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Tej Chajed
stdpp
Commits
10a74299
Commit
10a74299
authored
Aug 04, 2016
by
Robbert Krebbers
Browse files
Injectivity instance for Z.of_nat.
Also cleanup the file a bit.
parent
099e760b
Changes
1
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Inline
Side-by-side
theories/numbers.v
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10a74299
...
...
@@ -231,16 +231,19 @@ Infix "`rem`" := Z.rem (at level 35) : Z_scope.
Infix
"≪"
:
=
Z
.
shiftl
(
at
level
35
)
:
Z_scope
.
Infix
"≫"
:
=
Z
.
shiftr
(
at
level
35
)
:
Z_scope
.
Instance
:
Inj
(=)
(=)
Zpos
.
Instance
Zpos_inj
:
Inj
(=)
(=)
Zpos
.
Proof
.
by
injection
1
.
Qed
.
Instance
:
Inj
(=)
(=)
Zneg
.
Instance
Zneg_inj
:
Inj
(=)
(=)
Zneg
.
Proof
.
by
injection
1
.
Qed
.
Instance
Z_of_nat_inj
:
Inj
(=)
(=)
Z
.
of_nat
.
Proof
.
intros
n1
n2
.
apply
Nat2Z
.
inj
.
Qed
.
Instance
Z_eq_dec
:
∀
x
y
:
Z
,
Decision
(
x
=
y
)
:
=
Z
.
eq_dec
.
Instance
Z_le_dec
:
∀
x
y
:
Z
,
Decision
(
x
≤
y
)
:
=
Z_le_dec
.
Instance
Z_lt_dec
:
∀
x
y
:
Z
,
Decision
(
x
<
y
)
:
=
Z_lt_dec
.
Instance
Z_inhabited
:
Inhabited
Z
:
=
populate
1
.
Instance
:
PartialOrder
(
≤
).
Instance
Z_le_order
:
PartialOrder
(
≤
).
Proof
.
repeat
split
;
red
.
apply
Z
.
le_refl
.
apply
Z
.
le_trans
.
apply
Z
.
le_antisymm
.
Qed
.
...
...
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