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Joshua Yanovski
iriscoq
Commits
fbedbd17
Commit
fbedbd17
authored
Feb 10, 2016
by
Ralf Jung
Browse files
remove some unused typeclasses and notation: EquivE and SubsetEqE
parent
5f393110
Changes
1
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prelude/base.v
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fbedbd17
...
@@ 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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