Q.
+Proof.
+  rewrite /uPred_except_0. apply (anti_symm _).
   - apply or_elim; last by auto.
     by rewrite -!or_intro_l -always_pure -always_later -always_sep_dup'.
   - rewrite sep_or_r sep_elim_l sep_or_l; auto.
 Qed.
-Lemma except_last_forall {A} (Φ : A → uPred M) : ◇ (∀ a, Φ a) ⊢ ∀ a, ◇ Φ a.
+Lemma except_0_forall {A} (Φ : A → uPred M) : ◇ (∀ a, Φ a) ⊢ ∀ a, ◇ Φ a.
 Proof. apply forall_intro=> a. by rewrite (forall_elim a). Qed.
-Lemma except_last_exist {A} (Φ : A → uPred M) : (∃ a, ◇ Φ a) ⊢ ◇ ∃ a, Φ a.
+Lemma except_0_exist {A} (Φ : A → uPred M) : (∃ a, ◇ Φ a) ⊢ ◇ ∃ a, Φ a.
 Proof. apply exist_elim=> a. by rewrite (exist_intro a). Qed.
-Lemma except_last_later P : ◇ ▷ P ⊢ ▷ P.
-Proof. by rewrite /uPred_except_last -later_or False_or. Qed.
-Lemma except_last_always P : ◇ □ P ⊣⊢ □ ◇ P.
-Proof. by rewrite /uPred_except_last always_or always_later always_pure. Qed.
-Lemma except_last_always_if p P : ◇ □?p P ⊣⊢ □?p ◇ P.
-Proof. destruct p; simpl; auto using except_last_always. Qed.
-Lemma except_last_frame_l P Q : P ★ ◇ Q ⊢ ◇ (P ★ Q).
-Proof. by rewrite {1}(except_last_intro P) except_last_sep. Qed.
-Lemma except_last_frame_r P Q : ◇ P ★ Q ⊢ ◇ (P ★ Q).
-Proof. by rewrite {1}(except_last_intro Q) except_last_sep. Qed.
+Lemma except_0_later P : ◇ ▷ P ⊢ ▷ P.
+Proof. by rewrite /uPred_except_0 -later_or False_or. Qed.
+Lemma except_0_always P : ◇ □ P ⊣⊢ □ ◇ P.
+Proof. by rewrite /uPred_except_0 always_or always_later always_pure. Qed.
+Lemma except_0_always_if p P : ◇ □?p P ⊣⊢ □?p ◇ P.
+Proof. destruct p; simpl; auto using except_0_always. Qed.
+Lemma except_0_frame_l P Q : P ★ ◇ Q ⊢ ◇ (P ★ Q).
+Proof. by rewrite {1}(except_0_intro P) except_0_sep. Qed.
+Lemma except_0_frame_r P Q : ◇ P ★ Q ⊢ ◇ (P ★ Q).
+Proof. by rewrite {1}(except_0_intro Q) except_0_sep. Qed.
 
 (* Own and valid derived *)
 Lemma always_ownM (a : M) : Persistent a → □ uPred_ownM a ⊣⊢ uPred_ownM a.
@@ -628,9 +628,9 @@ Proof.
   intros; rewrite (bupd_ownM_updateP _ (y =)); last by apply cmra_update_updateP.
   by apply bupd_mono, exist_elim=> y'; apply pure_elim_l=> ->.
 Qed.
-Lemma except_last_bupd P : ◇ (|==> P) ⊢ (|==> ◇ P).
+Lemma except_0_bupd P : ◇ (|==> P) ⊢ (|==> ◇ P).
 Proof.
-  rewrite /uPred_except_last. apply or_elim; auto using bupd_mono.
+  rewrite /uPred_except_0. apply or_elim; auto using bupd_mono.
   by rewrite -bupd_intro -or_intro_l.
 Qed.
 
