Uniform syntax for selecting hypotheses.

Used in iRevert, iClear, iFrame, and for generalizing the IH in
iInduction and iLöb.

ProofMode.md

@@ -23,13 +23,12 @@ Context management
 - `iIntros (x1 ... xn) "ipat1 ... ipatn"` : introduce universal quantifiers
   using Coq introduction patterns `x1 ... xn` and implications/wands using proof
   mode introduction patterns `ipat1 ... ipatn`.
-- `iClear (x1 ... xn) "H1 ... Hn"` : clear the hypothesis `H1 ... Hn` as well as
-  the Coq level hypotheses/variables `x1 ... xn`. The symbol `★` can be used to
-  clear entire spatial context.
-- `iRevert (x1 ... xn) "H1 ... Hn"` : revert the proof mode hypotheses
-  `H1 ... Hn` into wands, as well as the Coq level hypotheses/variables
-  `x1 ... xn` into universal quantifiers. The symbol `★` can be used to revert
-  the entire spatial context.
+- `iClear (x1 ... xn) "selpat"` : clear the hypotheses given by the selection
+  pattern `selpat` and the Coq level hypotheses/variables `x1 ... xn`.
+- `iRevert (x1 ... xn) "selpat"` : revert the hypotheses given by the selection
+  pattern `selpat` into wands, and the Coq level hypotheses/variables
+  `x1 ... xn` into universal quantifiers. Persistent hypotheses are wrapped into
+  the always modality.
 - `iRename "H1" into "H2"` : rename the hypothesis `H1` into `H2`.
 - `iSpecialize pm_trm` : instantiate universal quantifiers and eliminate
   implications/wands of a hypothesis `pm_trm`. See proof mode terms below.
@@ -83,9 +82,9 @@ Elimination of logical connectives
 Separating logic specific tactics
 ---------------------------------
 
-- `iFrame (t1 .. tn) "H0 ... Hn"` : cancel the Coq terms (or Coq hypotheses)
-  `t1 ... tn` and Iris hypotheses `H0 ... Hn` in the goal. Apart from
-  hypotheses, the following symbols can be used:
+- `iFrame (t1 .. tn) "selpat"` : cancel the Coq terms (or Coq hypotheses)
+  `t1 ... tn` and Iris hypotheses given by `selpat` in the goal. The constructs
+  of the selection pattern have the following meaning:
 
   + `%` : repeatedly frame hypotheses from the Coq context.
   + `#` : repeatedly frame hypotheses from the persistent context.
@@ -102,16 +101,19 @@ Separating logic specific tactics
 The later modality
 ------------------
 - `iNext` : introduce a later by stripping laters from all hypotheses.
-- `iLöb as "IH" forall (x1 ... xn)` : perform Löb induction while generalizing
-  over the Coq level variables `x1 ... xn` and the entire spatial context.
+- `iLöb as "IH" forall (x1 ... xn)` : perform Löb induction by generating a
+  hypothesis `IH : ▷ goal`. The tactic generalizes over the Coq level variables
+  `x1 ... xn`, the hypotheses given by the selection pattern `selpat`, and the
+  spatial context.
 
 Induction
 ---------
-- `iInduction x as cpat "IH" forall (x1 ... xn)` : perform induction on the Coq
-  term `x`. The Coq introduction pattern is used to name the introduced
+- `iInduction x as cpat "IH" forall (x1 ... xn) "selpat"` : perform induction on
+  the Coq term `x`. The Coq introduction pattern is used to name the introduced
   variables. The induction hypotheses are inserted into the persistent context
   and given fresh names prefixed `IH`. The tactic generalizes over the Coq level
-  variables `x1 ... xn` and the entire spatial context.
+  variables `x1 ... xn`, the hypotheses given by the selection pattern `selpat`,
+  and the spatial context.
 
 Rewriting
 ---------
@@ -141,14 +143,26 @@ Miscellaneous
   existential quantifiers, implications and wand, always and later modalities,
   primitive view shifts, and pure connectives.
 
