Documentation
Init
.
Grind
.
Ordered
.
Module
Search
return to top
source
Imports
Init.Data.Int.Order
Init.Grind.Module.Basic
Init.Grind.Ordered.Order
Imported by
Lean
.
Grind
.
IntModule
.
IsOrdered
Lean
.
Grind
.
IntModule
.
IsOrdered
.
le_neg_iff
Lean
.
Grind
.
IntModule
.
IsOrdered
.
neg_lt_iff
Lean
.
Grind
.
IntModule
.
IsOrdered
.
lt_neg_iff
Lean
.
Grind
.
IntModule
.
IsOrdered
.
neg_nonneg_iff
Lean
.
Grind
.
IntModule
.
IsOrdered
.
neg_pos_iff
Lean
.
Grind
.
IntModule
.
IsOrdered
.
add_lt_left
Lean
.
Grind
.
IntModule
.
IsOrdered
.
add_le_right
Lean
.
Grind
.
IntModule
.
IsOrdered
.
add_lt_right
Lean
.
Grind
.
IntModule
.
IsOrdered
.
hmul_neg
Lean
.
Grind
.
IntModule
.
IsOrdered
.
hmul_nonpos
source
class
Lean
.
Grind
.
IntModule
.
IsOrdered
(
M
:
Type
u)
[
Preorder
M
]
[
IntModule
M
]
:
Prop
neg_le_iff
(
a
b
:
M
)
:
-
a
≤
b
↔
-
b
≤
a
add_le_left
{
a
b
:
M
}
:
a
≤
b
→
∀ (
c
:
M
),
a
+
c
≤
b
+
c
hmul_pos
(
k
:
Int
)
{
a
:
M
}
:
0
<
a
→ (
0
<
k
↔
0
<
k
*
a
)
hmul_nonneg
{
k
:
Int
}
{
a
:
M
}
:
0
≤
k
→
0
≤
a
→
0
≤
k
*
a
Instances
source
theorem
Lean
.
Grind
.
IntModule
.
IsOrdered
.
le_neg_iff
{
M
:
Type
u}
[
Preorder
M
]
[
IntModule
M
]
[
IsOrdered
M
]
{
a
b
:
M
}
:
a
≤
-
b
↔
b
≤
-
a
source
theorem
Lean
.
Grind
.
IntModule
.
IsOrdered
.
neg_lt_iff
{
M
:
Type
u}
[
Preorder
M
]
[
IntModule
M
]
[
IsOrdered
M
]
{
a
b
:
M
}
:
-
a
<
b
↔
-
b
<
a
source
theorem
Lean
.
Grind
.
IntModule
.
IsOrdered
.
lt_neg_iff
{
M
:
Type
u}
[
Preorder
M
]
[
IntModule
M
]
[
IsOrdered
M
]
{
a
b
:
M
}
:
a
<
-
b
↔
b
<
-
a
source
theorem
Lean
.
Grind
.
IntModule
.
IsOrdered
.
neg_nonneg_iff
{
M
:
Type
u}
[
Preorder
M
]
[
IntModule
M
]
[
IsOrdered
M
]
{
a
:
M
}
:
0
≤
-
a
↔
a
≤
0
source
theorem
Lean
.
Grind
.
IntModule
.
IsOrdered
.
neg_pos_iff
{
M
:
Type
u}
[
Preorder
M
]
[
IntModule
M
]
[
IsOrdered
M
]
{
a
:
M
}
:
0
<
-
a
↔
a
<
0
source
theorem
Lean
.
Grind
.
IntModule
.
IsOrdered
.
add_lt_left
{
M
:
Type
u}
[
Preorder
M
]
[
IntModule
M
]
[
IsOrdered
M
]
{
a
b
:
M
}
(
h
:
a
<
b
)
(
c
:
M
)
:
a
+
c
<
b
+
c
source
theorem
Lean
.
Grind
.
IntModule
.
IsOrdered
.
add_le_right
{
M
:
Type
u}
[
Preorder
M
]
[
IntModule
M
]
[
IsOrdered
M
]
(
a
:
M
)
{
b
c
:
M
}
(
h
:
b
≤
c
)
:
a
+
b
≤
a
+
c
source
theorem
Lean
.
Grind
.
IntModule
.
IsOrdered
.
add_lt_right
{
M
:
Type
u}
[
Preorder
M
]
[
IntModule
M
]
[
IsOrdered
M
]
(
a
:
M
)
{
b
c
:
M
}
(
h
:
b
<
c
)
:
a
+
b
<
a
+
c
source
theorem
Lean
.
Grind
.
IntModule
.
IsOrdered
.
hmul_neg
{
M
:
Type
u}
[
Preorder
M
]
[
IntModule
M
]
[
IsOrdered
M
]
(
k
:
Int
)
{
a
:
M
}
(
h
:
a
<
0
)
:
0
<
k
↔
k
*
a
<
0
source
theorem
Lean
.
Grind
.
IntModule
.
IsOrdered
.
hmul_nonpos
{
M
:
Type
u}
[
Preorder
M
]
[
IntModule
M
]
[
IsOrdered
M
]
{
k
:
Int
}
{
a
:
M
}
(
hk
:
0
≤
k
)
(
ha
:
a
≤
0
)
:
k
*
a
≤
0