The diff might be hard to read, because I had to change the order. The following
lemmas have been added:

```coq
Lemma view_auth_frac_op_validN n q1 q2 a1 a2 :
  ✓{n} (●V{q1} a1 ⋅ ●V{q2} a2)  ✓ (q1 + q2)%Qp ∧ a1 ≡{n}≡ a2 ∧ rel n a1 ε.
Lemma view_auth_op_validN n a1 a2 : ✓{n} (●V a1 ⋅ ●V a2)  False.

Lemma view_auth_frac_op_valid q1 q2 a1 a2 :
  ✓ (●V{q1} a1 ⋅ ●V{q2} a2)  ✓ (q1 + q2)%Qp ∧ a1 ≡ a2 ∧ ∀ n, rel n a1 ε.
Lemma view_auth_op_valid a1 a2 : ✓ (●V a1 ⋅ ●V a2)  False.

Lemma auth_auth_frac_op_validN n q1 q2 a1 a2 :
  ✓{n} (●{q1} a1 ⋅ ●{q2} a2)  ✓ (q1 + q2)%Qp ∧ a1 ≡{n}≡ a2 ∧ ✓{n} a1.
Lemma auth_auth_op_validN n a1 a2 : ✓{n} (● a1 ⋅ ● a2)  False.

Lemma auth_auth_frac_op_valid q1 q2 a1 a2 :
  ✓ (●{q1} a1 ⋅ ●{q2} a2)  ✓ (q1 + q2)%Qp ∧ a1 ≡ a2 ∧ ✓ a1.
Lemma auth_auth_op_valid a1 a2 : ✓ (● a1 ⋅ ● a2)  False.
```