active
U101
tt
V2
mark
U102
isLNat
V2
active
U102
tt
mark
tt
active
U11
tt
N
XS
mark
U12
isLNat
XS
N
XS
active
U111
tt
mark
tt
active
U12
tt
N
XS
mark
snd
splitAt
N
XS
active
U121
tt
mark
tt
active
U131
tt
V2
mark
U132
isLNat
V2
active
U132
tt
mark
tt
active
U141
tt
V2
mark
U142
isLNat
V2
active
U142
tt
mark
tt
active
U151
tt
V2
mark
U152
isLNat
V2
active
U152
tt
mark
tt
active
U161
tt
N
mark
cons
N
natsFrom
s
N
active
U171
tt
N
XS
mark
U172
isLNat
XS
N
XS
active
U172
tt
N
XS
mark
head
afterNth
N
XS
active
U181
tt
Y
mark
U182
isLNat
Y
Y
active
U182
tt
Y
mark
Y
active
U191
tt
XS
mark
pair
nil
XS
active
U201
tt
N
X
XS
mark
U202
isNatural
X
N
X
XS
active
U202
tt
N
X
XS
mark
U203
isLNat
XS
N
X
XS
active
U203
tt
N
X
XS
mark
U204
splitAt
N
XS
X
active
U204
pair
YS
ZS
X
mark
pair
cons
X
YS
ZS
active
U21
tt
X
Y
mark
U22
isLNat
Y
X
active
U211
tt
XS
mark
U212
isLNat
XS
XS
active
U212
tt
XS
mark
XS
active
U22
tt
X
mark
X
active
U221
tt
N
XS
mark
U222
isLNat
XS
N
XS
active
U222
tt
N
XS
mark
fst
splitAt
N
XS
active
U31
tt
N
XS
mark
U32
isLNat
XS
N
active
U32
tt
N
mark
N
active
U41
tt
V2
mark
U42
isLNat
V2
active
U42
tt
mark
tt
active
U51
tt
V2
mark
U52
isLNat
V2
active
U52
tt
mark
tt
active
U61
tt
mark
tt
active
U71
tt
mark
tt
active
U81
tt
mark
tt
active
U91
tt
mark
tt
active
afterNth
N
XS
mark
U11
isNatural
N
N
XS
active
fst
pair
X
Y
mark
U21
isLNat
X
X
Y
active
head
cons
N
XS
mark
U31
isNatural
N
N
XS
active
isLNat
nil
mark
tt
active
isLNat
afterNth
V1
V2
mark
U41
isNatural
V1
V2
active
isLNat
cons
V1
V2
mark
U51
isNatural
V1
V2
active
isLNat
fst
V1
mark
U61
isPLNat
V1
active
isLNat
natsFrom
V1
mark
U71
isNatural
V1
active
isLNat
snd
V1
mark
U81
isPLNat
V1
active
isLNat
tail
V1
mark
U91
isLNat
V1
active
isLNat
take
V1
V2
mark
U101
isNatural
V1
V2
active
isNatural
0
mark
tt
active
isNatural
head
V1
mark
U111
isLNat
V1
active
isNatural
s
V1
mark
U121
isNatural
V1
active
isNatural
sel
V1
V2
mark
U131
isNatural
V1
V2
active
isPLNat
pair
V1
V2
mark
U141
isLNat
V1
V2
active
isPLNat
splitAt
V1
V2
mark
U151
isNatural
V1
V2
active
natsFrom
N
mark
U161
isNatural
N
N
active
sel
N
XS
mark
U171
isNatural
N
N
XS
active
snd
pair
X
Y
mark
U181
isLNat
X
Y
active
splitAt
0
XS
mark
U191
isLNat
XS
XS
active
splitAt
s
N
cons
X
XS
mark
U201
isNatural
N
N
X
XS
active
tail
cons
N
XS
mark
U211
isNatural
N
XS
active
take
N
XS
mark
U221
isNatural
N
N
XS
active
U101
X1
X2
U101
active
X1
X2
active
U102
X
U102
active
X
active
U11
X1
