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stdpp
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add size_difference
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Ralf Jung
requested to merge
ralf/size_difference
into
master
3 years ago
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e0ea5658
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3 years ago
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theories/fin_sets.v
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@@ -193,6 +193,17 @@ Proof.
rewrite
<-
union_difference
,
(
comm
(
∪
));
set_solver
.
Qed
.
Lemma
size_difference
X
Y
:
Y
⊆
X
→
size
(
X
∖
Y
)
=
size
X
-
size
Y
.
Proof
.
intros
.
rewrite
(
union_difference
Y
X
)
at
2
by
done
.
rewrite
size_union
by
set_solver
.
lia
.
Qed
.
Lemma
size_difference_alt
X
Y
:
size
(
X
∖
Y
)
=
size
X
-
size
(
X
∩
Y
)
.
Proof
.
intros
.
rewrite
<-
size_difference
by
set_solver
.
apply
set_size_proper
.
set_solver
.
Qed
.
Lemma
subseteq_size
X
Y
:
X
⊆
Y
→
size
X
≤
size
Y
.
Proof
.
intros
.
rewrite
(
union_difference
X
Y
),
size_union_alt
by
done
.
lia
.
Qed
.
Lemma
subset_size
X
Y
:
X
⊂
Y
→
size
X
<
size
Y
.
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