@@ -643,25 +643,25 @@ Global Instance valid_timeless {A : cmraT} `{CMRADiscrete A} (a : A) :
   TimelessP (✓ a : uPred M)%I.
 Proof. rewrite /TimelessP !discrete_valid. apply (timelessP _). Qed.
 Global Instance and_timeless P Q: TimelessP P → TimelessP Q → TimelessP (P ∧ Q).
-Proof. intros; rewrite /TimelessP except_last_and later_and; auto. Qed.
+Proof. intros; rewrite /TimelessP except_0_and later_and; auto. Qed.
 Global Instance or_timeless P Q : TimelessP P → TimelessP Q → TimelessP (P ∨ Q).
-Proof. intros; rewrite /TimelessP except_last_or later_or; auto. Qed.
+Proof. intros; rewrite /TimelessP except_0_or later_or; auto. Qed.
 Global Instance impl_timeless P Q : TimelessP Q → TimelessP (P → Q).
 Proof.
   rewrite /TimelessP=> HQ. rewrite later_false_excluded_middle.
   apply or_mono, impl_intro_l; first done.
   rewrite -{2}(löb Q); apply impl_intro_l.
-  rewrite HQ /uPred_except_last !and_or_r. apply or_elim; last auto.
+  rewrite HQ /uPred_except_0 !and_or_r. apply or_elim; last auto.
   by rewrite assoc (comm _ _ P) -assoc !impl_elim_r.
 Qed.
 Global Instance sep_timeless P Q: TimelessP P → TimelessP Q → TimelessP (P ★ Q).
-Proof. intros; rewrite /TimelessP except_last_sep later_sep; auto. Qed.
+Proof. intros; rewrite /TimelessP except_0_sep later_sep; auto. Qed.
 Global Instance wand_timeless P Q : TimelessP Q → TimelessP (P -★ Q).
 Proof.
   rewrite /TimelessP=> HQ. rewrite later_false_excluded_middle.
   apply or_mono, wand_intro_l; first done.
   rewrite -{2}(löb Q); apply impl_intro_l.
-  rewrite HQ /uPred_except_last !and_or_r. apply or_elim; last auto.
+  rewrite HQ /uPred_except_0 !and_or_r. apply or_elim; last auto.
   rewrite -(always_pure) -always_later always_and_sep_l'.
   by rewrite assoc (comm _ _ P) -assoc -always_and_sep_l' impl_elim_r wand_elim_r.
 Qed.
@@ -671,18 +671,18 @@ Proof.
   rewrite /TimelessP=> HQ. rewrite later_false_excluded_middle.
   apply or_mono; first done. apply forall_intro=> x.
   rewrite -(löb (Ψ x)); apply impl_intro_l.
-  rewrite HQ /uPred_except_last !and_or_r. apply or_elim; last auto.
+  rewrite HQ /uPred_except_0 !and_or_r. apply or_elim; last auto.
   by rewrite impl_elim_r (forall_elim x).
 Qed.
 Global Instance exist_timeless {A} (Ψ : A → uPred M) :
   (∀ x, TimelessP (Ψ x)) → TimelessP (∃ x, Ψ x).
 Proof.
   rewrite /TimelessP=> ?. rewrite later_exist_false. apply or_elim.
-  - rewrite /uPred_except_last; auto.
+  - rewrite /uPred_except_0; auto.
   - apply exist_elim=> x. rewrite -(exist_intro x); auto.
 Qed.
 Global Instance always_timeless P : TimelessP P → TimelessP (□ P).
-Proof. intros; rewrite /TimelessP except_last_always -always_later; auto. Qed.
+Proof. intros; rewrite /TimelessP except_0_always -always_later; auto. Qed.
 Global Instance always_if_timeless p P : TimelessP P → TimelessP (□?p P).
 Proof. destruct p; apply _. Qed.
 Global Instance eq_timeless {A : cofeT} (a b : A) :
@@ -691,8 +691,8 @@ Proof. intros. rewrite /TimelessP !timeless_eq. apply (timelessP _). Qed.
 Global Instance ownM_timeless (a : M) : Timeless a → TimelessP (uPred_ownM a).
 Proof.
   intros ?. rewrite /TimelessP later_ownM. apply exist_elim=> b.
-  rewrite (timelessP (a≡b)) (except_last_intro (uPred_ownM b)) -except_last_and.
-  apply except_last_mono. rewrite eq_sym.
+  rewrite (timelessP (a≡b)) (except_0_intro (uPred_ownM b)) -except_0_and.
+  apply except_0_mono. rewrite eq_sym.
   apply (eq_rewrite b a (uPred_ownM)); first apply _; auto.
 Qed.
 
