Commit f5082bd5 authored by Zhen Zhang's avatar Zhen Zhang

tweak the Qp lemmas

parent 1a18f2ff
......@@ -35,6 +35,3 @@ Global Instance frac_full_exclusive : Exclusive 1%Qp.
Proof.
move=> y /Qcle_not_lt [] /=. by rewrite -{1}(Qcplus_0_r 1) -Qcplus_lt_mono_l.
Qed.
Lemma invalid_plus_q: (q: Qp), ¬ (1 + q)%Qp.
Proof. intros q H. by apply (Qp_ge_1 q). Qed.
......@@ -567,9 +567,12 @@ Proof.
apply Qp_eq; simpl. ring.
Qed.
Lemma Qp_ge_1 (q: Qp): ¬ ((1 + q)%Qp 1%Qp)%Qc.
Lemma Qp_not_plus_q_ge_1 (q: Qp): ¬ ((1 + q)%Qp 1%Qp)%Qc.
Proof.
intros Hle.
apply (Qcplus_le_mono_l q 0 1) in Hle.
apply Qcle_ngt in Hle. by destruct q.
apply Qcle_ngt in Hle. apply Hle, Qp_prf.
Qed.
Lemma Qp_ge_0 (q: Qp): (0 q)%Qc.
Proof. apply Qclt_le_weak, Qp_prf. Qed.
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