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Actris
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661e6d86
Commit
661e6d86
authored
4 years ago
by
Jonas Kastberg
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Added type former for a type appended N times
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_CoqProject
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_CoqProject
theories/logrel/napp.v
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theories/logrel/napp.v
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View file @
661e6d86
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@@ -36,6 +36,7 @@ theories/logrel/term_typing_judgment.v
theories/logrel/subtyping_rules.v
theories/logrel/term_typing_rules.v
theories/logrel/session_typing_rules.v
theories/logrel/napp.v
theories/logrel/lib/mutex.v
theories/logrel/lib/par_start.v
theories/logrel/examples/double.v
...
...
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theories/logrel/napp.v
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661e6d86
From
actris
.
logrel
Require
Import
term_typing_rules
session_types
subtyping_rules
.
From
actris
.
channel
Require
Import
proofmode
.
Section
with_Σ
.
Context
`{
!
heapG
Σ
}
.
Fixpoint
lty_napp
(
R
:
lsty
Σ
)
(
n
:
nat
)
:=
match
n
with
|
O
=>
END
|
S
n
=>
R
<++>
lty_napp
R
n
end
%
lty
.
Lemma
lty_napp_S_l
R
n
:
lty_napp
R
(
S
n
)
≡
(
R
<++>
lty_napp
R
n
)
%
lty
.
Proof
.
eauto
.
Qed
.
Lemma
lty_napp_S_r
R
n
:
lty_napp
R
(
S
n
)
≡
(
lty_napp
R
n
<++>
R
)
%
lty
.
Proof
.
induction
n
;
simpl
;
[
by
rewrite
lty_app_end_l
lty_app_end_r
|
]
.
rewrite
-
(
assoc
_
_
(
lty_napp
R
n
)
R
)
.
by
rewrite
-
IHn
.
Qed
.
Lemma
lty_napp_flip
R
n
:
(
lty_napp
R
n
<++>
R
)
%
lty
≡
(
R
<++>
lty_napp
R
n
)
%
lty
.
Proof
.
by
rewrite
-
lty_napp_S_l
lty_napp_S_r
.
Qed
.
Lemma
napp_swap
T
R
n
:
R
<++>
T
<:
T
<++>
R
-∗
lty_napp
R
n
<++>
T
<:
T
<++>
lty_napp
R
n
.
Proof
.
iIntros
"#Hle"
.
iInduction
n
as
[|
n
]
"IHn"
;
[
by
rewrite
lty_app_end_l
lty_app_end_r
|
]
.
rewrite
-
assoc
.
iApply
lty_le_trans
.
{
iApply
lty_le_app
;
[
iApply
lty_le_refl
|
iApply
"IHn"
]
.
}
rewrite
assoc
.
iApply
lty_le_trans
.
{
iApply
lty_le_app
;
[
iApply
"Hle"
|
iApply
lty_le_refl
]
.
}
rewrite
assoc
.
iApply
lty_le_refl
.
Qed
.
End
with_Σ
.
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