active
U101
tt
N
XS
mark
fst
splitAt
N
XS
active
U11
tt
N
XS
mark
snd
splitAt
N
XS
active
U21
tt
X
mark
X
active
U31
tt
N
mark
N
active
U41
tt
N
mark
cons
N
natsFrom
s
N
active
U51
tt
N
XS
mark
head
afterNth
N
XS
active
U61
tt
Y
mark
Y
active
U71
tt
XS
mark
pair
nil
XS
active
U81
tt
N
X
XS
mark
U82
splitAt
N
XS
X
active
U82
pair
YS
ZS
X
mark
pair
cons
X
YS
ZS
active
U91
tt
XS
mark
XS
active
afterNth
N
XS
mark
U11
and
isNatural
N
isLNat
XS
N
XS
active
and
tt
X
mark
X
active
fst
pair
X
Y
mark
U21
and
isLNat
X
isLNat
Y
X
active
head
cons
N
XS
mark
U31
and
isNatural
N
isLNat
XS
N
active
isLNat
nil
mark
tt
active
isLNat
afterNth
V1
V2
mark
and
isNatural
V1
isLNat
V2
active
isLNat
cons
V1
V2
mark
and
isNatural
V1
isLNat
V2
active
isLNat
fst
V1
mark
isPLNat
V1
active
isLNat
natsFrom
V1
mark
isNatural
V1
active
isLNat
snd
V1
mark
isPLNat
V1
active
isLNat
tail
V1
mark
isLNat
V1
active
isLNat
take
V1
V2
mark
and
isNatural
V1
isLNat
V2
active
isNatural
0
mark
tt
active
isNatural
head
V1
mark
isLNat
V1
active
isNatural
s
V1
mark
isNatural
V1
active
isNatural
sel
V1
V2
mark
and
isNatural
V1
isLNat
V2
active
isPLNat
pair
V1
V2
mark
and
isLNat
V1
isLNat
V2
active
isPLNat
splitAt
V1
V2
mark
and
isNatural
V1
isLNat
V2
active
natsFrom
N
mark
U41
isNatural
N
N
active
sel
N
XS
mark
U51
and
isNatural
N
isLNat
XS
N
XS
active
snd
pair
X
Y
mark
U61
and
isLNat
X
isLNat
Y
Y
active
splitAt
0
XS
mark
U71
isLNat
XS
XS
active
splitAt
s
N
cons
X
XS
mark
U81
and
isNatural
N
and
isNatural
X
isLNat
XS
N
X
XS
active
tail
cons
N
XS
mark
U91
and
isNatural
N
isLNat
XS
XS
active
take
N
XS
mark
U101
and
isNatural
N
isLNat
XS
N
XS
active
U101
X1
X2
X3
U101
active
X1
X2
X3
active
fst
X
fst
active
X
active
splitAt
X1
X2
splitAt
active
X1
X2
active
splitAt
X1
X2
splitAt
X1
active
X2
active
U11
X1
X2
X3
U11
active
X1
X2
X3
active
snd
X
snd
active
X
active
U21
X1
X2
U21
active
X1
X2
active
U31
X1
X2
U31
active
X1
X2
active
U41
X1
X2
U41
active
X1
X2
active
cons
X1
X2
cons
active
X1
X2
active
natsFrom
X
natsFrom
active
X
active
s
X
s
active
X
active
U51
X1
X2
X3
U51
active
X1
X2
X3
active
head
X
head
active
X
active
afterNth
X1
X2
afterNth
active
X1
X2
active
afterNth
X1
X2
afterNth
X1
active
X2
active
U61
X1
X2
U61
active
X1
X2
active
U71
X1
X2
U71
active
X1
X2
active
pair
X1
X2
pair
active
X1
X2
active
pair
X1
X2
pair
X1
active
X2
active
U81
X1
X2
X3
X4
U81
active
X1
X2
X3
X4
active
U82
X1
X2
U82
active
X1
X2
active
U91
X1
