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Pierre Rousselin
jscoq-light
Commits
54aa2995
Commit
54aa2995
authored
2 years ago
by
Shachar Itzhaky
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[doc] [bugfix] Typo in sqrt_2 example.
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examples/sqrt_2.v
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examples/sqrt_2.v
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examples/sqrt_2.v
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54aa2995
...
...
@@ -105,12 +105,12 @@ End sqrt2_decrease.
(
**
The
proof
proceeds
by
well
-
founded
induction
on
q
.
We
apply
the
induction
hypothesis
with
the
numbers
<<
3
*
q
-
2
*
q
>>
We
apply
the
induction
hypothesis
with
the
numbers
<<
3
*
q
-
2
*
p
>>
and
<<
3
*
p
-
4
*
q
>>
.
This
leaves
two
key
proof
goals
:
-
<<
3
*
q
-
2
*
p
<>
0
>>
,
which
we
prove
using
arithmetic
and
the
[
comparison2
]
lemma
above
[
comparison2
]
lemma
above
.
-
<<
(
3
*
p
-
4
*
q
)
*
(
3
*
p
-
4
*
q
)
=
2
*
((
3
*
q
-
2
*
p
)
*
(
3
*
q
-
2
*
p
))
>>
,
which
we
prove
using
the
[
new_equality
]
lemma
above
which
we
prove
using
the
[
new_equality
]
lemma
above
.
*
)
Theorem
sqrt2_not_rational
:
forall
p
q
:
nat
,
q
<>
0
->
¬
p
^
2
=
2
*
(
q
^
2
).
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