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stdpp
Commits
b9ff487e
Commit
b9ff487e
authored
9 years ago
by
Robbert Krebbers
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Use "clear -H" for set_solver.
Also, use "set_solver by tac" to specify a tactic.
parent
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theories/collections.v
+11
-12
11 additions, 12 deletions
theories/collections.v
with
11 additions
and
12 deletions
theories/collections.v
+
11
−
12
View file @
b9ff487e
...
...
@@ -253,19 +253,18 @@ Ltac set_unfold :=
(** Since [firstorder] fails or loops on very small goals generated by
[set_solver] already. We use the [naive_solver] tactic as a substitute.
This tactic either fails or proves the goal. *)
Tactic
Notation
"set_solver"
tactic3
(
tac
)
:=
Tactic
Notation
"set_solver"
"by"
tactic3
(
tac
)
:=
setoid_subst
;
decompose_empty
;
set_unfold
;
naive_solver
tac
.
Tactic
Notation
"set_solver"
"-"
hyp_list
(
Hs
)
"
/
"
tactic3
(
tac
)
:=
clear
Hs
;
set_solver
tac
.
Tactic
Notation
"set_solver"
"+"
hyp_list
(
Hs
)
"
/
"
tactic3
(
tac
)
:=
revert
Hs
;
clear
;
set_solver
tac
.
Tactic
Notation
"set_solver"
:=
set_solver
idtac
.
Tactic
Notation
"set_solver"
"-"
hyp_list
(
Hs
)
"
by
"
tactic3
(
tac
)
:=
clear
Hs
;
set_solver
by
tac
.
Tactic
Notation
"set_solver"
"+"
hyp_list
(
Hs
)
"
by
"
tactic3
(
tac
)
:=
clear
-
Hs
;
set_solver
by
tac
.
Tactic
Notation
"set_solver"
:=
set_solver
by
idtac
.
Tactic
Notation
"set_solver"
"-"
hyp_list
(
Hs
)
:=
clear
Hs
;
set_solver
.
Tactic
Notation
"set_solver"
"+"
hyp_list
(
Hs
)
:=
revert
Hs
;
clear
;
set_solver
.
Tactic
Notation
"set_solver"
"+"
hyp_list
(
Hs
)
:=
clear
-
Hs
;
set_solver
.
(** * More theorems *)
Section
collection
.
...
...
@@ -537,10 +536,10 @@ Section collection_monad.
Global
Instance
collection_fmap_mono
{
A
B
}
:
Proper
(
pointwise_relation
_
(
=
)
==>
(
⊆
)
==>
(
⊆
))
(
@
fmap
M
_
A
B
)
.
Proof
.
intros
f
g
?
X
Y
?;
set_solver
eauto
.
Qed
.
Proof
.
intros
f
g
?
X
Y
?;
set_solver
by
eauto
.
Qed
.
Global
Instance
collection_fmap_proper
{
A
B
}
:
Proper
(
pointwise_relation
_
(
=
)
==>
(
≡
)
==>
(
≡
))
(
@
fmap
M
_
A
B
)
.
Proof
.
intros
f
g
?
X
Y
[??];
split
;
set_solver
eauto
.
Qed
.
Proof
.
intros
f
g
?
X
Y
[??];
split
;
set_solver
by
eauto
.
Qed
.
Global
Instance
collection_bind_mono
{
A
B
}
:
Proper
(((
=
)
==>
(
⊆
))
==>
(
⊆
)
==>
(
⊆
))
(
@
mbind
M
_
A
B
)
.
Proof
.
unfold
respectful
;
intros
f
g
Hfg
X
Y
?;
set_solver
.
Qed
.
...
...
@@ -575,12 +574,12 @@ Section collection_monad.
l
∈
mapM
f
k
↔
Forall2
(
λ
x
y
,
x
∈
f
y
)
l
k
.
Proof
.
split
.
-
revert
l
.
induction
k
;
set_solver
eauto
.
-
revert
l
.
induction
k
;
set_solver
by
eauto
.
-
induction
1
;
set_solver
.
Qed
.
Lemma
collection_mapM_length
{
A
B
}
(
f
:
A
→
M
B
)
l
k
:
l
∈
mapM
f
k
→
length
l
=
length
k
.
Proof
.
revert
l
;
induction
k
;
set_solver
eauto
.
Qed
.
Proof
.
revert
l
;
induction
k
;
set_solver
by
eauto
.
Qed
.
Lemma
elem_of_mapM_fmap
{
A
B
}
(
f
:
A
→
B
)
(
g
:
B
→
M
A
)
l
k
:
Forall
(
λ
x
,
∀
y
,
y
∈
g
x
→
f
y
=
x
)
l
→
k
∈
mapM
g
l
→
fmap
f
k
=
l
.
Proof
.
...
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