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Joshua Yanovski
iris-coq
Commits
b99023e7
Commit
b99023e7
authored
Mar 24, 2017
by
Robbert Krebbers
Browse files
Derive monoid_right_id.
parent
7fd895dd
Changes
1
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Inline
Side-by-side
theories/algebra/monoid.v
View file @
b99023e7
...
...
@@ -23,10 +23,11 @@ Class Monoid {M : ofeT} (o : M → M → M) := {
monoid_assoc
:
Assoc
(
≡
)
o
;
monoid_comm
:
Comm
(
≡
)
o
;
monoid_left_id
:
LeftId
(
≡
)
monoid_unit
o
;
monoid_right_id
:
RightId
(
≡
)
monoid_unit
o
;
}
.
Lemma
monoid_proper
`
{
Monoid
M
o
}
:
Proper
((
≡
)
==>
(
≡
)
==>
(
≡
))
o
.
Proof
.
apply
ne_proper_2
,
monoid_ne
.
Qed
.
Lemma
monoid_right_id
`
{
Monoid
M
o
}
:
RightId
(
≡
)
monoid_unit
o
.
Proof
.
intros
x
.
etrans
;
[
apply
monoid_comm
|
apply
monoid_left_id
].
Qed
.
(
**
The
[
Homomorphism
]
classes
give
rise
to
generic
lemmas
about
big
operators
commuting
with
each
other
.
*
)
...
...
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