X2
X3
U11
active
X1
X2
X3
active
U12
X1
X2
X3
U12
active
X1
X2
X3
active
U111
X
U111
active
X
active
snd
X
snd
active
X
active
splitAt
X1
X2
splitAt
active
X1
X2
active
splitAt
X1
X2
splitAt
X1
active
X2
active
U121
X
U121
active
X
active
U131
X1
X2
U131
active
X1
X2
active
U132
X
U132
active
X
active
U141
X1
X2
U141
active
X1
X2
active
U142
X
U142
active
X
active
U151
X1
X2
U151
active
X1
X2
active
U152
X
U152
active
X
active
U161
X1
X2
U161
active
X1
X2
active
cons
X1
X2
cons
active
X1
X2
active
natsFrom
X
natsFrom
active
X
active
s
X
s
active
X
active
U171
X1
X2
X3
U171
active
X1
X2
X3
active
U172
X1
X2
X3
U172
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
U181
X1
X2
U181
active
X1
X2
active
U182
X1
X2
U182
active
X1
X2
active
U191
X1
X2
U191
active
X1
X2
active
pair
X1
X2
pair
active
X1
X2
active
pair
X1
X2
pair
X1
active
X2
active
U201
X1
X2
X3
X4
U201
active
X1
X2
X3
X4
active
U202
X1
X2
X3
X4
U202
active
X1
X2
X3
X4
active
U203
X1
X2
X3
X4
U203
active
X1
X2
X3
X4
active
U204
X1
X2
U204
active
X1
X2
active
U21
X1
X2
X3
U21
active
X1
X2
X3
active
U22
X1
X2
U22
active
X1
X2
active
U211
X1
X2
U211
active
X1
X2
active
U212
X1
X2
U212
active
X1
X2
active
U221
X1
X2
X3
U221
active
X1
X2
X3
active
U222
X1
X2
X3
U222
active
X1
X2
X3
active
fst
X
fst
active
X
active
U31
X1
X2
X3
U31
active
X1
X2
X3
active
U32
X1
X2
U32
active
X1
X2
active
U41
X1
X2
U41
active
X1
X2
active
U42
X
U42
active
X
active
U51
X1
X2
U51
active
X1
X2
active
U52
X
U52
active
X
active
U61
X
U61
active
X
active
U71
X
U71
active
X
active
U81
X
U81
active
X
active
U91
X
U91
active
X
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
mark
U101
X1
X2
U102
mark
X
mark
U102
X
U11
mark
X1
X2
X3
mark
U11
X1
X2
X3
U12
mark
X1
X2
X3
mark
U12
X1
X2
X3
U111
mark
X
mark
U111
X
snd
mark
X
mark
snd
X
splitAt
mark
X1
X2
mark
splitAt
X1
X2
splitAt
X1
mark
X2
mark
splitAt
X1
X2
U121
mark
X
mark
U121
X
U131
mark
X1
X2
mark
U131
X1
X2
U132
mark
X
mark
U132
X
U141
mark
X1
X2
mark
U141
X1
X2
U142
mark
X
mark
U142
X
U151
mark
X1
X2
mark
U151
X1
X2
U152
mark
X
mark
U152
X
U161
mark
X1
X2
mark
U161
X1
X2
cons
mark
X1
X2
mark
cons
X1
X2
natsFrom
mark
X
mark
natsFrom
X
s
mark
X
mark
s
X
U171
mark
X1
X2
X3
mark
U171
X1
X2
X3
U172
mark
X1
X2
X3
mark
U172
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
U181
mark
X1
X2
mark
U181
X1
X2
U182
mark
X1
X2
mark
U182
X1
X2
U191
mark
X1
X2
mark
U191
X1
X2
pair
mark
X1
X2
mark
pair
X1
X2
pair
X1
mark
