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fce8b28c
Commit
fce8b28c
authored
Jun 01, 2016
by
Robbert Krebbers
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Simplify prod_leibniz.
parent
455b5b26
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#1257
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prelude/base.v
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fce8b28c
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@@ -466,10 +466,8 @@ Instance fst_proper `{Equiv A, Equiv B} : Proper ((≡) ==> (≡)) (@fst A B) :=
Instance
snd_proper
`
{
Equiv
A
,
Equiv
B
}
:
Proper
((
≡
)
==>
(
≡
))
(@
snd
A
B
)
:
=
_
.
Typeclasses
Opaque
prod_equiv
.
Instance
prod_leibniz
`
{
LeibnizEquiv
A
,
!
Equivalence
((
≡
)
:
relation
A
),
LeibnizEquiv
B
,
!
Equivalence
((
≡
)
:
relation
B
)}
:
LeibnizEquiv
(
A
*
B
).
Proof
.
intros
[]
[]
[]
;
fold_leibniz
;
simpl
;
congruence
.
Qed
.
Instance
prod_leibniz
`
{
LeibnizEquiv
A
,
LeibnizEquiv
B
}
:
LeibnizEquiv
(
A
*
B
).
Proof
.
intros
[??]
[??]
[??]
;
f_equal
;
apply
leibniz_equiv
;
auto
.
Qed
.
(** ** Sums *)
Definition
sum_map
{
A
A'
B
B'
}
(
f
:
A
→
A'
)
(
g
:
B
→
B'
)
(
xy
:
A
+
B
)
:
A'
+
B'
:
=
...
...
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