X2
U91
active
X1
X2
active
and
X1
X2
and
active
X1
X2
active
tail
X
tail
active
X
active
take
X1
X2
take
active
X1
X2
active
take
X1
X2
take
X1
active
X2
active
sel
X1
X2
sel
active
X1
X2
active
sel
X1
X2
sel
X1
active
X2
U101
mark
X1
X2
X3
mark
U101
X1
X2
X3
fst
mark
X
mark
fst
X
splitAt
mark
X1
X2
mark
splitAt
X1
X2
splitAt
X1
mark
X2
mark
splitAt
X1
X2
U11
mark
X1
X2
X3
mark
U11
X1
X2
X3
snd
mark
X
mark
snd
X
U21
mark
X1
X2
mark
U21
X1
X2
U31
mark
X1
X2
mark
U31
X1
X2
U41
mark
X1
X2
mark
U41
X1
X2
cons
mark
X1
X2
mark
cons
X1
X2
natsFrom
mark
X
mark
natsFrom
X
s
mark
X
mark
s
X
U51
mark
X1
X2
X3
mark
U51
X1
X2
X3
head
mark
X
mark
head
X
afterNth
mark
X1
X2
mark
afterNth
X1
X2
afterNth
X1
mark
X2
mark
afterNth
X1
X2
U61
mark
X1
X2
mark
U61
X1
X2
U71
mark
X1
X2
mark
U71
X1
X2
pair
mark
X1
X2
mark
pair
X1
X2
pair
X1
mark
X2
mark
pair
X1
X2
U81
mark
X1
X2
X3
X4
mark
U81
X1
X2
X3
X4
U82
mark
X1
X2
mark
U82
X1
X2
U91
mark
X1
X2
mark
U91
X1
X2
and
mark
X1
X2
mark
and
X1
X2
tail
mark
X
mark
tail
X
take
mark
X1
X2
mark
take
X1
X2
take
X1
mark
X2
mark
take
X1
X2
sel
mark
X1
X2
mark
sel
X1
X2
sel
X1
mark
X2
mark
sel
X1
X2
proper
U101
X1
X2
X3
U101
proper
X1
proper
X2
proper
X3
proper
tt
ok
tt
proper
fst
X
fst
proper
X
proper
splitAt
X1
X2
splitAt
proper
X1
proper
X2
proper
U11
X1
X2
X3
U11
proper
X1
proper
X2
proper
X3
proper
snd
X
snd
proper
X
proper
U21
X1
X2
U21
proper
X1
proper
X2
proper
U31
X1
X2
U31
proper
X1
proper
X2
proper
U41
X1
X2
U41
proper
X1
proper
X2
proper
cons
X1
X2
cons
proper
X1
proper
X2
proper
natsFrom
X
natsFrom
proper
X
proper
s
X
s
proper
X
proper
U51
X1
X2
X3
U51
proper
X1
proper
X2
proper
X3
proper
head
X
head
proper
X
proper
afterNth
X1
X2
afterNth
proper
X1
proper
X2
proper
U61
X1
X2
U61
proper
X1
proper
X2
proper
U71
X1
X2
U71
proper
X1
proper
X2
proper
pair
X1
X2
pair
proper
X1
proper
X2
proper
nil
ok
nil
proper
U81
X1
X2
X3
X4
U81
proper
X1
proper
X2
proper
X3
proper
X4
proper
U82
X1
X2
U82
proper
X1
proper
X2
proper
U91
X1
X2
U91
proper
X1
proper
X2
proper
and
X1
X2
and
proper
X1
proper
X2
proper
isNatural
X
isNatural
proper
X
proper
isLNat
X
isLNat
proper
X
proper
isPLNat
X
isPLNat
proper
X
proper
tail
X
tail
proper
X
proper
take
X1
X2
take
proper
X1
proper
X2
proper
0
ok
0
proper
sel
X1
X2
sel
proper
X1
proper
X2
U101
ok
X1
ok
X2
ok
X3
ok
U101
X1
X2
X3
fst
ok
X
ok
fst
X
splitAt
ok
X1
ok
X2
ok
splitAt
X1
X2
U11
ok
X1
ok
X2
ok
X3
ok
U11
X1
X2
X3
snd
ok
