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Dan Frumin
iris-coq
Commits
175ae7e6
Commit
175ae7e6
authored
May 31, 2016
by
Robbert Krebbers
Browse files
Prove (P ≡ Q) ⊢ (P
↔
Q).
parent
5e384379
Changes
1
Hide whitespace changes
Inline
Side-by-side
algebra/upred.v
View file @
175ae7e6
...
...
@@ -683,6 +683,7 @@ Lemma const_elim_r φ Q R : (φ → Q ⊢ R) → (Q ∧ ■ φ) ⊢ R.
Proof
.
intros
;
apply
const_elim
with
φ
;
eauto
.
Qed
.
Lemma
const_equiv
(
φ
:
Prop
)
:
φ
→
(
■
φ
)
⊣⊢
True
.
Proof
.
intros
;
apply
(
anti_symm
_
);
auto
using
const_intro
.
Qed
.
Lemma
eq_refl
'
{
A
:
cofeT
}
(
a
:
A
)
P
:
P
⊢
(
a
≡
a
).
Proof
.
rewrite
(
True_intro
P
).
apply
eq_refl
.
Qed
.
Hint
Resolve
eq_refl
'
.
...
...
@@ -690,6 +691,10 @@ Lemma equiv_eq {A : cofeT} P (a b : A) : a ≡ b → P ⊢ (a ≡ b).
Proof
.
by
intros
->
.
Qed
.
Lemma
eq_sym
{
A
:
cofeT
}
(
a
b
:
A
)
:
(
a
≡
b
)
⊢
(
b
≡
a
).
Proof
.
apply
(
eq_rewrite
a
b
(
λ
b
,
b
≡
a
)
%
I
);
auto
.
solve_proper
.
Qed
.
Lemma
eq_iff
P
Q
:
(
P
≡
Q
)
⊢
(
P
↔
Q
).
Proof
.
apply
(
eq_rewrite
P
Q
(
λ
Q
,
P
↔
Q
))
%
I
;
first
solve_proper
;
auto
using
iff_refl
.
Qed
.
(
*
BI
connectives
*
)
Lemma
sep_mono
P
P
'
Q
Q
'
:
P
⊢
Q
→
P
'
⊢
Q
'
→
(
P
★
P
'
)
⊢
(
Q
★
Q
'
).
...
...
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