+Selection patterns
+==================
+
+Selection patterns are used to select hypotheses in the tactics `iRevert`,
+`iClear`, `iFrame`, `iLöb` and `iInduction`. The proof mode supports the
+following _selection patterns_:
+
+- `H` : select the hypothesis named `H`.
+- `%` : select the entire pure/Coq context.
+- `#` : select the entire persistent context.
+- `★` : select the entire spatial context.
+
 Introduction patterns
 =====================
 
 Introduction patterns are used to perform introductions and eliminations of
 multiple connectives on the fly. The proof mode supports the following
-introduction patterns:
+_introduction patterns_:
 
-- `H` : create a hypothesis named H.
+- `H` : create a hypothesis named `H`.
 - `?` : create an anonymous hypothesis.
 - `_` : remove the hypothesis.
 - `$` : frame the hypothesis in the goal.
@@ -197,9 +211,9 @@ Specialization patterns
 =======================
 
 Since we are reasoning in a spatial logic, when eliminating a lemma or
-hypotheses of type ``P_0 -★ ... -★ P_n -★ R`` one has to specify how the
+hypothesis of type ``P_0 -★ ... -★ P_n -★ R``, one has to specify how the
 hypotheses are split between the premises. The proof mode supports the following
-so called specification patterns to express this splitting:
+_specification patterns_ to express splitting of hypotheses:
 
 - `H` : use the hypothesis `H` (it should match the premise exactly). If `H` is
   spatial, it will be consumed.

_CoqProject

@@ -120,6 +120,7 @@ proofmode/pviewshifts.v
 proofmode/environments.v
 proofmode/intro_patterns.v
 proofmode/spec_patterns.v
+proofmode/sel_patterns.v
 proofmode/tactics.v
 proofmode/notation.v
 proofmode/invariants.v

program_logic/counter_examples.v

@@ -152,7 +152,7 @@ Module inv. Section inv.
     iDestruct (finished_dup with "Hf") as "[Hf Hf']".
     iApply pvs_intro. iSplitL "Hf'"; first by eauto.
     (* Step 2: Open the Q-invariant. *)
-    iClear "HiP". clear i. iDestruct "HsQ" as (i) "HiQ".
+    iClear (i) "HiP ". iDestruct "HsQ" as (i) "HiQ".
     iApply (inv_open' i). iSplit; first done.
     iIntros "[HaQ | [_ #HQ]]".
     { iExFalso. iApply finished_not_start. by iFrame. }

proofmode/coq_tactics.v

@@ -82,6 +82,9 @@ Definition env_spatial_is_nil {M} (Δ : envs M) :=
 Definition envs_clear_spatial {M} (Δ : envs M) : envs M :=
   Envs (env_persistent Δ) Enil.
 
+Definition envs_clear_persistent {M} (Δ : envs M) : envs M :=
+  Envs Enil (env_spatial Δ).
+
 Fixpoint envs_split_go {M}
     (js : list string) (Δ1 Δ2 : envs M) : option (envs M * envs M) :=
   match js with
@@ -272,12 +275,6 @@ Proof.
   destruct Hwf; constructor; simpl; auto using Enil_wf.
 Qed.
 
-Lemma env_fold_wand Γ Q : env_fold uPred_wand Q Γ ⊣⊢ ([★] Γ -★ Q).
-Proof.
-  revert Q; induction Γ as [|Γ IH i P]=> Q /=; [by rewrite wand_True|].
-  by rewrite IH wand_curry (comm uPred_sep).
-Qed.
-
 Lemma env_spatial_is_nil_persistent Δ :
   env_spatial_is_nil Δ = true → PersistentP Δ.
 Proof. intros; destruct Δ as [? []]; simplify_eq/=; apply _. Qed.
@@ -385,9 +382,6 @@ Qed.
 Lemma tac_clear Δ Δ' i p P Q :
   envs_lookup_delete i Δ = Some (p,P,Δ') → (Δ' ⊢ Q) → Δ ⊢ Q.
 Proof. intros. by rewrite envs_lookup_delete_sound // sep_elim_r. Qed.
-Lemma tac_clear_spatial Δ Δ' Q :
-  envs_clear_spatial Δ = Δ' → (Δ' ⊢ Q) → Δ ⊢ Q.
-Proof. intros <- ?. by rewrite envs_clear_spatial_sound // sep_elim_l. Qed.
 
 (** * False *)
 Lemma tac_ex_falso Δ Q : (Δ ⊢ False) → Δ ⊢ Q.
@@ -612,12 +606,6 @@ Proof.
   - by rewrite HQ wand_elim_r.
 Qed.
 
