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Rodolphe Lepigre
Iris
Commits
b99023e7
Commit
b99023e7
authored
Mar 24, 2017
by
Robbert Krebbers
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Derive monoid_right_id.
parent
7fd895dd
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theories/algebra/monoid.v
theories/algebra/monoid.v
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theories/algebra/monoid.v
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b99023e7
...
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@@ -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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