X2
mark
pair
X1
X2
U201
mark
X1
X2
X3
X4
mark
U201
X1
X2
X3
X4
U202
mark
X1
X2
X3
X4
mark
U202
X1
X2
X3
X4
U203
mark
X1
X2
X3
X4
mark
U203
X1
X2
X3
X4
U204
mark
X1
X2
mark
U204
X1
X2
U21
mark
X1
X2
X3
mark
U21
X1
X2
X3
U22
mark
X1
X2
mark
U22
X1
X2
U211
mark
X1
X2
mark
U211
X1
X2
U212
mark
X1
X2
mark
U212
X1
X2
U221
mark
X1
X2
X3
mark
U221
X1
X2
X3
U222
mark
X1
X2
X3
mark
U222
X1
X2
X3
fst
mark
X
mark
fst
X
U31
mark
X1
X2
X3
mark
U31
X1
X2
X3
U32
mark
X1
X2
mark
U32
X1
X2
U41
mark
X1
X2
mark
U41
X1
X2
U42
mark
X
mark
U42
X
U51
mark
X1
X2
mark
U51
X1
X2
U52
mark
X
mark
U52
X
U61
mark
X
mark
U61
X
U71
mark
X
mark
U71
X
U81
mark
X
mark
U81
X
U91
mark
X
mark
U91
X
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
U101
proper
X1
proper
X2
proper
tt
ok
tt
proper
U102
X
U102
proper
X
proper
isLNat
X
isLNat
proper
X
proper
U11
X1
X2
X3
U11
proper
X1
proper
X2
proper
X3
proper
U12
X1
X2
X3
U12
proper
X1
proper
X2
proper
X3
proper
U111
X
U111
proper
X
proper
snd
X
snd
proper
X
proper
splitAt
X1
X2
splitAt
proper
X1
proper
X2
proper
U121
X
U121
proper
X
proper
U131
X1
X2
U131
proper
X1
proper
X2
proper
U132
X
U132
proper
X
proper
U141
X1
X2
U141
proper
X1
proper
X2
proper
U142
X
U142
proper
X
proper
U151
X1
X2
U151
proper
X1
proper
X2
proper
U152
X
U152
proper
X
proper
U161
X1
X2
U161
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
U171
X1
X2
X3
U171
proper
X1
proper
X2
proper
X3
proper
U172
X1
X2
X3
U172
proper
X1
proper
X2
proper
X3
proper
head
X
head
proper
X
proper
afterNth
X1
X2
afterNth
proper
X1
proper
X2
proper
U181
X1
X2
U181
proper
X1
proper
X2
proper
U182
X1
X2
U182
proper
X1
proper
X2
proper
U191
X1
X2
U191
proper
X1
proper
X2
proper
pair
X1
X2
pair
proper
X1
proper
X2
proper
nil
ok
nil
proper
U201
X1
X2
X3
X4
U201
proper
X1
proper
X2
proper
X3
proper
X4
proper
U202
X1
X2
X3
X4
U202
proper
X1
proper
X2
proper
X3
proper
X4
proper
isNatural
X
isNatural
proper
X
proper
U203
X1
X2
X3
X4
U203
proper
X1
proper
X2
proper
X3
proper
X4
proper
U204
X1
X2
U204
proper
X1
proper
X2
proper
U21
X1
X2
X3
U21
proper
X1
proper
X2
proper
X3
proper
U22
X1
X2
U22
proper
X1
proper
X2
proper
U211
X1
X2
U211
proper
X1
proper
X2
proper
U212
X1
X2
U212
proper
X1
proper
X2
proper
U221
X1
X2
X3
U221
proper
X1
proper
X2
proper
X3
proper
U222
X1
X2
X3
U222
proper
X1
proper
X2
proper
X3
proper
fst
X
fst
proper
X
proper
U31
X1
X2
X3
U31
proper
X1
proper
X2
proper
X3
proper
U32
X1
X2
U32
proper
X1
proper
X2
proper
U41
