Define `iAssert` using `iSpecialize`.

This made the definition much simpler, and provides support for all
specialization patterns (although most are not very useful in
combination with `iAssert`).

theories/proofmode/coq_tactics.v

@@ -913,40 +913,12 @@ Proof.
   by rewrite -{1}persistently_idemp !affinely_persistently_elim impl_elim_r.
 Qed.
 
-Lemma tac_assert Δ Δ1 Δ2 Δ2' neg js j P P' Q :
-  AddModal P' P Q →
-  envs_split (if neg is true then Right else Left) js Δ = Some (Δ1,Δ2) →
-  envs_app false (Esnoc Enil j P) Δ2 = Some Δ2' →
-  envs_entails Δ1 P' → envs_entails Δ2' Q → envs_entails Δ Q.
-Proof.
-  rewrite envs_entails_eq=>??? HP HQ. rewrite envs_split_sound //.
-  rewrite (envs_app_singleton_sound Δ2) //; simpl. by rewrite HP HQ.
-Qed.
-
-Lemma tac_assert_persistent Δ Δ1 Δ2 Δ' neg js j P P' Q :
-  envs_split (if neg is true then Right else Left) js Δ = Some (Δ1,Δ2) →
-  Persistent P →
-  FromAffinely P' P →
-  envs_app false (Esnoc Enil j P') Δ = Some Δ' →
-  envs_entails Δ1 P → envs_entails Δ' Q → envs_entails Δ Q.
-Proof.
-  rewrite envs_entails_eq => ???? HP <-.
-  rewrite -(idemp bi_and (of_envs Δ)) {1}envs_split_sound //.
-  rewrite HP. rewrite (persistent_persistently_2 P) sep_elim_l.
-  rewrite persistently_and_affinely_sep_l -affinely_idemp.
-  rewrite affinely_persistently_elim from_affinely envs_app_singleton_sound //=.
-  by rewrite wand_elim_r.
-Qed.
-
-Lemma tac_assert_pure Δ Δ' j P P' φ Q :
-  FromPure true P φ →
-  FromAffinely P' P →
-  envs_app false (Esnoc Enil j P') Δ = Some Δ' →
-  φ → envs_entails Δ' Q → envs_entails Δ Q.
+Lemma tac_assert Δ Δ' j P Q :
+  envs_app true (Esnoc Enil j (P -∗ P)%I) Δ = Some Δ' →
+  envs_entails Δ' Q → envs_entails Δ Q.
 Proof.
-  rewrite envs_entails_eq => ???? <-. rewrite envs_app_singleton_sound //=.
-  rewrite -(from_affinely P') -(from_pure _ P) pure_True //.
-  by rewrite affinely_idemp affinely_True_emp affinely_emp emp_wand.
+  rewrite envs_entails_eq=> ? <-. rewrite (envs_app_singleton_sound Δ) //; simpl.
+  by rewrite -(entails_wand P) // affinely_persistently_emp emp_wand.
 Qed.
 
 Lemma tac_pose_proof Δ Δ' j P Q :
@@ -1244,7 +1216,7 @@ Lemma tac_next Δ Δ' n Q Q' :
   envs_entails Δ' Q' → envs_entails Δ Q.
 Proof.
   rewrite envs_entails_eq => ?? HQ.
-    by rewrite -(from_laterN n Q) into_laterN_env_sound HQ.
+  by rewrite -(from_laterN n Q) into_laterN_env_sound HQ.
 Qed.
 
 Lemma tac_löb Δ Δ' i Q :

theories/proofmode/tactics.v

@@ -1687,56 +1687,15 @@ only contains `#` or `%` patterns at the top-level, and [false] otherwise. *)
 Tactic Notation "iAssertCore" open_constr(Q)
     "with" constr(Hs) "as" constr(p) tactic(tac) :=
   iStartProof;
-  let p := intro_pat_persistent p in
+  let pats := spec_pat.parse Hs in
+  lazymatch pats with
+  | [_] => idtac
+  | _ => fail "iAssert: exactly one specialization pattern should be given"
+  end;
   let H := iFresh in
-  let Hs := spec_pat.parse Hs in
-  lazymatch Hs with
-  | [SPureGoal ?d] =>
-     eapply tac_assert_pure with _ H Q _ _;
-       [apply _ || fail "iAssert:" Q "not pure"
-       |apply _
-       |env_reflexivity
-       |done_if d (*goal*)
-       |tac H]
-  | [SGoal (SpecGoal GPersistent _ ?Hs_frame [] ?d)] =>
-     eapply tac_assert_persistent with _ _ _ true [] H Q _;
-       [env_reflexivity
-       |apply _ || fail "iAssert:" Q "not persistent"
-       |apply _
-       |env_reflexivity
-       |iFrame Hs_frame; done_if d (*goal*)
-       |tac H]
-  | [SGoal (SpecGoal GPersistent false ?Hs_frame _ ?d)] =>
-     fail "iAssert: cannot select hypotheses for persistent proposition"
-  | [SGoal (SpecGoal ?m ?lr ?Hs_frame ?Hs ?d)] =>
-     let Hs' := eval cbv in (if lr then Hs else Hs_frame ++ Hs) in
-     let p' := eval cbv in (match m with GModal => false | _ => p end) in
-     lazymatch p' with
-     | false =>
-       eapply tac_assert with _ _ _ lr Hs' H Q _;
-         [lazymatch m with
-          | GSpatial => apply add_modal_id
-          | GModal => apply _ || fail "iAssert: goal not a modality"
-          end
-         |env_reflexivity ||
-          let Hs' := iMissingHyps Hs' in
-          fail "iAssert: hypotheses" Hs' "not found"
-         |env_reflexivity
-         |iFrame Hs_frame; done_if d (*goal*)
-         |tac H]
-     | true =>
-       eapply tac_assert_persistent with _ _ _ lr Hs' H Q _;
-         [env_reflexivity ||
-          let Hs' := iMissingHyps Hs' in
-          fail "iAssert: hypotheses" Hs' "not found"
-         |apply _ || fail "iAssert:" Q "not persistent"
-         |apply _
-         |env_reflexivity
-         |done_if d (*goal*)
-         |tac H]
-     end
-  | ?pat => fail "iAssert: invalid pattern" pat
-  end.
+  eapply tac_assert with _ H Q;
+    [env_reflexivity
+    |iSpecializeCore H with hnil pats as p; [..|tac H]].
 
 Tactic Notation "iAssertCore" open_constr(Q) "as" constr(p) tactic(tac) :=
   let p := intro_pat_persistent p in