Commit 2e98600d authored by Zhen Zhang's avatar Zhen Zhang
Browse files

Add lemmas about Qp and fraction

parent 5c27499c
......@@ -35,3 +35,6 @@ Global Instance frac_full_exclusive : Exclusive 1%Qp.
move=> y /Qcle_not_lt [] /=. by rewrite -{1}(Qcplus_0_r 1) -Qcplus_lt_mono_l.
Lemma invalid_plus_q: (q: Qp), ¬ (1 + q)%Qp.
Proof. intros q H. by apply (Qp_ge_1 q). Qed.
......@@ -566,3 +566,10 @@ Proof.
exists (mk_Qp (q2 - q1 / 2%Z) Hq2'). split; [by rewrite Qp_div_2|].
apply Qp_eq; simpl. ring.
Lemma Qp_ge_1 (q: Qp): ¬ ((1 + q)%Qp 1%Qp)%Qc.
intros Hle.
apply (Qcplus_le_mono_l q 0 1) in Hle.
apply Qcle_ngt in Hle. by destruct q.
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