X
ok
snd
X
U21
ok
X1
ok
X2
ok
U21
X1
X2
U31
ok
X1
ok
X2
ok
U31
X1
X2
U41
ok
X1
ok
X2
ok
U41
X1
X2
cons
ok
X1
ok
X2
ok
cons
X1
X2
natsFrom
ok
X
ok
natsFrom
X
s
ok
X
ok
s
X
U51
ok
X1
ok
X2
ok
X3
ok
U51
X1
X2
X3
head
ok
X
ok
head
X
afterNth
ok
X1
ok
X2
ok
afterNth
X1
X2
U61
ok
X1
ok
X2
ok
U61
X1
X2
U71
ok
X1
ok
X2
ok
U71
X1
X2
pair
ok
X1
ok
X2
ok
pair
X1
X2
U81
ok
X1
ok
X2
ok
X3
ok
X4
ok
U81
X1
X2
X3
X4
U82
ok
X1
ok
X2
ok
U82
X1
X2
U91
ok
X1
ok
X2
ok
U91
X1
X2
and
ok
X1
ok
X2
ok
and
X1
X2
isNatural
ok
X
ok
isNatural
X
isLNat
ok
X
ok
isLNat
X
isPLNat
ok
X
ok
isPLNat
X
tail
ok
X
ok
tail
X
take
ok
X1
ok
X2
ok
take
X1
X2
sel
ok
X1
ok
X2
ok
sel
X1
X2
top
mark
X
top
proper
X
top
ok
X
top
active
X
2.2
active
U11
tt
N
XS
splitAt
N
XS
proper
U51
X1
X2
X3
proper
X2
U31
mark
X1
X2
U31
X1
X2
active
U101
X1
X2
X3
U101
active
X1
X2
X3
active
U101
tt
N
XS
fst
splitAt
N
XS
proper
cons
X1
X2
cons
proper
X1
proper
X2
proper
U81
X1
X2
X3
X4
proper
X4
isNatural
ok
X
isNatural
X
proper
U91
X1
X2
U91
proper
X1
proper
X2
active
U41
tt
N
s
N
active
U61
X1
X2
U61
active
X1
X2
proper
take
X1
X2
proper
X2
active
head
cons
N
XS
and
isNatural
N
isLNat
XS
take
mark
X1
X2
take
X1
X2
proper
U21
X1
X2
U21
proper
X1
proper
X2
active
take
N
XS
U101
and
isNatural
N
isLNat
XS
N
XS
active
isNatural
sel
V1
V2
isLNat
V2
active
isNatural
head
V1
isLNat
V1
active
U81
X1
X2
X3
X4
U81
active
X1
X2
X3
X4
proper
fst
X
proper
X
top
mark
X
proper
X
proper
cons
X1
X2
proper
X2
active
head
cons
N
XS
U31
and
isNatural
N
isLNat
XS
N
proper
U11
X1
X2
X3
proper
X1
splitAt
X1
mark
X2
splitAt
X1
X2
proper
afterNth
X1
X2
proper
X1
splitAt
mark
X1
X2
splitAt
X1
X2
active
U82
pair
YS
ZS
X
cons
X
YS
natsFrom
mark
X
natsFrom
X
active
U81
tt
N
X
XS
splitAt
N
XS
proper
U61
X1
X2
U61
proper
X1
proper
X2
active
U61
X1
X2
active
X1
active
take
X1
X2
take
X1
active
X2
active
splitAt
s
N
cons
X
XS
and
isNatural
X
isLNat
XS
U71
ok
X1
ok
X2
U71
X1
X2
cons
mark
X1
X2
cons
X1
X2
proper
U41
X1
X2
U41
proper
X1
proper
X2
proper
isPLNat
X
isPLNat
proper
X
active
take
N
XS
isNatural
N
active
U91
X1
X2
U91
active
X1
X2
active
U51
X1
X2
X3
U51
active
X1
X2
X3
proper
s
X
s
proper
X
snd
mark
X
snd
X
active
head
X
head
active
X
active
sel
N
XS
and
isNatural
N
isLNat
XS
proper
U61
X1
X2
proper
X2
active
head
cons
N
XS
isLNat
XS
active
U31
X1
X2
U31
active
X1
X2
active
U41
X1
X2
U41
active
X1
X2
proper
U61
X1
X2
proper
X1
active
splitAt
0
XS
U71
isLNat
XS
XS
active