X1
X2
U41
proper
X1
proper
X2
proper
U42
X
U42
proper
X
proper
U51
X1
X2
U51
proper
X1
proper
X2
proper
U52
X
U52
proper
X
proper
U61
X
U61
proper
X
proper
U71
X
U71
proper
X
proper
U81
X
U81
proper
X
proper
U91
X
U91
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
U101
X1
X2
U102
ok
X
ok
U102
X
isLNat
ok
X
ok
isLNat
X
U11
ok
X1
ok
X2
ok
X3
ok
U11
X1
X2
X3
U12
ok
X1
ok
X2
ok
X3
ok
U12
X1
X2
X3
U111
ok
X
ok
U111
X
snd
ok
X
ok
snd
X
splitAt
ok
X1
ok
X2
ok
splitAt
X1
X2
U121
ok
X
ok
U121
X
U131
ok
X1
ok
X2
ok
U131
X1
X2
U132
ok
X
ok
U132
X
U141
ok
X1
ok
X2
ok
U141
X1
X2
U142
ok
X
ok
U142
X
U151
ok
X1
ok
X2
ok
U151
X1
X2
U152
ok
X
ok
U152
X
U161
ok
X1
ok
X2
ok
U161
X1
X2
cons
ok
X1
ok
X2
ok
cons
X1
X2
natsFrom
ok
X
ok
natsFrom
X
s
ok
X
ok
s
X
U171
ok
X1
ok
X2
ok
X3
ok
U171
X1
X2
X3
U172
ok
X1
ok
X2
ok
X3
ok
U172
X1
X2
X3
head
ok
X
ok
head
X
afterNth
ok
X1
ok
X2
ok
afterNth
X1
X2
U181
ok
X1
ok
X2
ok
U181
X1
X2
U182
ok
X1
ok
X2
ok
U182
X1
X2
U191
ok
X1
ok
X2
ok
U191
X1
X2
pair
ok
X1
ok
X2
ok
pair
X1
X2
U201
ok
X1
ok
X2
ok
X3
ok
X4
ok
U201
X1
X2
X3
X4
U202
ok
X1
ok
X2
ok
X3
ok
X4
ok
U202
X1
X2
X3
X4
isNatural
ok
X
ok
isNatural
X
U203
ok
X1
ok
X2
ok
X3
ok
X4
ok
U203
X1
X2
X3
X4
U204
ok
X1
ok
X2
ok
U204
X1
X2
U21
ok
X1
ok
X2
ok
X3
ok
U21
X1
X2
X3
U22
ok
X1
ok
X2
ok
U22
X1
X2
U211
ok
X1
ok
X2
ok
U211
X1
X2
U212
ok
X1
ok
X2
ok
U212
X1
X2
U221
ok
X1
ok
X2
ok
X3
ok
U221
X1
X2
X3
U222
ok
X1
ok
X2
ok
X3
ok
U222
X1
X2
X3
fst
ok
X
ok
fst
X
U31
ok
X1
ok
X2
ok
X3
ok
U31
X1
X2
X3
U32
ok
X1
ok
X2
ok
U32
X1
X2
U41
ok
X1
ok
X2
ok
U41
X1
X2
U42
ok
X
ok
U42
X
U51
ok
X1
ok
X2
ok
U51
X1
X2
U52
ok
X
ok
U52
X
U61
ok
X
ok
U61
X
U71
ok
X
ok
U71
X
U81
ok
X
ok
U81
X
U91
ok
X
ok
U91
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
afterNth
X1
X2
active
X2
active
snd
pair
X
Y
U181
isLNat
X
Y
active
U22
X1
X2
U22
active
X1
X2
proper
U52
X
U52
proper
X
active
U204
X1
X2
active
X1
active
isNatural
s
V1
U121
isNatural
V1
proper
U151
X1
X2
U151
proper
X1
proper
X2
U191
ok
X1
ok
X2
U191
X1
X2
U221
ok
X1
ok
X2
ok
X3
U221
X1
X2
X3
active
splitAt
s
N
cons
X
XS
U201
isNatural
N
N
X
XS
U42
ok
X
U42
X
active
U141
X1
X2
U141
active
X1
X2
active
U121
X
U121
active
X
U52
ok
X
U52
X
top
mark
X
proper
X
proper
U161
X1
X2
proper
X2
proper
U141
X1
X2
U141
proper
X1
proper
X2
proper
U172
X1
X2
X3
proper
X2
active
U12
tt
N
XS
snd
splitAt
N
XS
active
U182
X1
X2
active
X1
U52
mark
X
U52
X
active
isLNat
cons
V1
V2
isNatural
V1
U152
mark
X
U152
