Finish a generative ADT example

From "State-Dependent Represenation Independence" by A. Ahmed, D. Dreyer, A. Rossberg.

theories/F_mu_ref_conc/rules.v

@@ -46,6 +46,15 @@ Section mapsto.
     by intros [_ ?%agree_op_invL'].
   Qed.
 
+  Lemma mapsto_half_combine l v1 v2 :
+    l ↦ᵢ{1/2} v1 -∗ l ↦ᵢ{1/2} v2 -∗ ⌜v1 = v2⌝ ∗ l ↦ᵢ v1.
+  Proof.
+    iIntros "Hl1 Hl2".
+    iDestruct (mapsto_agree with "Hl1 Hl2") as %?. simplify_eq.
+    iSplit; eauto.
+    iApply (fractional_half_2 with "Hl1 Hl2").
+  Qed.
+
 End mapsto.
 
 Section lang_rules.

theories/logrel/threadpool.v

 (* The threadpool RA *)
 From iris.algebra Require Import auth gmap agree list.
 From iris.base_logic Require Export gen_heap invariants fractional.
+From iris.proofmode Require Import tactics.
 From iris_logrel.F_mu_ref_conc Require Import lang.
 Import uPred.
 
@@ -141,4 +142,13 @@ Section mapsto.
     by intros [_ ?%agree_op_invL'].
   Qed.
 
+  Lemma mapsto_half_combine l v1 v2 :
+    l ↦ₛ{1/2} v1 -∗ l ↦ₛ{1/2} v2 -∗ ⌜v1 = v2⌝ ∗ l ↦ₛ v1.
+  Proof.
+    iIntros "Hl1 Hl2".
+    iDestruct (mapsto_agree with "Hl1 Hl2") as %?. simplify_eq.
+    iSplit; eauto.
+    iApply (fractional_half_2 with "Hl1 Hl2").
+  Qed.
+
 End mapsto.