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b2ba69ee
Commit
b2ba69ee
authored
Oct 02, 2016
by
Robbert Krebbers
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Prove that included on frac corresponds to the order on Qp.
Thanks to Aleš Bizjak.
parent
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#2744
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algebra/frac.v
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b2ba69ee
...
...
@@ -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
.
Proof
.
split
.
-
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
.
Qed
.
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
.
Proof
.
split
;
try
apply
_;
try
done
.
...
...
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