diff --git a/program_logic/fancy_updates.v b/program_logic/fancy_updates.v
index 7d5a78443584e531f64707c83fc634d3b64fc324..14f8e54f791cab14f9239f6695a4ef5bc4f88e67 100644
--- a/program_logic/fancy_updates.v
+++ b/program_logic/fancy_updates.v
@@ -52,11 +52,11 @@ Lemma fupd_intro_mask E1 E2 P : E2 ⊆ E1 → P ⊢ |={E1,E2}=> |={E2,E1}=> P.
 Proof.
   intros (E1''&->&?)%subseteq_disjoint_union_L.
   rewrite fupd_eq /fupd_def ownE_op //. iIntros "H ($ & $ & HE) !==>".
-  iApply except_last_intro. iIntros "[$ $] !==>" . iApply except_last_intro.
+  iApply except_0_intro. iIntros "[$ $] !==>" . iApply except_0_intro.
   by iFrame.
 Qed.
 
-Lemma except_last_fupd E1 E2 P : ◇ (|={E1,E2}=> P) ={E1,E2}=★ P.
+Lemma except_0_fupd E1 E2 P : ◇ (|={E1,E2}=> P) ={E1,E2}=★ P.
 Proof.
   rewrite fupd_eq. iIntros "H [Hw HE]". iTimeless "H". iApply "H"; by iFrame.
 Qed.
@@ -64,7 +64,7 @@ Qed.
 Lemma bupd_fupd E P : (|==> P) ={E}=★ P.
 Proof.
   rewrite fupd_eq /fupd_def. iIntros "H [$ $]"; iUpd "H".
-  iUpdIntro. by iApply except_last_intro.
+  iUpdIntro. by iApply except_0_intro.
 Qed.
 
 Lemma fupd_mono E1 E2 P Q : (P ⊢ Q) → (|={E1,E2}=> P) ={E1,E2}=★ Q.
@@ -85,7 +85,7 @@ Proof.
   intros. rewrite fupd_eq /fupd_def ownE_op //. iIntros "Hvs (Hw & HE1 &HEf)".
   iUpd ("Hvs" with "[Hw HE1]") as ">($ & HE2 & HP)"; first by iFrame.
   iDestruct (ownE_op' with "[HE2 HEf]") as "[? $]"; first by iFrame.
-  iUpdIntro; iApply except_last_intro. by iApply "HP".
+  iUpdIntro; iApply except_0_intro. by iApply "HP".
 Qed.
 
 Lemma fupd_frame_r E1 E2 P Q : (|={E1,E2}=> P) ★ Q ={E1,E2}=★ P ★ Q.
@@ -102,8 +102,8 @@ Lemma fupd_intro E P : P ={E}=★ P.
 Proof. iIntros "HP". by iApply bupd_fupd. Qed.
 Lemma fupd_intro_mask' E1 E2 : E2 ⊆ E1 → True ⊢ |={E1,E2}=> |={E2,E1}=> True.
 Proof. exact: fupd_intro_mask. Qed.
-Lemma fupd_except_last E1 E2 P : (|={E1,E2}=> ◇ P) ={E1,E2}=★ P.
-Proof. by rewrite {1}(fupd_intro E2 P) except_last_fupd fupd_trans. Qed.
+Lemma fupd_except_0 E1 E2 P : (|={E1,E2}=> ◇ P) ={E1,E2}=★ P.
+Proof. by rewrite {1}(fupd_intro E2 P) except_0_fupd fupd_trans. Qed.
 
