Commit 41e81796 authored by Ralf Jung's avatar Ralf Jung
Browse files

remove _frac_ lemmas, the corresponding _dfrac_ lemmas are sufficient

parent 1503fb75
......@@ -40,9 +40,6 @@ Section mono_nat.
rewrite (comm _ ({dq2} _)) -!assoc (assoc _ ( _)).
by rewrite -core_id_dup (comm _ ( _)).
Qed.
Lemma mono_nat_auth_frac_op q1 q2 n :
MN{#(q1 + q2)} n MN{#q1} n MN{#q2} n.
Proof. by rewrite -mono_nat_auth_dfrac_op dfrac_op_own. Qed.
Lemma mono_nat_lb_op n1 n2 :
MN (n1 `max` n2) = MN n1 MN n2.
......@@ -79,9 +76,6 @@ Section mono_nat.
- intros [? ->]. rewrite -core_id_dup -auth_auth_dfrac_op.
by apply auth_both_dfrac_valid_discrete.
Qed.
Lemma mono_nat_auth_frac_op_valid q1 q2 n1 n2 :
(MN{#q1} n1 MN{#q2} n2) (q1 + q2 1)%Qp n1 = n2.
Proof. by apply mono_nat_auth_dfrac_op_valid. Qed.
Lemma mono_nat_auth_op_valid n1 n2 :
(MN n1 MN n2) False.
Proof. rewrite mono_nat_auth_dfrac_op_valid. naive_solver. Qed.
......
......@@ -53,7 +53,7 @@ Section mono_nat.
Global Instance mono_nat_auth_own_fractional γ n :
Fractional (λ q, mono_nat_auth_own γ q n).
Proof. unseal. intros p q. rewrite -own_op mono_nat_auth_frac_op //. Qed.
Proof. unseal. intros p q. rewrite -own_op -mono_nat_auth_dfrac_op //. Qed.
Global Instance mono_nat_auth_own_as_fractional γ q n :
AsFractional (mono_nat_auth_own γ q n) (λ q, mono_nat_auth_own γ q n) q.
Proof. split; [auto|apply _]. Qed.
......
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