U82
X1
X2
U82
active
X1
X2
and
ok
X1
ok
X2
and
X1
X2
active
fst
pair
X
Y
isLNat
Y
active
U41
X1
X2
active
X1
active
splitAt
X1
X2
active
X1
active
tail
X
tail
active
X
proper
U11
X1
X2
X3
proper
X2
proper
head
X
head
proper
X
active
isLNat
natsFrom
V1
isNatural
V1
proper
U21
X1
X2
proper
X1
fst
ok
X
fst
X
active
isPLNat
splitAt
V1
V2
and
isNatural
V1
isLNat
V2
active
isNatural
s
V1
isNatural
V1
active
isNatural
sel
V1
V2
and
isNatural
V1
isLNat
V2
proper
isLNat
X
isLNat
proper
X
active
U82
X1
X2
active
X1
active
splitAt
s
N
cons
X
XS
isLNat
XS
proper
isNatural
X
proper
X
proper
U71
X1
X2
U71
proper
X1
proper
X2
proper
pair
X1
X2
proper
X1
proper
U91
X1
X2
proper
X1
active
isLNat
afterNth
V1
V2
isLNat
V2
proper
fst
X
fst
proper
X
active
head
X
active
X
active
U81
tt
N
X
XS
U82
splitAt
N
XS
X
pair
ok
X1
ok
X2
pair
X1
X2
active
afterNth
X1
X2
active
X2
U11
ok
X1
ok
X2
ok
X3
U11
X1
X2
X3
active
s
X
s
active
X
s
ok
X
s
X
U71
mark
X1
X2
U71
X1
X2
active
tail
cons
N
XS
U91
and
isNatural
N
isLNat
XS
XS
take
ok
X1
ok
X2
take
X1
X2
active
tail
cons
N
XS
isNatural
N
active
snd
pair
X
Y
isLNat
Y
proper
afterNth
X1
X2
afterNth
proper
X1
proper
X2
proper
U31
X1
X2
U31
proper
X1
proper
X2
U91
mark
X1
X2
U91
X1
X2
U41
mark
X1
X2
U41
X1
X2
active
U71
X1
X2
active
X1
active
isNatural
sel
V1
V2
isNatural
V1
U41
ok
X1
ok
X2
U41
X1
X2
sel
mark
X1
X2
sel
X1
X2
active
splitAt
s
N
cons
X
XS
isNatural
N
proper
isNatural
X
isNatural
proper
X
proper
splitAt
X1
X2
proper
X2
proper
U101
X1
X2
X3
proper
X1
proper
U71
X1
X2
proper
X2
active
U51
tt
N
XS
afterNth
N
XS
proper
U101
X1
X2
X3
U101
proper
X1
proper
X2
proper
X3
active
isLNat
snd
V1
isPLNat
V1
active
pair
X1
X2
active
X2
active
splitAt
X1
X2
active
X2
active
afterNth
N
XS
U11
and
isNatural
N
isLNat
XS
N
XS
active
pair
X1
X2
active
X1
active
natsFrom
X
active
X
active
U81
X1
X2
X3
X4
active
X1
active
and
X1
X2
and
active
X1
X2
U81
ok
X1
ok
X2
ok
X3
ok
X4
U81
X1
X2
X3
X4
active
U51
tt
N
XS
head
afterNth
N
XS
active
isLNat
afterNth
V1
V2
isNatural
V1
sel
X1
mark
X2
sel
X1
X2
active
tail
cons
N
XS
isLNat
XS
proper
U81
X1
X2
X3
X4
U81
proper
X1
proper
X2
proper
X3
proper
X4
take
X1
mark
X2
take
X1
X2
active
isLNat
cons
V1
V2
isNatural
V1
U101
ok
X1
ok
X2
ok
X3
U101
X1
X2
X3
fst
mark
X
fst
X
proper
pair
X1
X2
proper
X2
active
afterNth
X1
X2
active
X1
proper
U71
X1
X2
proper
X1
tail
mark
X
tail
X
afterNth
mark
X1
X2
afterNth
X1
X2
U51
mark
X1
X2
X3
U51
