Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
What's new
10
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
Open sidebar
Iris
Iris
Commits
f6664df5
Commit
f6664df5
authored
Feb 14, 2016
by
Robbert Krebbers
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Left and right mononicity properties for uPred_and and uPred_or.
parent
a8c1821a
Changes
1
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
8 additions
and
0 deletions
+8
-0
algebra/upred.v
algebra/upred.v
+8
-0
No files found.
algebra/upred.v
View file @
f6664df5
...
...
@@ -436,8 +436,16 @@ Lemma const_mono φ1 φ2 : (φ1 → φ2) → ■ φ1 ⊑ ■ φ2.
Proof
.
intros
;
apply
const_elim
with
φ
1
;
eauto
using
const_intro
.
Qed
.
Lemma
and_mono
P
P'
Q
Q'
:
P
⊑
Q
→
P'
⊑
Q'
→
(
P
∧
P'
)
⊑
(
Q
∧
Q'
).
Proof
.
auto
.
Qed
.
Lemma
and_mono_l
P
P'
Q
:
P
⊑
Q
→
(
P
∧
P'
)
⊑
(
Q
∧
P'
).
Proof
.
by
intros
;
apply
and_mono
.
Qed
.
Lemma
and_mono_r
P
P'
Q'
:
P'
⊑
Q'
→
(
P
∧
P'
)
⊑
(
P
∧
Q'
).
Proof
.
by
apply
and_mono
.
Qed
.
Lemma
or_mono
P
P'
Q
Q'
:
P
⊑
Q
→
P'
⊑
Q'
→
(
P
∨
P'
)
⊑
(
Q
∨
Q'
).
Proof
.
auto
.
Qed
.
Lemma
or_mono_l
P
P'
Q
:
P
⊑
Q
→
(
P
∨
P'
)
⊑
(
Q
∨
P'
).
Proof
.
by
intros
;
apply
or_mono
.
Qed
.
Lemma
or_mono_r
P
P'
Q'
:
P'
⊑
Q'
→
(
P
∨
P'
)
⊑
(
P
∨
Q'
).
Proof
.
by
apply
or_mono
.
Qed
.
Lemma
impl_mono
P
P'
Q
Q'
:
Q
⊑
P
→
P'
⊑
Q'
→
(
P
→
P'
)
⊑
(
Q
→
Q'
).
Proof
.
intros
HP
HQ'
;
apply
impl_intro_l
;
rewrite
-
HQ'
.
...
...
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