-Lemma tac_revert_spatial Δ Q :
-  (envs_clear_spatial Δ ⊢ env_fold uPred_wand Q (env_spatial Δ)) → Δ ⊢ Q.
-Proof.
-  intros HΔ. by rewrite envs_clear_spatial_sound HΔ env_fold_wand wand_elim_l.
-Qed.
-
 Lemma tac_revert_ih Δ P Q :
   env_spatial_is_nil Δ = true →
   (of_envs Δ ⊢ P) →

proofmode/environments.v

@@ -38,12 +38,6 @@ Instance: Params (@env_to_list) 1.
 Fixpoint env_dom {A} (Γ : env A) : list string :=
   match Γ with Enil => [] | Esnoc Γ i _ => i :: env_dom Γ end.
 
-Fixpoint env_fold {A B} (f : B → A → A) (x : A) (Γ : env B) : A :=
-  match Γ with
-  | Enil => x
-  | Esnoc Γ _ y => env_fold f (f y x) Γ
-  end.
-
 Fixpoint env_app {A} (Γapp : env A) (Γ : env A) : option (env A) :=
   match Γapp with
   | Enil => Some Γ

proofmode/sel_patterns.v

+From iris.prelude Require Export strings.
+
+Inductive sel_pat :=
+  | SelPure
+  | SelPersistent
+  | SelSpatial
+  | SelName : string → sel_pat.
+
+Fixpoint sel_pat_pure (ps : list sel_pat) : bool :=
+  match ps with
+  | [] => false
+  | SelPure :: ps => true
+  | _ :: ps => sel_pat_pure ps
+  end.
+
+Module sel_pat.
+Fixpoint cons_name (kn : string) (k : list sel_pat) : list sel_pat :=
+  match kn with "" => k | _ => SelName (string_rev kn) :: k end.
+
+Fixpoint parse_go (s : string) (k : list sel_pat) (kn : string) : list sel_pat :=
+  match s with
+  | "" => rev (cons_name kn k)
+  | String " " s => parse_go s (cons_name kn k) ""
+  | String "%" s => parse_go s (SelPure :: cons_name kn k) ""
+  | String "#" s => parse_go s (SelPersistent :: cons_name kn k) ""
+  | String (Ascii.Ascii false true false false false true true true) (* unicode ★ *)
+      (String (Ascii.Ascii false false false true true false false true)
+      (String (Ascii.Ascii true false true false false false false true) s)) =>
+     parse_go s (SelSpatial :: cons_name kn k) ""
+  | String a s => parse_go s k (String a kn)
+  end.
+Definition parse (s : string) : list sel_pat := parse_go s [] "".
+
+Ltac parse s :=
+  lazymatch type of s with
+  | list sel_pat => s
+  | list string => eval vm_compute in (SelName <$> s)
+  | string => eval vm_compute in (parse s)
+  end.
+End sel_pat.

proofmode/tactics.v

-From iris.proofmode Require Import coq_tactics intro_patterns spec_patterns.
+From iris.proofmode Require Import coq_tactics.
+From iris.proofmode Require Import intro_patterns spec_patterns sel_patterns.
 From iris.algebra Require Export upred.
 From iris.proofmode Require Export classes notation.
 From iris.proofmode Require Import class_instances.
 From iris.prelude Require Import stringmap hlist.
 
 Declare Reduction env_cbv := cbv [
-  env_lookup env_fold env_lookup_delete env_delete env_app env_replace
+  env_lookup env_lookup_delete env_delete env_app env_replace env_dom
   decide (* operational classes *)
   sumbool_rec sumbool_rect (* sumbool *)
   bool_eq_dec bool_rec bool_rect bool_dec eqb andb (* bool *)
   assci_eq_dec ascii_to_digits Ascii.ascii_dec Ascii.ascii_rec Ascii.ascii_rect
   string_eq_dec string_rec string_rect (* strings *)
-  env_persistent env_spatial env_spatial_is_nil
+  env_persistent env_spatial env_spatial_is_nil envs_dom
   envs_lookup envs_lookup_delete envs_delete envs_snoc envs_app
-    envs_simple_replace envs_replace envs_split envs_clear_spatial
+    envs_simple_replace envs_replace envs_split
+    envs_clear_spatial envs_clear_persistent
     envs_split_go envs_split].
 Ltac env_cbv :=
   match goal with |- ?u => let v := eval env_cbv in u in change v end.
@@ -33,7 +35,7 @@ Ltac iFresh := iFresh' "~".
 
