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POTTIER Francois
mpri2.4public
Commits
6fbea55f
Commit
6fbea55f
authored
Sep 20, 2019
by
POTTIER Francois
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Small tweaks in the Coq demo.
parent
da9cb531
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coq/DemoSyntaxReduction.v
coq/DemoSyntaxReduction.v
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coq/DemoSyntaxReduction.v
View file @
6fbea55f
...
...
@@ 37,11 +37,14 @@ Goal
Lam
(
App
(
Var
0
)
(
sigma
0
).[
ren
(
+
1
)]).
Proof
.
intros
.
(
*
The
tactic
[
autosubst
]
proves
this
equality
.
*
)
(
*
The
two
sides
of
this
equation
are
distinct
terms
:
the
built

in
tactic
[
reflexivity
]
cannot
prove
this
equation
.
*
)
Fail
reflexivity
.
(
*
The
tactic
[
autosubst
]
is
able
to
prove
this
equality
.
*
)
autosubst
.
Restart
.
intros
.
(
*
If
desired
,
we
can
first
simplify
this
equality
using
[
asimpl
].
*
)
(
*
Another
way
of
proceeding
is
to
first
simplify
the
goal
using
[
asimpl
].
*
)
asimpl
.
(
*
[
ids
],
the
identity
substitution
,
maps
0
to
[
Var
0
],
1
to
[
Var
1
],
and
so
on
,
so
it
is
really
equal
to
[
Var
]
itself
.
As
a
result
,
the
...
...
@@ 171,6 +174,7 @@ Proof.
induction
1
;
intros
.
(
*
Case
:
[
RedBeta
].
*
)
{
subst
u
.
asimpl
.
eapply
RedBeta
.
(
*
Wow

we
have
to
prove
a
complicated

looking
commutation
property
of
substitutions
.
Fortunately
,
[
autosubst
]
is
here
for
us
!
*
)
...
...
@@ 211,6 +215,7 @@ Restart.
are
no
longer
distinguished
:
*
)
Restart
.
induction
1
;
intros
;
subst
;
asimpl
;
econstructor
;
eauto
with
autosubst
.
(
*
Actually
,
[
asimpl
]
on
the
previous
line
seems
not
even
needed
.
*
)
(
*
The
proof
is
now
finished
(
yet
again
).
*
)
(
*
There
are
several
lessons
that
one
can
draw
from
this
demo
:
...
...
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