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stdpp
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95cee475
Commit
95cee475
authored
Nov 18, 2016
by
Robbert Krebbers
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More big_opMS lemmas.
parent
d5646054
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theories/gmultiset.v
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theories/gmultiset.v
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95cee475
...
...
@@ -157,6 +157,14 @@ Proof.
rewrite
multiplicity_difference
,
multiplicity_empty
;
omega
.
Qed
.
(* Order stuff *)
Lemma
gmultiset_elem_of_subseteq
x
X
:
x
∈
X
→
{[
x
]}
⊆
X
.
Proof
.
rewrite
elem_of_multiplicity
.
intros
Hx
y
;
destruct
(
decide
(
x
=
y
))
as
[->|].
-
rewrite
multiplicity_singleton
;
omega
.
-
rewrite
multiplicity_singleton_ne
by
done
;
omega
.
Qed
.
(* Properties of the elements operation *)
Lemma
gmultiset_elements_empty
:
elements
(
∅
:
gmultiset
A
)
=
[].
Proof
.
...
...
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