Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
C
coqstdpp
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
0
Issues
0
List
Boards
Labels
Service Desk
Milestones
Merge Requests
0
Merge Requests
0
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
Incidents
Environments
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Snippets
Snippets
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
David Swasey
coqstdpp
Commits
7a5e6ea4
Commit
7a5e6ea4
authored
Nov 23, 2016
by
Robbert Krebbers
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Make some arguments explicit that could not be infered.
parent
28344922
Changes
2
Hide whitespace changes
Inline
Sidebyside
Showing
2 changed files
with
10 additions
and
12 deletions
+10
12
theories/fin_collections.v
theories/fin_collections.v
+5
5
theories/list.v
theories/list.v
+5
7
No files found.
theories/fin_collections.v
View file @
7a5e6ea4
...
...
@@ 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
:
...
...
theories/list.v
View file @
7a5e6ea4
...
...
@@ 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
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a 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