Revert "Some results about `frac_auth` by Danny and Ales."

These results turned out to be neither that useful nor canonical, and can easily
be derived from local updates.

This reverts commit 465dd9f4.

theories/algebra/frac_auth.v

@@ -105,17 +105,4 @@ Section frac_auth.
   Proof.
     intros. by apply auth_update, option_local_update, prod_local_update_2.
   Qed.
-
-  Lemma frac_auth_update_alloc q a b c :
-    (∀ n : nat, ✓{n} a → ✓{n} (c ⋅ a)) →
-    ●! a ⋅ ◯!{q} b ~~> ●! (c ⋅ a) ⋅ ◯!{q} (c ⋅ b).
-  Proof. intros ?. by apply frac_auth_update, op_local_update. Qed.
-
-  Lemma frac_auth_dealloc q a b c `{!Cancelable c} :
-    ●! (c ⋅ a) ⋅ ◯!{q} (c ⋅ b) ~~> ●! a ⋅ ◯!{q} b.
-  Proof.
-    apply frac_auth_update.
-    move=> n [x|] /= Hvalid Heq; split; eauto using cmra_validN_op_r.
-    eapply (cancelableN c); by rewrite ?assoc.
-  Qed.
 End frac_auth.