 Lemma fupd_frame_l E1 E2 P Q : (P ★ |={E1,E2}=> Q) ={E1,E2}=★ P ★ Q.
 Proof. rewrite !(comm _ P); apply fupd_frame_r. Qed.
@@ -180,8 +180,8 @@ Section proofmode_classes.
     Frame R P Q → Frame R (|={E1,E2}=> P) (|={E1,E2}=> Q).
   Proof. rewrite /Frame=><-. by rewrite fupd_frame_l. Qed.
 
-  Global Instance is_except_last_fupd E1 E2 P : IsExceptLast (|={E1,E2}=> P).
-  Proof. by rewrite /IsExceptLast except_last_fupd. Qed.
+  Global Instance is_except_0_fupd E1 E2 P : IsExcept0 (|={E1,E2}=> P).
+  Proof. by rewrite /IsExcept0 except_0_fupd. Qed.
 
   Global Instance from_upd_fupd E P : FromUpd (|={E}=> P) P.
   Proof. by rewrite /FromUpd -bupd_fupd. Qed.
diff --git a/program_logic/invariants.v b/program_logic/invariants.v
index 0a5bda89a793cb14c6ce7b7df439e2cae9ec29e7..9f76aaf775956adf6cde10b5458bbdb5214091da 100644
--- a/program_logic/invariants.v
+++ b/program_logic/invariants.v
@@ -39,7 +39,7 @@ Proof.
     eapply nclose_infinite, (difference_finite_inv _ _), Hfin.
     apply of_gset_finite.
   - by iFrame.
-  - rewrite /uPred_except_last; eauto.
+  - rewrite /uPred_except_0; eauto.
 Qed.
 
 Lemma inv_open E N P :
@@ -49,9 +49,9 @@ Proof.
   iDestruct "Hi" as % ?%elem_of_subseteq_singleton.
   rewrite {1 4}(union_difference_L (nclose N) E) // ownE_op; last set_solver.
   rewrite {1 5}(union_difference_L {[ i ]} (nclose N)) // ownE_op; last set_solver.
-  iIntros "(Hw & [HE $] & $)"; iUpdIntro; iApply except_last_intro.
+  iIntros "(Hw & [HE $] & $)"; iUpdIntro; iApply except_0_intro.
   iDestruct (ownI_open i P with "[Hw HE]") as "($ & $ & HD)"; first by iFrame.
-  iIntros "HP [Hw $] !==>"; iApply except_last_intro. iApply ownI_close; by iFrame.
+  iIntros "HP [Hw $] !==>"; iApply except_0_intro. iApply ownI_close; by iFrame.
 Qed.
 
 Lemma inv_open_timeless E N P `{!TimelessP P} :
diff --git a/program_logic/weakestpre.v b/program_logic/weakestpre.v
index e38b71ea66e2c87eddde95f63215508a541ebbc4..2bdd6f6583d5e5d798ee28c87901a0faacfaf60d 100644
--- a/program_logic/weakestpre.v
+++ b/program_logic/weakestpre.v
@@ -222,8 +222,8 @@ Section proofmode_classes.
     (∀ v, Frame R (Φ v) (Ψ v)) → Frame R (WP e @ E {{ Φ }}) (WP e @ E {{ Ψ }}).
   Proof. rewrite /Frame=> HR. rewrite wp_frame_l. apply wp_mono, HR. Qed.
 
-  Global Instance is_except_last_wp E e Φ : IsExceptLast (WP e @ E {{ Φ }}).
-  Proof. by rewrite /IsExceptLast -{2}fupd_wp -except_last_fupd -fupd_intro. Qed.
+  Global Instance is_except_0_wp E e Φ : IsExcept0 (WP e @ E {{ Φ }}).
+  Proof. by rewrite /IsExcept0 -{2}fupd_wp -except_0_fupd -fupd_intro. Qed.
 
