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PierreMarie Pédrot
stdpp
Commits
f024eb62
Commit
f024eb62
authored
Feb 10, 2016
by
Ralf Jung
Browse files
remove some unused typeclasses and notation: EquivE and SubsetEqE
parent
1bef8f4a
Changes
1
Show whitespace changes
Inline
Sidebyside
theories/base.v
View file @
f024eb62
...
@@ 163,17 +163,6 @@ Notation "X ≢ Y":= (¬X ≡ Y) (at level 70, no associativity) : C_scope.
...
@@ 163,17 +163,6 @@ Notation "X ≢ Y":= (¬X ≡ Y) (at level 70, no associativity) : C_scope.
Notation
"( X ≢)"
:
=
(
λ
Y
,
X
≢
Y
)
(
only
parsing
)
:
C_scope
.
Notation
"( X ≢)"
:
=
(
λ
Y
,
X
≢
Y
)
(
only
parsing
)
:
C_scope
.
Notation
"(≢ X )"
:
=
(
λ
Y
,
Y
≢
X
)
(
only
parsing
)
:
C_scope
.
Notation
"(≢ X )"
:
=
(
λ
Y
,
Y
≢
X
)
(
only
parsing
)
:
C_scope
.
Class
EquivE
E
A
:
=
equivE
:
E
→
relation
A
.
Instance
:
Params
(@
equivE
)
4
.
Notation
"X ≡{ Γ } Y"
:
=
(
equivE
Γ
X
Y
)
(
at
level
70
,
format
"X ≡{ Γ } Y"
)
:
C_scope
.
Notation
"(≡{ Γ } )"
:
=
(
equivE
Γ
)
(
only
parsing
,
Γ
at
level
1
)
:
C_scope
.
Notation
"X ≡{ Γ1 , Γ2 , .. , Γ3 } Y"
:
=
(
equivE
(
pair
..
(
Γ
1
,
Γ
2
)
..
Γ
3
)
X
Y
)
(
at
level
70
,
format
"'[' X ≡{ Γ1 , Γ2 , .. , Γ3 } '/' Y ']'"
)
:
C_scope
.
Notation
"(≡{ Γ1 , Γ2 , .. , Γ3 } )"
:
=
(
equivE
(
pair
..
(
Γ
1
,
Γ
2
)
..
Γ
3
))
(
only
parsing
,
Γ
1
at
level
1
)
:
C_scope
.
(** The type class [LeibnizEquiv] collects setoid equalities that coincide
(** The type class [LeibnizEquiv] collects setoid equalities that coincide
with Leibniz equality. We provide the tactic [fold_leibniz] to transform such
with Leibniz equality. We provide the tactic [fold_leibniz] to transform such
setoid equalities into Leibniz equalities, and [unfold_leibniz] for the
setoid equalities into Leibniz equalities, and [unfold_leibniz] for the
...
@@ 211,8 +200,6 @@ equality. *)
...
@@ 211,8 +200,6 @@ equality. *)
Instance
equiv_default_relation
`
{
Equiv
A
}
:
DefaultRelation
(
≡
)

3
.
Instance
equiv_default_relation
`
{
Equiv
A
}
:
DefaultRelation
(
≡
)

3
.
Hint
Extern
0
(
?x
≡
?y
)
=>
reflexivity
.
Hint
Extern
0
(
?x
≡
?y
)
=>
reflexivity
.
Hint
Extern
0
(
_
≡
_
)
=>
symmetry
;
assumption
.
Hint
Extern
0
(
_
≡
_
)
=>
symmetry
;
assumption
.
Hint
Extern
0
(
?x
≡
{
_
}
?y
)
=>
reflexivity
.
Hint
Extern
0
(
_
≡
{
_
}
_
)
=>
symmetry
;
assumption
.
(** ** Operations on collections *)
(** ** Operations on collections *)
(** We define operational type classes for the traditional operations and
(** We define operational type classes for the traditional operations and
...
@@ 292,35 +279,6 @@ Hint Extern 0 (_ ⊆ _) => reflexivity.
...
@@ 292,35 +279,6 @@ Hint Extern 0 (_ ⊆ _) => reflexivity.
Hint
Extern
0
(
_
⊆
*
_
)
=>
reflexivity
.
Hint
Extern
0
(
_
⊆
*
_
)
=>
reflexivity
.
Hint
Extern
0
(
_
⊆
**
_
)
=>
reflexivity
.
