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Iris
Iris
Commits
b95c0bc7
Commit
b95c0bc7
authored
Jul 02, 2016
by
Robbert Krebbers
Browse files
Add lemma pure_iff.
parent
65296d1a
Pipeline
#1888
passed with stage
Changes
1
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1
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Inline
Side-by-side
algebra/upred.v
View file @
b95c0bc7
...
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@@ -564,6 +564,8 @@ Proof. intros ->; apply iff_refl. Qed.
Lemma
pure_mono
φ
1
φ
2
:
(
φ
1
→
φ
2
)
→
■
φ
1
⊢
■
φ
2
.
Proof
.
intros
;
apply
pure_elim
with
φ
1
;
eauto
using
pure_intro
.
Qed
.
Lemma
pure_iff
φ
1
φ
2
:
(
φ
1
↔
φ
2
)
→
■
φ
1
⊣
⊢
■
φ
2
.
Proof
.
intros
[??]
;
apply
(
anti_symm
_
)
;
auto
using
pure_mono
.
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'
.
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