 Tactic Notation "iTypeOf" constr(H) tactic(tac):=
   let Δ := match goal with |- of_envs ?Δ ⊢ _ => Δ end in
-  match eval env_cbv in (envs_lookup H Δ) with
+  lazymatch eval env_cbv in (envs_lookup H Δ) with
   | Some (?p,?P) => tac p P
   end.
 
@@ -56,16 +58,45 @@ Tactic Notation "iRename" constr(H1) "into" constr(H2) :=
     [env_cbv; reflexivity || fail "iRename:" H1 "not found"
     |env_cbv; reflexivity || fail "iRename:" H2 "not fresh"|].
 
+Local Inductive esel_pat :=
+  | ESelPure
+  | ESelName : bool → string → esel_pat.
+
+Ltac iElaborateSelPat pat tac :=
+  let rec go pat Δ Hs :=
+    lazymatch pat with
+    | [] => let Hs' := eval cbv in Hs in tac Hs'
+    | SelPure :: ?pat => go pat Δ (ESelPure :: Hs)
+    | SelPersistent :: ?pat =>
+       let Hs' := eval env_cbv in (env_dom (env_persistent Δ)) in
+       let Δ' := eval env_cbv in (envs_clear_persistent Δ) in
+       go pat Δ' ((ESelName true <$> Hs') ++ Hs)
+    | SelSpatial :: ?pat =>
+       let Hs' := eval env_cbv in (env_dom (env_spatial Δ)) in
+       let Δ' := eval env_cbv in (envs_clear_spatial Δ) in
+       go pat Δ' ((ESelName false <$> Hs') ++ Hs)
+    | SelName ?H :: ?pat =>
+       lazymatch eval env_cbv in (envs_lookup_delete H Δ) with
+       | Some (?p,_,?Δ') => go pat Δ' (ESelName p H :: Hs)
+       | None => fail "iElaborateSelPat:" H "not found"
+       end
+    end in
+  lazymatch goal with
+  | |- of_envs ?Δ ⊢ _ =>
+    let pat := sel_pat.parse pat in go pat Δ (@nil esel_pat)
+  end.
+
 Tactic Notation "iClear" constr(Hs) :=
   let rec go Hs :=
     lazymatch Hs with
     | [] => idtac
-    | "★" :: ?Hs => eapply tac_clear_spatial; [env_cbv; reflexivity|go Hs]
-    | ?H :: ?Hs =>
+    | ESelPure :: ?Hs => clear; go Hs
+    | ESelName _ ?H :: ?Hs =>
        eapply tac_clear with _ H _ _; (* (i:=H) *)
          [env_cbv; reflexivity || fail "iClear:" H "not found"|go Hs]
     end in
-  let Hs := words Hs in go Hs.
+  iElaborateSelPat Hs go.
+
 Tactic Notation "iClear" "(" ident_list(xs) ")" constr(Hs) :=
   iClear Hs; clear xs.
 
@@ -192,12 +223,12 @@ Tactic Notation "iFrame" constr(Hs) :=
   let rec go Hs :=
     match Hs with
     | [] => idtac
-    | "%" :: ?Hs => iFrameAnyPure; go Hs
-    | "#" :: ?Hs => iFrameAnyPersistent; go Hs
-    | "★" :: ?Hs => iFrameAnySpatial; go Hs
-    | ?H :: ?Hs => iFrameHyp H; go Hs
+    | SelPure :: ?Hs => iFrameAnyPure; go Hs
+    | SelPersistent :: ?Hs => iFrameAnyPersistent; go Hs
+    | SelSpatial :: ?Hs => iFrameAnySpatial; go Hs
+    | SelName ?H :: ?Hs => iFrameHyp H; go Hs
     end
-  in let Hs := words Hs in go Hs.
+  in let Hs := sel_pat.parse Hs in go Hs.
 Tactic Notation "iFrame" "(" constr(t1) ")" constr(Hs) :=
   iFramePure t1; iFrame Hs.
 Tactic Notation "iFrame" "(" constr(t1) constr(t2) ")" constr(Hs) :=
@@ -403,17 +434,18 @@ Local Tactic Notation "iForallRevert" ident(x) :=
   end || fail "iRevert: cannot revert" x.
 
