Commit aa942ca8 authored by Robbert Krebbers's avatar Robbert Krebbers

Misc result about Qp.

parent 6916990f
......@@ -660,6 +660,21 @@ Proof.
- by rewrite (assoc_L _), (comm_L Qp_plus a').
Qed.
Lemma Qp_bounded_split (p r : Qp) : q1 q2 : Qp, (q1 r)%Qc p = (q1 + q2)%Qp.
Proof.
destruct (Qclt_le_dec r p) as [?|?].
- assert (0 < p - r)%Qc as Hpos.
{ apply (Qcplus_lt_mono_r _ _ r). rewrite <-Qcplus_assoc, (Qcplus_comm (-r)).
by rewrite Qcplus_opp_r, Qcplus_0_l, Qcplus_0_r. }
exists r, (mk_Qp _ Hpos); simpl; split; [done|].
apply Qp_eq; simpl. rewrite Qcplus_comm, <-Qcplus_assoc, (Qcplus_comm (-r)).
by rewrite Qcplus_opp_r, Qcplus_0_r.
- exists (p / 2)%Qp, (p / 2)%Qp; split.
+ trans p; [|done]. apply Qclt_le_weak, Qp_lt_sum.
exists (p / 2)%Qp. by rewrite Qp_div_2.
+ by rewrite Qp_div_2.
Qed.
Lemma Qp_not_plus_q_ge_1 (q: Qp): ¬ ((1 + q)%Qp 1%Qp)%Qc.
Proof.
intros Hle.
......
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