Commit b2ba69ee authored by Robbert Krebbers's avatar Robbert Krebbers
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Prove that included on frac corresponds to the order on Qp.

Thanks to Aleš Bizjak.
parent 1270ae08
......@@ -10,6 +10,17 @@ Instance frac_valid : Valid frac := λ x, (x ≤ 1)%Qc.
Instance frac_pcore : PCore frac := λ _, None.
Instance frac_op : Op frac := λ x y, (x + y)%Qp.
Lemma frac_included (x y : frac) : x y (x < y)%Qc.
- intros [z ->%leibniz_equiv]; simpl.
rewrite -{1}(Qcplus_0_r x). apply Qcplus_lt_mono_l, Qp_prf.
- intros Hlt%Qclt_minus_iff. exists (mk_Qp (y - x) Hlt). apply Qp_eq; simpl.
by rewrite (Qcplus_comm y) Qcplus_assoc Qcplus_opp_r Qcplus_0_l.
Corollary frac_included_weak (x y : frac) : x y (x y)%Qc.
Proof. intros ?%frac_included. auto using Qclt_le_weak. Qed.
Definition frac_ra_mixin : RAMixin frac.
split; try apply _; try done.
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