X1
X2
X3
U101
mark
X1
X2
X3
U101
X1
X2
X3
proper
and
X1
X2
proper
X1
active
isLNat
take
V1
V2
isLNat
V2
active
isPLNat
pair
V1
V2
isLNat
V2
active
tail
X
active
X
active
U101
X1
X2
X3
active
X1
proper
tail
X
tail
proper
X
U91
ok
X1
ok
X2
U91
X1
X2
active
s
X
active
X
isLNat
ok
X
isLNat
X
proper
U101
X1
X2
X3
proper
X2
cons
ok
X1
ok
X2
cons
X1
X2
proper
isLNat
X
proper
X
afterNth
X1
mark
X2
afterNth
X1
X2
and
mark
X1
X2
and
X1
X2
proper
U82
X1
X2
proper
X1
active
U31
X1
X2
active
X1
head
mark
X
head
X
proper
isPLNat
X
proper
X
active
afterNth
X1
X2
afterNth
active
X1
X2
active
isPLNat
splitAt
V1
V2
isNatural
V1
proper
and
X1
X2
proper
X2
proper
U11
X1
X2
X3
proper
X3
snd
ok
X
snd
X
active
head
cons
N
XS
isNatural
N
active
fst
pair
X
Y
and
isLNat
X
isLNat
Y
proper
snd
X
snd
proper
X
active
tail
cons
N
XS
and
isNatural
N
isLNat
XS
proper
splitAt
X1
X2
splitAt
proper
X1
proper
X2
active
take
N
XS
and
isNatural
N
isLNat
XS
active
U41
tt
N
cons
N
natsFrom
s
N
active
afterNth
N
XS
and
isNatural
N
isLNat
XS
proper
splitAt
X1
X2
proper
X1
active
fst
X
active
X
proper
U81
X1
X2
X3
X4
proper
X2
proper
U41
X1
X2
proper
X1
active
U91
X1
X2
active
X1
active
U82
pair
YS
ZS
X
pair
cons
X
YS
ZS
active
isPLNat
pair
V1
V2
isLNat
V1
active
afterNth
N
XS
isNatural
N
active
U21
X1
X2
active
X1
active
natsFrom
X
natsFrom
active
X
sel
ok
X1
ok
X2
sel
X1
X2
active
U51
X1
X2
X3
active
X1
active
U11
X1
X2
X3
active
X1
proper
natsFrom
X
proper
X
active
isLNat
fst
V1
isPLNat
V1
tail
ok
X
tail
X
active
pair
X1
X2
pair
X1
active
X2
active
sel
X1
X2
active
X1
proper
tail
X
proper
X
proper
sel
X1
X2
sel
proper
X1
proper
X2
proper
U81
X1
X2
X3
X4
proper
X3
active
splitAt
0
XS
isLNat
XS
active
isPLNat
pair
V1
V2
and
isLNat
V1
isLNat
V2
proper
U51
X1
X2
X3
U51
proper
X1
proper
X2
proper
X3
proper
U51
X1
X2
X3
proper
X3
active
snd
pair
X
Y
and
isLNat
X
isLNat
Y
pair
mark
X1
X2
pair
X1
X2
active
splitAt
X1
X2
splitAt
active
X1
X2
proper
sel
X1
X2
proper
X2
active
U11
X1
X2
X3
U11
active
X1
X2
X3
proper
U41
X1
X2
proper
X2
active
fst
pair
X
Y
isLNat
X
active
natsFrom
N
isNatural
N
active
take
X1
X2
active
X1
U51
ok
X1
ok
X2
ok
X3
U51
X1
X2
X3
active
U71
X1
X2
U71
active
X1
X2
splitAt
ok
X1
ok
X2
splitAt
X1
X2
U21
ok
X1
ok
X2
U21
X1
X2
afterNth
ok
X1
ok
X2
afterNth
X1
X2
active
isLNat
afterNth
V1
V2
and
isNatural
V1
isLNat
V2
proper
U21
X1
X2
proper
X2
active
isLNat
cons
V1
V2
and
isNatural
V1
isLNat
V2
proper
cons
X1
