Show the compatibility lemma for the derived parallel composition

F_mu_ref_conc/examples/par.v

+From iris.proofmode Require Import tactics.
+From iris.algebra Require Import auth.
+From iris.base_logic Require Import lib.auth.
+From iris_logrel.F_mu_ref_conc Require Export examples.lock.
+From iris_logrel.F_mu_ref_conc Require Import tactics rel_tactics soundness_binary relational_properties.
+From iris.program_logic Require Import adequacy.
+
+From iris_logrel.F_mu_ref_conc Require Import hax.
+
+Definition par : val := λ: "e1" "e2",
+  let: "x1" := ref InjL #() in
+  Fork ("x1" <- InjR ("e1" #()));;
+  let: "x2" := "e2" #() in
+  let: "f" := rec: "f" <> := case: !"x1" of
+                              InjL => λ: <>, "f" #()
+                            | InjR => λ: "v", "v"
+                            end
+  in ("f" #(), "x2").
+
+Lemma par_type Γ τ1 τ2 :
+  typed Γ par
+        (TArrow (TArrow TUnit τ1) (TArrow (TArrow TUnit τ2)
+            (TProd τ1 τ2))).
+Proof.    
+  unfold par. unlock.
+  eauto 40 with typeable.
+Qed.
+
+Hint Resolve par_type : typeable.
+
+Section compatibility.
+  Context `{heapIG Σ, cfgSG Σ}.
+
+  Lemma bin_log_related_par Γ E e1 e2 e1' e2' τ1 τ2 :
+    ↑specN ⊆ E →
+    ↑logN ⊆ E →
+    {E,E;Γ} ⊨ e1 ≤log≤ e1' : TArrow TUnit τ1 -∗
+    {E,E;Γ} ⊨ e2 ≤log≤ e2' : TArrow TUnit τ2 -∗
+    {E,E;Γ} ⊨ par e1 e2 ≤log≤ par e1' e2' : TProd τ1 τ2.
+  Proof.
+    iIntros (??) "He1 He2".
+    iApply (bin_log_related_app with "[He1] He2").
+    iApply (bin_log_related_app with "[] He1").
+    iApply binary_fundamental_masked; eauto with typeable.
+  Qed.
+End compatibility.

_CoqProject

@@ -24,6 +24,7 @@ F_mu_ref_conc/notation.v
 F_mu_ref_conc/examples/lock.v
 F_mu_ref_conc/examples/counter.v
 F_mu_ref_conc/examples/lateearlychoice.v
+F_mu_ref_conc/examples/par.v
 #F_mu_ref_conc/examples/stack/stack_rules.v
 #F_mu_ref_conc/examples/stack/CG_stack.v
 #F_mu_ref_conc/examples/stack/FG_stack.v