Hint
Extern
0
(
_
⊆
**
_
)
=>
reflexivity
.
Class
SubsetEqE
E
A
:
=
subseteqE
:
E
→
relation
A
.
Instance
:
Params
(@
subseteqE
)
4
.
Notation
"X ⊆{ Γ } Y"
:
=
(
subseteqE
Γ
X
Y
)
(
at
level
70
,
format
"X ⊆{ Γ } Y"
)
:
C_scope
.
Notation
"(⊆{ Γ } )"
:
=
(
subseteqE
Γ
)
(
only
parsing
,
Γ
at
level
1
)
:
C_scope
.
Notation
"X ⊈{ Γ } Y"
:
=
(
¬
X
⊆
{
Γ
}
Y
)
(
at
level
70
,
format
"X ⊈{ Γ } Y"
)
:
C_scope
.
Notation
"(⊈{ Γ } )"
:
=
(
λ
X
Y
,
X
⊈
{
Γ
}
Y
)
(
only
parsing
,
Γ
at
level
1
)
:
C_scope
.
Notation
"Xs ⊆{ Γ }* Ys"
:
=
(
Forall2
(
⊆
{
Γ
})
Xs
Ys
)
(
at
level
70
,
format
"Xs ⊆{ Γ }* Ys"
)
:
C_scope
.
Notation
"(⊆{ Γ }* )"
:
=
(
Forall2
(
⊆
{
Γ
}))
(
only
parsing
,
Γ
at
level
1
)
:
C_scope
.
Notation
"X ⊆{ Γ1 , Γ2 , .. , Γ3 } Y"
:
=
(
subseteqE
(
pair
..
(
Γ
1
,
Γ
2
)
..
Γ
3
)
X
Y
)
(
at
level
70
,
format
"'[' X ⊆{ Γ1 , Γ2 , .. , Γ3 } '/' Y ']'"
)
:
C_scope
.
Notation
"(⊆{ Γ1 , Γ2 , .. , Γ3 } )"
:
=
(
subseteqE
(
pair
..
(
Γ
1
,
Γ
2
)
..
Γ
3
))
(
only
parsing
,
Γ
1
at
level
1
)
:
C_scope
.
Notation
"X ⊈{ Γ1 , Γ2 , .. , Γ3 } Y"
:
=
(
¬
X
⊆
{
pair
..
(
Γ
1
,
Γ
2
)
..
Γ
3
}
Y
)
(
at
level
70
,
format
"X ⊈{ Γ1 , Γ2 , .. , Γ3 } Y"
)
:
C_scope
.
Notation
"(⊈{ Γ1 , Γ2 , .. , Γ3 } )"
:
=
(
λ
X
Y
,
X
⊈
{
pair
..
(
Γ
1
,
Γ
2
)
..
Γ
3
}
Y
)
(
only
parsing
)
:
C_scope
.
Notation
"Xs ⊆{ Γ1 , Γ2 , .. , Γ3 }* Ys"
:
=
(
Forall2
(
⊆
{
pair
..
(
Γ
1
,
Γ
2
)
..
Γ
3
})
Xs
Ys
)
(
at
level
70
,
format
"Xs ⊆{ Γ1 , Γ2 , .. , Γ3 }* Ys"
)
:
C_scope
.
Notation
"(⊆{ Γ1 , Γ2 , .. , Γ3 }* )"
:
=
(
Forall2
(
⊆
{
pair
..
(
Γ
1
,
Γ
2
)
..
Γ
3
}))
(
only
parsing
,
Γ
1
at
level
1
)
:
C_scope
.
Hint
Extern
0
(
_
⊆
{
_
}
_
)
=>
reflexivity
.
Definition
strict
{
A
}
(
R
:
relation
A
)
:
relation
A
:
=
λ
X
Y
,
R
X
Y
∧
¬
R
Y
X
.
Definition
strict
{
A
}
(
R
:
relation
A
)
:
relation
A
:
=
λ
X
Y
,
R
X
Y
∧
¬
R
Y
X
.
Instance
:
Params
(@
strict
)
2
.
Instance
:
Params
(@
strict
)
2
.
Infix
"⊂"
:
=
(
strict
(
⊆
))
(
at
level
70
)
:
C_scope
.
Infix
"⊂"
:
=
(
strict
(
⊆
))
(
at
level
70
)
:
C_scope
.
...
...
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