X2
proper
X1
head
ok
X
head
X
pair
X1
mark
X2
pair
X1
X2
proper
take
X1
X2
proper
X1
U21
mark
X1
X2
U21
X1
X2
active
snd
X
snd
active
X
proper
take
X1
X2
take
proper
X1
proper
X2
proper
U81
X1
X2
X3
X4
proper
X1
proper
U82
X1
X2
U82
proper
X1
proper
X2
active
natsFrom
N
U41
isNatural
N
N
active
sel
N
XS
isLNat
XS
active
isLNat
cons
V1
V2
isLNat
V2
proper
U31
X1
X2
proper
X2
active
snd
pair
X
Y
U61
and
isLNat
X
isLNat
Y
Y
active
splitAt
s
N
cons
X
XS
isNatural
X
active
isLNat
tail
V1
isLNat
V1
active
U41
tt
N
natsFrom
s
N
active
fst
X
fst
active
X
active
fst
pair
X
Y
U21
and
isLNat
X
isLNat
Y
X
top
mark
X
top
proper
X
proper
snd
X
proper
X
active
isLNat
take
V1
V2
isNatural
V1
proper
U101
X1
X2
X3
proper
X3
proper
afterNth
X1
X2
proper
X2
proper
U51
X1
X2
X3
proper
X1
s
mark
X
s
X
active
sel
X1
X2
active
X2
active
sel
N
XS
U51
and
isNatural
N
isLNat
XS
N
XS
active
snd
pair
X
Y
isLNat
X
proper
U91
X1
X2
proper
X2
U31
ok
X1
ok
X2
U31
X1
X2
U61
mark
X1
X2
U61
X1
X2
proper
U11
X1
X2
X3
U11
proper
X1
proper
X2
proper
X3
proper
U82
X1
X2
proper
X2
active
cons
X1
X2
active
X1
U81
mark
X1
X2
X3
X4
U81
X1
X2
X3
X4
top
ok
X
top
active
X
proper
sel
X1
X2
proper
X1
active
pair
X1
X2
pair
active
X1
X2
active
U11
tt
N
XS
snd
splitAt
N
XS
proper
s
X
proper
X
active
sel
N
XS
isNatural
N
proper
pair
X1
X2
pair
proper
X1
proper
X2
U82
mark
X1
X2
U82
X1
X2
active
U71
tt
XS
pair
nil
XS
active
take
N
XS
isLNat
XS
active
and
X1
X2
active
X1
top
ok
X
active
X
active
isPLNat
splitAt
V1
V2
isLNat
V2
proper
and
X1
X2
and
proper
X1
proper
X2
proper
head
X
proper
X
active
sel
X1
X2
sel
active
X1
X2
U82
ok
X1
ok
X2
U82
X1
X2
active
take
X1
X2
take
active
X1
X2
active
afterNth
N
XS
isLNat
XS
active
sel
X1
X2
sel
X1
active
X2
proper
natsFrom
X
natsFrom
proper
X
active
cons
X1
X2
cons
active
X1
X2
active
afterNth
X1
X2
afterNth
X1
active
X2
natsFrom
ok
X
natsFrom
X
active
splitAt
s
N
cons
X
XS
and
isNatural
N
and
isNatural
X
isLNat
XS
U11
mark
X1
X2
X3
U11
X1
X2
X3
proper
U31
X1
X2
proper
X1
active
take
X1
X2
active
X2
active
U21
X1
X2
U21
active
X1
X2
active
splitAt
s
N
cons
X
XS
U81
and
isNatural
N
and
isNatural
X
isLNat
XS
N
X
XS
active
isLNat
take
V1
V2
and
isNatural
V1
isLNat
V2
active
splitAt
X1
X2
splitAt
X1
active
X2
U61
ok
X1
ok
X2
U61
X1
X2
active
snd
X
active
X
isPLNat
ok
X
isPLNat
X
active
U101
tt
N
XS
splitAt
N
XS
true
top
ok
X
top
active
X
top
mark
X
top
proper
X
true
Failed!
NaTT
certifiable-1.6