   Global Instance elim_upd_bupd_wp E e P Φ :
     ElimUpd (|==> P) P (WP e @ E {{ Φ }}) (WP e @ E {{ Φ }}).
diff --git a/proofmode/class_instances.v b/proofmode/class_instances.v
index 7dc421a0e2e50cc3a196a4ac352add992de6d670..19f5d49cd38eeb5d47a87cc95601682bd1ca06b2 100644
--- a/proofmode/class_instances.v
+++ b/proofmode/class_instances.v
@@ -298,17 +298,17 @@ Proof.
   rewrite /Frame /MakeLater /IntoLater=>-> <- <-. by rewrite later_sep.
 Qed.
 
-Class MakeExceptLast (P Q : uPred M) := make_except_last : ◇ P ⊣⊢ Q.
-Global Instance make_except_last_True : MakeExceptLast True True.
-Proof. by rewrite /MakeExceptLast except_last_True. Qed.
-Global Instance make_except_last_default P : MakeExceptLast P (â—‡ P) | 100.
+Class MakeExcept0 (P Q : uPred M) := make_except_0 : ◇ P ⊣⊢ Q.
+Global Instance make_except_0_True : MakeExcept0 True True.
+Proof. by rewrite /MakeExcept0 except_0_True. Qed.
+Global Instance make_except_0_default P : MakeExcept0 P (â—‡ P) | 100.
 Proof. done. Qed.
 
-Global Instance frame_except_last R P Q Q' :
-  Frame R P Q → MakeExceptLast Q Q' → Frame R (◇ P) Q'.
+Global Instance frame_except_0 R P Q Q' :
+  Frame R P Q → MakeExcept0 Q Q' → Frame R (◇ P) Q'.
 Proof.
-  rewrite /Frame /MakeExceptLast=><- <-.
-  by rewrite except_last_sep -(except_last_intro R).
+  rewrite /Frame /MakeExcept0=><- <-.
+  by rewrite except_0_sep -(except_0_intro R).
 Qed.
 
 Global Instance frame_exist {A} R (Φ Ψ : A → uPred M) :
@@ -357,21 +357,21 @@ Global Instance into_exist_always {A} P (Φ : A → uPred M) :
   IntoExist P Φ → IntoExist (□ P) (λ a, □ (Φ a))%I.
 Proof. rewrite /IntoExist=> HP. by rewrite HP always_exist. Qed.
 
-(* IntoExceptLast *)
-Global Instance into_except_last_except_last P : IntoExceptLast (â—‡ P) P.
+(* IntoExcept0 *)
+Global Instance into_except_0_except_0 P : IntoExcept0 (â—‡ P) P.
 Proof. done. Qed.
-Global Instance into_except_last_timeless P : TimelessP P → IntoExceptLast (▷ P) P.
+Global Instance into_except_0_timeless P : TimelessP P → IntoExcept0 (▷ P) P.
 Proof. done. Qed.
 
-(* IsExceptLast *)
-Global Instance is_except_last_except_last P : IsExceptLast (â—‡ P).
-Proof. by rewrite /IsExceptLast except_last_idemp. Qed.
-Global Instance is_except_last_later P : IsExceptLast (â–· P).
-Proof. by rewrite /IsExceptLast except_last_later. Qed.
-Global Instance is_except_last_bupd P : IsExceptLast P → IsExceptLast (|==> P).
+(* IsExcept0 *)
+Global Instance is_except_0_except_0 P : IsExcept0 (â—‡ P).
+Proof. by rewrite /IsExcept0 except_0_idemp. Qed.
+Global Instance is_except_0_later P : IsExcept0 (â–· P).
+Proof. by rewrite /IsExcept0 except_0_later. Qed.
+Global Instance is_except_0_bupd P : IsExcept0 P → IsExcept0 (|==> P).
 Proof.
-  rewrite /IsExceptLast=> HP.
-  by rewrite -{2}HP -(except_last_idemp P) -except_last_bupd -(except_last_intro P).
+  rewrite /IsExcept0=> HP.
+  by rewrite -{2}HP -(except_0_idemp P) -except_0_bupd -(except_0_intro P).
 Qed.
 