 Tactic Notation "iRevert" constr(Hs) :=
-  let rec go H2s :=
-    match H2s with
+  let rec go Hs :=
+    lazymatch Hs with
     | [] => idtac
-    | "★" :: ?H2s => go H2s; eapply tac_revert_spatial; env_cbv
-    | ?H2 :: ?H2s =>
-       go H2s;
-       eapply tac_revert with _ H2 _ _; (* (i:=H2) *)
-         [env_cbv; reflexivity || fail "iRevert:" H2 "not found"
-         |env_cbv]
+    | ESelPure :: ?Hs =>
+       repeat match goal with x : _ |- _ => revert x end;
+       go Hs
+    | ESelName _ ?H :: ?Hs =>
+       eapply tac_revert with _ H _ _; (* (i:=H2) *)
+         [env_cbv; reflexivity || fail "iRevert:" H "not found"
+         |env_cbv; go Hs]
     end in
-  let Hs := words Hs in go Hs.
+  iElaborateSelPat Hs go.
 
 Tactic Notation "iRevert" "(" ident(x1) ")" :=
   iForallRevert x1.
@@ -793,37 +825,71 @@ Tactic Notation "iIntros" "(" simple_intropattern(x1) simple_intropattern(x2)
     ")" constr(p) :=
   iIntros ( x1 x2 x3 x4 x5 x6 x7 x8 ); iIntros p.
 
