Skip to content
GitLab
Projects
Groups
Snippets
/
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
Menu
Open sidebar
George Pirlea
Iris
Commits
546ed060
Commit
546ed060
authored
Nov 23, 2016
by
Robbert Krebbers
Browse files
Make some arguments explicit that could not be infered.
parent
b81fb420
Changes
2
Hide whitespace changes
Inline
Sidebyside
prelude/fin_collections.v
View file @
546ed060
...
...
@@ 254,21 +254,21 @@ Proof. rewrite Forall_forall. by setoid_rewrite elem_of_elements. Qed.
Lemma
set_Exists_elements
P
X
:
set_Exists
P
X
↔
Exists
P
(
elements
X
).
Proof
.
rewrite
Exists_exists
.
by
setoid_rewrite
elem_of_elements
.
Qed
.
Lemma
set_Forall_Exists_dec
{
P
Q
:
A
→
Prop
}
(
dec
:
∀
x
,
{
P
x
}
+
{
Q
x
})
X
:
Lemma
set_Forall_Exists_dec
(
P
Q
:
A
→
Prop
)
(
dec
:
∀
x
,
{
P
x
}
+
{
Q
x
})
X
:
{
set_Forall
P
X
}
+
{
set_Exists
Q
X
}.
Proof
.
refine
(
cast_if
(
Forall_Exists_dec
dec
(
elements
X
)))
;
refine
(
cast_if
(
Forall_Exists_dec
P
Q
dec
(
elements
X
)))
;
[
by
apply
set_Forall_elements

by
apply
set_Exists_elements
].
Defined
.
Lemma
not_set_Forall_Exists
P
`
{
dec
:
∀
x
,
Decision
(
P
x
)}
X
:
¬
set_Forall
P
X
→
set_Exists
(
not
∘
P
)
X
.
Proof
.
intro
.
by
destruct
(
set_Forall_Exists_dec
dec
X
).
Qed
.
Proof
.
intro
.
by
destruct
(
set_Forall_Exists_dec
P
(
not
∘
P
)
dec
X
).
Qed
.
Lemma
not_set_Exists_Forall
P
`
{
dec
:
∀
x
,
Decision
(
P
x
)}
X
:
¬
set_Exists
P
X
→
set_Forall
(
not
∘
P
)
X
.
Proof
.
by
destruct
(
@
set_Forall_Exists_dec
(
not
∘
P
)
_
(
λ
x
,
swap_if
(
decide
(
P
x
)))
X
).
by
destruct
(
set_Forall_Exists_dec
(
not
∘
P
)
P
(
λ
x
,
swap_if
(
decide
(
P
x
)))
X
).
Qed
.
Global
Instance
set_Forall_dec
(
P
:
A
→
Prop
)
`
{
∀
x
,
Decision
(
P
x
)}
X
:
...
...
prelude/list.v
View file @
546ed060
...
...
@@ 2051,7 +2051,7 @@ Lemma list_subseteq_nil l : [] ⊆ l.
Proof
.
intros
x
.
by
rewrite
elem_of_nil
.
Qed
.
(** ** Properties of the [Forall] and [Exists] predicate *)
Lemma
Forall_Exists_dec
{
P
Q
:
A
→
Prop
}
(
dec
:
∀
x
,
{
P
x
}
+
{
Q
x
})
:
Lemma
Forall_Exists_dec
(
P
Q
:
A
→
Prop
)
(
dec
:
∀
x
,
{
P
x
}
+
{
Q
x
})
:
∀
l
,
{
Forall
P
l
}
+
{
Exists
Q
l
}.
Proof
.
refine
(
...
...
@@ 2232,21 +2232,19 @@ Section Forall_Exists.
Context
{
dec
:
∀
x
,
Decision
(
P
x
)}.
Lemma
not_Forall_Exists
l
:
¬
Forall
P
l
→
Exists
(
not
∘
P
)
l
.
Proof
.
intro
.
destruct
(
Forall_Exists_dec
dec
l
)
;
intuition
.
Qed
.
Proof
.
intro
.
by
destruct
(
Forall_Exists_dec
P
(
not
∘
P
)
dec
l
)
.
Qed
.
Lemma
not_Exists_Forall
l
:
¬
Exists
P
l
→
Forall
(
not
∘
P
)
l
.
Proof
.
(* TODO: Coq 8.6 needs type annotation here, Coq 8.5 did not.
Should we report this? *)
by
destruct
(@
Forall_Exists_dec
(
not
∘
P
)
_
by
destruct
(
Forall_Exists_dec
(
not
∘
P
)
P
(
λ
x
:
A
,
swap_if
(
decide
(
P
x
)))
l
).
Qed
.
Global
Instance
Forall_dec
l
:
Decision
(
Forall
P
l
)
:
=
match
Forall_Exists_dec
dec
l
with
match
Forall_Exists_dec
P
(
not
∘
P
)
dec
l
with

left
H
=>
left
H

right
H
=>
right
(
Exists_not_Forall
_
H
)
end
.
Global
Instance
Exists_dec
l
:
Decision
(
Exists
P
l
)
:
=
match
Forall_Exists_dec
(
λ
x
,
swap_if
(
decide
(
P
x
)))
l
with
match
Forall_Exists_dec
(
not
∘
P
)
P
(
λ
x
,
swap_if
(
decide
(
P
x
)))
l
with

left
H
=>
right
(
Forall_not_Exists
_
H
)

right
H
=>
left
H
end
.
...
...
Write
Preview
Supports
Markdown
0%
Try again
or
attach a new file
.
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment