Not all [Qp]s are [frac]s, so make the notation only parsing.

algebra/frac.v

@@ -2,10 +2,9 @@ From Coq.QArith Require Import Qcanon.
 From iris.algebra Require Export cmra.
 From iris.algebra Require Import upred.
 
-Notation frac := Qp.
+Notation frac := Qp (only parsing).
 
 Section frac.
-
 Canonical Structure fracC := leibnizC frac.
 
 Instance frac_valid : Valid frac := λ x, (x ≤ 1)%Qc.
@@ -19,20 +18,16 @@ Proof.
   rewrite -{1}(Qcplus_0_r x) -Qcplus_le_mono_l; auto using Qclt_le_weak.
 Qed.
 Canonical Structure fracR := discreteR frac frac_ra_mixin.
-
 End frac.
 
 (** Internalized properties *)
-Lemma frac_equivI {M} (x y : frac) :
-  x ≡ y ⊣⊢ (x = y : uPred M).
+Lemma frac_equivI {M} (x y : frac) : x ≡ y ⊣⊢ (x = y : uPred M).
 Proof. by uPred.unseal. Qed.
-Lemma frac_validI {M} (x : frac) :
-  ✓ x ⊣⊢ (■ (x ≤ 1)%Qc : uPred M).
+Lemma frac_validI {M} (x : frac) : ✓ x ⊣⊢ (■ (x ≤ 1)%Qc : uPred M).
 Proof. by uPred.unseal. Qed.
 
 (** Exclusive *)
 Global Instance frac_full_exclusive : Exclusive 1%Qp.
 Proof.
-  move => ? /Qcle_not_lt[]; simpl in *.
-  by rewrite -{1}(Qcplus_0_r 1) -Qcplus_lt_mono_l.
+  move=> y /Qcle_not_lt [] /=. by rewrite -{1}(Qcplus_0_r 1) -Qcplus_lt_mono_l.
 Qed.