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Simon Spies
Iris
Commits
becd6e2e
Commit
becd6e2e
authored
Jul 12, 2018
by
Robbert Krebbers
Browse files
Support `iInduction ... using`; this closes issue
#204
.
parent
af5493d0
Changes
2
Show whitespace changes
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Sidebyside
Showing
2 changed files
with
125 additions
and
20 deletions
+125
20
tests/proofmode.v
tests/proofmode.v
+9
0
theories/proofmode/ltac_tactics.v
theories/proofmode/ltac_tactics.v
+116
20
No files found.
tests/proofmode.v
View file @
becd6e2e
...
...
@@ 267,6 +267,15 @@ Proof.
rewrite
(
inj_iff
S
).
by
iApply
(
"IH"
with
"[%]"
)
;
first
omega
.
Qed
.
Lemma
test_iInduction_using
(
m
:
gmap
nat
nat
)
(
Φ
:
nat
→
nat
→
PROP
)
y
:
([
∗
map
]
x
↦
i
∈
m
,
Φ
y
x
)

∗
([
∗
map
]
x
↦
i
∈
m
,
emp
∗
Φ
y
x
).
Proof
.
iIntros
"Hm"
.
iInduction
m
as
[
i
x
m
]
"IH"
using
map_ind
forall
(
y
).

by
rewrite
!
big_sepM_empty
.

rewrite
!
big_sepM_insert
//.
iDestruct
"Hm"
as
"[$ ?]"
.
by
iApply
"IH"
.
Qed
.
Lemma
test_iIntros_start_proof
:
(
True
:
PROP
)%
I
.
Proof
.
...
...
theories/proofmode/ltac_tactics.v
View file @
becd6e2e
...
...
@@ 1630,7 +1630,7 @@ result in the following actions:
 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
)
:
=
Tactic
Notation
"iInductionCore"
tactic
(
tac
)
"as"
constr
(
IH
)
:
=
let
rec
fix_ihs
rev_tac
:
=
lazymatch
goal
with

H
:
context
[
envs_entails
_
_
]

_
=>
...
...
@@ 1646,7 +1646,7 @@ Tactic Notation "iInductionCore" constr(x) "as" simple_intropattern(pat) constr(
rev_tac
j
)

_
=>
rev_tac
0
%
N
end
in
induction
x
as
pat
;
fix_ihs
ltac
:
(
fun
_
=>
idtac
).
tac
;
fix_ihs
ltac
:
(
fun
_
=>
idtac
).
Ltac
iHypsContaining
x
:
=
let
rec
go
Γ
x
Hs
:
=
...
...
@@ 1672,65 +1672,161 @@ Tactic Notation "iInductionRevert" constr(x) constr(Hs) "with" tactic(tac) :=
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
:
=
iInductionRevert
x
""
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
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
)
")"
:
=
iInductionRevert
x
""
with
(
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
(
induction
x
as
pat
)
as
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
)
")"
:
=
iInductionRevert
x
""
with
(
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
(
induction
x
as
pat
)
as
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
)
")"
:
=
iInductionRevert
x
""
with
(
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
(
induction
x
as
pat
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
Hs
with
(
iInductionCore
(
induction
x
as
pat
)
as
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
")"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
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
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
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
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
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
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
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
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
(
iInductionCore
x
as
pat
IH
)).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
(
iInductionCore
(
induction
x
as
pat
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
:
=
iInductionRevert
x
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
:
=
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
")"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
")"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
")"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
")"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"using"
uconstr
(
u
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
constr
(
Hs
)
:
=
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
(
iInductionCore
(
induction
x
as
pat
using
u
)
as
IH
)).
(** * Löb Induction *)
Tactic
Notation
"iLöbCore"
"as"
constr
(
IH
)
:
=
...
...
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