Generalize `det_head_step_pureexec`.

theories/heap_lang/lifting.v

@@ -87,7 +87,6 @@ Local Ltac solve_pureexec :=
   | H: IntoVal ?e _ |- _ => rewrite -(of_to_val e _ into_val); clear H
   | H: AsRec _ _ _ _ |- _ => rewrite H; clear H
   end;
-  apply hoist_pred_pureexec; intros; destruct_and?;
   apply det_head_step_pureexec; [ solve_exec_safe | solve_exec_puredet ].
 
 Global Instance pure_rec f x (erec e1 e2 : expr) (v2 : val)

theories/program_logic/ectx_language.v

@@ -151,16 +151,16 @@ Section ectx_language.
       econstructor; eauto.
   Qed.
 
-  Lemma det_head_step_pureexec e1 e2 :
-    (∀ σ, head_reducible e1 σ) →
-    (∀ σ1 e2' σ2 efs, head_step e1 σ1 e2' σ2 efs → σ1 = σ2 ∧ e2=e2' ∧ efs = []) →
-    PureExec True e1 e2.
+  Lemma det_head_step_pureexec (P : Prop) e1 e2 :
+    (∀ σ, P → head_reducible e1 σ) →
+    (∀ σ1 e2' σ2 efs,
+      P → head_step e1 σ1 e2' σ2 efs → σ1 = σ2 ∧ e2=e2' ∧ efs = []) →
+    PureExec P e1 e2.
   Proof.
     intros Hp1 Hp2. split.
-    - intros σ _. destruct (Hp1 σ) as (e2' & σ2 & efs & ?).
-      eexists e2', σ2, efs.
-      eapply (Ectx_step _ _ _ _ _ empty_ectx); eauto using fill_empty.
-    - intros σ1 e2' σ2 efs _ ?%head_reducible_prim_step; eauto.
+    - intros σ ?. destruct (Hp1 σ) as (e2' & σ2 & efs & ?); first done.
+      eexists e2', σ2, efs. by apply head_prim_step.
+    - intros σ1 e2' σ2 efs ? ?%head_reducible_prim_step; eauto.
   Qed.
 End ectx_language.