 (* FromUpd *)
diff --git a/proofmode/classes.v b/proofmode/classes.v
index 3c3316bf206b7c6dc7ed883138e3cdaee9ab7931..fae732c160a9d9ff2f2f55455f6e88130b1ccad4 100644
--- a/proofmode/classes.v
+++ b/proofmode/classes.v
@@ -62,11 +62,11 @@ Class IntoExist {A} (P : uPred M) (Φ : A → uPred M) :=
   into_exist : P ⊢ ∃ x, Φ x.
 Global Arguments into_exist {_} _ _ {_}.
 
-Class IntoExceptLast (P Q : uPred M) := into_except_last : P ⊢ ◇ Q.
-Global Arguments into_except_last : clear implicits.
+Class IntoExcept0 (P Q : uPred M) := into_except_0 : P ⊢ ◇ Q.
+Global Arguments into_except_0 : clear implicits.
 
-Class IsExceptLast (Q : uPred M) := is_except_last : ◇ Q ⊢ Q.
-Global Arguments is_except_last : clear implicits.
+Class IsExcept0 (Q : uPred M) := is_except_0 : ◇ Q ⊢ Q.
+Global Arguments is_except_0 : clear implicits.
 
 Class FromUpd (P Q : uPred M) := from_upd : (|==> Q) ⊢ P.
 Global Arguments from_upd : clear implicits.
diff --git a/proofmode/coq_tactics.v b/proofmode/coq_tactics.v
index 30a1dfd38c26e5a25c74bd19b08bd2271755947c..a3bc5266817a0a149ecc47bc2258fb941efa86d9 100644
--- a/proofmode/coq_tactics.v
+++ b/proofmode/coq_tactics.v
@@ -446,14 +446,14 @@ Proof.
 Qed.
 
 Lemma tac_timeless Δ Δ' i p P P' Q :
-  IsExceptLast Q →
-  envs_lookup i Δ = Some (p, P) → IntoExceptLast P P' →
+  IsExcept0 Q →
+  envs_lookup i Δ = Some (p, P) → IntoExcept0 P P' →
   envs_simple_replace i p (Esnoc Enil i P') Δ = Some Δ' →
   (Δ' ⊢ Q) → Δ ⊢ Q.
 Proof.
   intros ???? HQ. rewrite envs_simple_replace_sound //; simpl.
-  rewrite right_id HQ -{2}(is_except_last Q).
-  by rewrite (into_except_last P) -except_last_always_if except_last_frame_r wand_elim_r.
+  rewrite right_id HQ -{2}(is_except_0 Q).
+  by rewrite (into_except_0 P) -except_0_always_if except_0_frame_r wand_elim_r.
 Qed.
 
 (** * Always *)
diff --git a/proofmode/tactics.v b/proofmode/tactics.v
index 06b6e95e91eb99e519976e11cd569f6330225a2b..047d9bb86cfc4102e5802252a5b8fe969d8c1124 100644
--- a/proofmode/tactics.v
+++ b/proofmode/tactics.v
@@ -612,10 +612,10 @@ Tactic Notation "iNext":=
 
 Tactic Notation "iTimeless" constr(H) :=
   eapply tac_timeless with _ H _ _ _;
-    [let Q := match goal with |- IsExceptLast ?Q => Q end in
+    [let Q := match goal with |- IsExcept0 ?Q => Q end in
      apply _ || fail "iTimeless: cannot remove later when goal is" Q
     |env_cbv; reflexivity || fail "iTimeless:" H "not found"
-    |let P := match goal with |- IntoExceptLast ?P _ => P end in
+    |let P := match goal with |- IntoExcept0 ?P _ => P end in
      apply _ || fail "iTimeless: cannot turn" P "into â—‡"
     |env_cbv; reflexivity|].