+(* Used for generalization in iInduction and iLöb *)
+Tactic Notation "iRevertIntros" constr(Hs) "with" tactic(tac) :=
+  let rec go Hs :=
+    lazymatch Hs with
+    | [] => tac
+    | ESelPure :: ?Hs => fail "iRevertIntros: % not supported"
+    | ESelName ?p ?H :: ?Hs =>
+       iRevert H; go Hs;
+       let H' :=
+         match p with true => constr:[IAlwaysElim (IName H)] | false => H end in
+       iIntros H'
+    end in
+  iElaborateSelPat Hs go.
+
+Tactic Notation "iRevertIntros" "(" ident(x1) ")" constr(Hs) "with" tactic(tac):=
+  iRevertIntros Hs with (iRevert (x1); tac; iIntros (x1)).
+Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ")" constr(Hs)
+    "with" tactic(tac):=
+  iRevertIntros Hs with (iRevert (x1 x2); tac; iIntros (x1 x2)).
+Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ")" constr(Hs)
+    "with" tactic(tac):=
+  iRevertIntros Hs with (iRevert (x1 x2 x3); tac; iIntros (x1 x2 x3)).
+Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ident(x4) ")"
+    constr(Hs) "with" tactic(tac):=
+  iRevertIntros Hs with (iRevert (x1 x2 x3 x4); tac; iIntros (x1 x2 x3 x4)).
+Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ident(x4)
+    ident(x5) ")" constr(Hs) "with" tactic(tac):=
+  iRevertIntros Hs with (iRevert (x1 x2 x3 x4 x5); tac; iIntros (x1 x2 x3 x4 x5)).
+Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ident(x4)
+    ident(x5) ident(x6) ")" constr(Hs) "with" tactic(tac):=
+  iRevertIntros Hs with (iRevert (x1 x2 x3 x4 x5 x6);
+    tac; iIntros (x1 x2 x3 x4 x5 x6)).
+Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ident(x4)
+    ident(x5) ident(x6) ident(x7) ")" constr(Hs) "with" tactic(tac):=
+  iRevertIntros Hs with (iRevert (x1 x2 x3 x4 x5 x6 x7);
+    tac; iIntros (x1 x2 x3 x4 x5 x6 x7)).
+Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ident(x4)
+    ident(x5) ident(x6) ident(x7) ident(x8) ")" constr(Hs) "with" tactic(tac):=
+  iRevertIntros Hs with (iRevert (x1 x2 x3 x4 x5 x6 x7 x8);
+    tac; iIntros (x1 x2 x3 x4 x5 x6 x7 x8)).
+
 Tactic Notation "iRevertIntros" "with" tactic(tac) :=
-  match goal with
-  | |- of_envs ?Δ ⊢ _ =>
-     let Hs := eval cbv in (reverse (env_dom (env_spatial Δ))) in
-     iRevert ["★"]; tac; iIntros Hs
-  end.
+  iRevertIntros "" with tac.
 Tactic Notation "iRevertIntros" "(" ident(x1) ")" "with" tactic(tac):=
-  iRevertIntros with (iRevert (x1); tac; iIntros (x1)).
+  iRevertIntros (x1) "" with tac.
 Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ")" "with" tactic(tac):=
-  iRevertIntros with (iRevert (x1 x2); tac; iIntros (x1 x2)).
+  iRevertIntros (x1 x2) "" with tac.
 Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ")"
     "with" tactic(tac):=
-  iRevertIntros with (iRevert (x1 x2 x3); tac; iIntros (x1 x2 x3)).
+  iRevertIntros (x1 x2 x3) "" with tac.
 Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ident(x4) ")"
     "with" tactic(tac):=
-  iRevertIntros with (iRevert (x1 x2 x3 x4); tac; iIntros (x1 x2 x3 x4)).
+  iRevertIntros (x1 x2 x3 x4) "" with tac.
 Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ident(x4)
     ident(x5) ")" "with" tactic(tac):=
-  iRevertIntros with (iRevert (x1 x2 x3 x4 x5); tac; iIntros (x1 x2 x3 x4 x5)).
+  iRevertIntros (x1 x2 x3 x4 x5) "" with tac.
 Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ident(x4)
     ident(x5) ident(x6) ")" "with" tactic(tac):=
-  iRevertIntros with (iRevert (x1 x2 x3 x4 x5 x6);
-    tac; iIntros (x1 x2 x3 x4 x5 x6)).
+  iRevertIntros (x1 x2 x3 x4 x5 x6) "" with tac.
 Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ident(x4)
     ident(x5) ident(x6) ident(x7) ")" "with" tactic(tac):=
-  iRevertIntros with (iRevert (x1 x2 x3 x4 x5 x6 x7);
-    tac; iIntros (x1 x2 x3 x4 x5 x6 x7)).
+  iRevertIntros (x1 x2 x3 x4 x5 x6 x7) "" with tac.
 Tactic Notation "iRevertIntros" "(" ident(x1) ident(x2) ident(x3) ident(x4)
     ident(x5) ident(x6) ident(x7) ident(x8) ")" "with" tactic(tac):=
-  iRevertIntros with (iRevert (x1 x2 x3 x4 x5 x6 x7 x8);
-    tac; iIntros (x1 x2 x3 x4 x5 x6 x7 x8)).
+  iRevertIntros (x1 x2 x3 x4 x5 x6 x7 x8) "" with tac.
 
 (** * Destruct tactic *)
 Tactic Notation "iDestructCore" open_constr(lem) "as" constr(p) tactic(tac) :=
@@ -893,7 +959,7 @@ Tactic Notation "iInductionCore" constr(x)
     lazymatch goal with
     | H : coq_tactics.of_envs _ ⊢ _ |- _ =>
        eapply tac_revert_ih;
-         [env_cbv; reflexivity
+         [reflexivity || fail "iInduction: persistent context not empty"
          |apply H|];
        clear H; fix_ihs;
        let IH' := iFresh' IH in iIntros [IAlwaysElim (IName IH')]
@@ -902,64 +968,122 @@ Tactic Notation "iInductionCore" constr(x)
   induction x as pat; fix_ihs.
 
 Tactic Notation "iInduction" constr(x) "as" simple_intropattern(pat) constr(IH) :=
-  iRevertIntros with (iInductionCore x as pat IH).
+  iRevertIntros "★" with (iInductionCore x as pat IH).
 Tactic Notation "iInduction" constr(x) "as" simple_intropattern(pat) constr(IH)
     "forall" "(" ident(x1) ")" :=
-  iRevertIntros(x1) with (iInductionCore x as pat IH).
+  iRevertIntros(x1) "★" with (iInductionCore x as pat IH).
 Tactic Notation "iInduction" constr(x) "as" simple_intropattern(pat) constr(IH)