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iris
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Tej Chajed
iris
Commits
a64bb337
Commit
a64bb337
authored
7 years ago
by
Robbert Krebbers
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Have `iInduction x as ...` revert all proofmode hyps involving `x`.
parent
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theories/proofmode/tactics.v
+78
-56
78 additions, 56 deletions
theories/proofmode/tactics.v
with
78 additions
and
56 deletions
theories/proofmode/tactics.v
+
78
−
56
View file @
a64bb337
...
...
@@ -1206,8 +1206,21 @@ Tactic Notation "iPoseProof" open_constr(lem) "as" "(" simple_intropattern(x1)
iPoseProofCore
lem
as
pat
false
(
fun
H
=>
iDestructHyp
H
as
(
x1
x2
x3
x4
x5
x6
x7
x8
)
pat
)
.
(** * Induction *)
Tactic
Notation
"iInductionCore"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
:=
(* An invocation of [iInduction (x) as pat IH forall (x1...xn) Hs] will
result in the following actions:
- Revert the proofmode hypotheses [Hs]
- Revert all remaining spatial hypotheses and the remaining persistent
hypotheses containing the induction variable [x]
- Revert the pure hypotheses [x1..xn]
- Actuall perform induction
- Introduce thee pure hypotheses [x1..xn]
- Introduce the spatial hypotheses and persistent hypotheses involving [x]
- Introduce the proofmode hypotheses [Hs]
*)
Tactic
Notation
"iInductionCore"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
:=
let
rec
fix_ihs
:=
lazymatch
goal
with
|
H
:
coq_tactics
.
of_envs
_
⊢
_
|
-
_
=>
...
...
@@ -1220,75 +1233,88 @@ Tactic Notation "iInductionCore" constr(x)
end
in
induction
x
as
pat
;
fix_ihs
.
Ltac
iHypsContaining
x
:=
let
rec
go
Γ
x
Hs
:=
lazymatch
Γ
with
|
Enil
=>
constr
:(
Hs
)
|
Esnoc
?Γ
?H
?Q
=>
match
Q
with
|
context
[
x
]
=>
go
Γ
x
(
H
::
Hs
)
|
_
=>
go
Γ
x
Hs
end
end
in
let
Γp
:=
lazymatch
goal
with
|
-
of_envs
(
Envs
?Γp
_)
⊢
_
=>
Γp
end
in
let
Γs
:=
lazymatch
goal
with
|
-
of_envs
(
Envs
_
?Γs
)
⊢
_
=>
Γs
end
in
let
Hs
:=
go
Γp
x
(
@
nil
string
)
in
go
Γs
x
Hs
.
Tactic
Notation
"iInductionRevert"
constr
(
x
)
constr
(
Hs
)
"with"
tactic
(
tac
)
:=
iRevertIntros
Hs
with
(
iRevertIntros
"∗"
with
(
let
Hsx
:=
iHypsContaining
x
in
iRevertIntros
Hsx
with
tac
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
:=
i
RevertIntros
"
∗
"
with
(
iInductionCore
x
as
pat
IH
)
.
i
InductionRevert
x
""
with
(
iInductionCore
x
as
pat
IH
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
")"
:=
iRevertIntros
(
x1
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
:=
iRevertIntros
(
x1
x2
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
:=
iRevertIntros
(
x1
x2
x3
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
)
"
∗
"
with
(
iInductionCore
x
as
a
at
IH
)
.
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iInductionCore
x
as
p
at
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
Hs
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
Hs
with
(
iInductionCore
x
as
pat
IH
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
)
Hs
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
)
""
with
(
iInductionCore
x
as
pat
IH
))
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
)
Hs
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iInductionCore
x
as
pat
IH
))
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
)
Hs
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iInductionCore
x
as
pat
IH
))
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
)
Hs
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iInductionCore
x
as
pat
IH
))
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
)
Hs
with
(
iInductionCore
x
as
aat
IH
)
.
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iInductionCore
x
as
pat
IH
))
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
Hs
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
""
with
(
iInductionCore
x
as
pat
IH
))
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
Hs
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
""
with
(
iInductionCore
x
as
pat
IH
))
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
Hs
with
(
iInductionCore
x
as
pat
IH
)
.
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
(
iInductionCore
x
as
pat
IH
))
.
(** * Löb Induction *)
Tactic
Notation
"iLöbCore"
"as"
constr
(
IH
)
:=
...
...
@@ -1297,65 +1323,61 @@ Tactic Notation "iLöbCore" "as" constr (IH) :=
[
reflexivity
||
fail
"iLöb: spatial context not empty, this should not happen"
|
env_reflexivity
||
fail
"iLöb:"
IH
"not fresh"
|]
.
Tactic
Notation
"iLöbRevert"
constr
(
Hs
)
"with"
tactic
(
tac
)
:=
iRevertIntros
Hs
with
(
iRevertIntros
"∗"
with
tac
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
:=
iRevert
Intros
"
∗
"
with
(
iLöbCore
as
IH
)
.
i
Löb
Revert
""
with
(
iLöbCore
as
IH
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
")"
:=
iRevertIntros
(
x1
)
"
∗
"
with
(
iLöbCore
as
IH
)
.
iLöbRevert
""
with
(
iRevertIntros
(
x1
)
""
with
(
iLöbCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
:=
iRevertIntros
(
x1
x2
)
"
∗
"
with
(
iLöbCore
as
IH
)
.
iLöbRevert
""
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iLöbCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
:=
iRevertIntros
(
x1
x2
x3
)
"
∗
"
with
(
iLöbCore
as
IH
)
.
iLöbRevert
""
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iLöbCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
)
"
∗
"
with
(
iLöbCore
as
IH
)
.
iLöbRevert
""
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iLöbCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
)
"
∗
"
with
(
iLöbCore
as
IH
)
.
iLöbRevert
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iLöbCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
"
∗
"
with
(
iLöbCore
as
IH
)
.
iLöbRevert
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
""
with
(
iLöbCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
"
∗
"
with
(
iLöbCore
as
IH
)
.
iLöbRevert
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
""
with
(
iLöbCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
:=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
"
∗
"
with
(
iLöbCore
as
IH
)
.
iLöbRevert
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
(
iLöbCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
Hs
with
(
iLöbCore
as
IH
)
.
iLöbRevert
Hs
with
(
iLöbCore
as
IH
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
)
Hs
with
(
iLöbCore
as
IH
)
.
iLöbRevert
Hs
with
(
iRevertIntros
(
x1
)
""
with
(
iLöbCore
as
IH
))
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
)
Hs
with
(
iLöbCore
as
IH
)
.
iLöbRevert
Hs
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iLöbCore
as
IH
))
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
)
Hs
with
(
iLöbCore
as
IH
)
.
iLöbRevert
Hs
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iLöbCore
as
IH
))
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
)
Hs
with
(
iLöbCore
as
IH
)
.
iLöbRevert
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iLöbCore
as
IH
))
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
)
Hs
with
(
iLöbCore
as
IH
)
.
iLöbRevert
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iLöbCore
as
IH
))
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
Hs
with
(
iLöbCore
as
IH
)
.
iLöbRevert
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
""
with
(
iLöbCore
as
IH
))
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
Hs
with
(
iLöbCore
as
IH
)
.
iLöbRevert
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
""
with
(
iLöbCore
as
IH
))
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
constr
(
Hs
)
:=
let
Hs
:=
constr
:(
Hs
+:+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
Hs
with
(
iLöbCore
as
IH
)
.
iLöbRevert
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
(
iLöbCore
as
IH
))
.
(** * Assert *)
(* The argument [p] denotes whether [Q] is persistent. It can either be a
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