X
active
take
N
XS
U221
isNatural
N
N
XS
proper
U211
X1
X2
U211
proper
X1
proper
X2
proper
U31
X1
X2
X3
proper
X1
active
tail
cons
N
XS
isNatural
N
U51
mark
X1
X2
U51
X1
X2
U102
ok
X
U102
X
proper
U121
X
proper
X
U152
ok
X
U152
X
active
U202
tt
N
X
XS
isLNat
XS
proper
isPLNat
X
isPLNat
proper
X
active
U182
X1
X2
U182
active
X1
X2
proper
U221
X1
X2
X3
proper
X3
active
take
X1
X2
take
active
X1
X2
active
U71
X
active
X
active
sel
X1
X2
active
X1
proper
U141
X1
X2
proper
X1
active
U151
X1
X2
active
X1
U212
mark
X1
X2
U212
X1
X2
active
U152
X
active
X
active
U131
X1
X2
active
X1
active
tail
X
tail
active
X
proper
isLNat
X
isLNat
proper
X
snd
mark
X
snd
X
active
pair
X1
X2
pair
X1
active
X2
proper
U131
X1
X2
U131
proper
X1
proper
X2
U91
ok
X
U91
X
proper
U202
X1
X2
X3
X4
U202
proper
X1
proper
X2
proper
X3
proper
X4
proper
tail
X
tail
proper
X
proper
U142
X
proper
X
active
isLNat
take
V1
V2
U101
isNatural
V1
V2
proper
U51
X1
X2
U51
proper
X1
proper
X2
active
U32
X1
X2
U32
active
X1
X2
active
afterNth
N
XS
U11
isNatural
N
N
XS
U51
ok
X1
ok
X2
U51
X1
X2
active
U11
X1
X2
X3
active
X1
active
U211
tt
XS
isLNat
XS
head
ok
X
head
X
U132
ok
X
U132
X
active
isLNat
tail
V1
isLNat
V1
active
U151
tt
V2
isLNat
V2
active
U141
tt
V2
U142
isLNat
V2
splitAt
X1
mark
X2
splitAt
X1
X2
active
pair
X1
X2
active
X2
active
U201
X1
X2
X3
X4
U201
active
X1
X2
X3
X4
active
fst
pair
X
Y
U21
isLNat
X
X
Y
active
U142
X
active
X
active
U131
tt
V2
isLNat
V2
active
U21
tt
X
Y
U22
isLNat
Y
X
proper
U171
X1
X2
X3
proper
X3
active
U142
X
U142
active
X
active
U203
X1
X2
X3
X4
U203
active
X1
X2
X3
X4
U141
ok
X1
ok
X2
U141
X1
X2
active
U51
tt
V2
U52
isLNat
V2
proper
isLNat
X
proper
X
proper
U21
X1
X2
X3
U21
proper
X1
proper
X2
proper
X3
active
U161
tt
N
s
N
active
U71
X
U71
active
X
cons
ok
X1
ok
X2
cons
X1
X2
U204
ok
X1
ok
X2
U204
X1
X2
active
take
X1
X2
active
X1
U151
ok
X1
ok
X2
U151
X1
X2
active
U221
X1
X2
X3
U221
active
X1
X2
X3
U212
ok
X1
ok
X2
U212
X1
X2
proper
U22
X1
X2
U22
proper
X1
proper
X2
proper
U31
X1
X2
X3
proper
X3
U202
ok
X1
ok
X2
ok
X3
ok
X4
U202
X1
X2
X3
X4
proper
U32
X1
X2
proper
X1
active
isPLNat
splitAt
V1
V2
U151
isNatural
V1
V2
proper
U71
X
proper
X
active
U101
tt
V2
isLNat
V2
active
U41
X1
X2
active
X1
U142
ok
X
U142
X
U222
mark
X1
X2
X3
U222
X1
X2
X3
active
U31
tt
N
XS
isLNat
XS
active
U181
tt
Y
U182
isLNat
Y
Y
active
head
X
head
active
X
active
U171
tt
N
XS
isLNat
XS
active
splitAt
X1
X2
splitAt
active
X1
X2
proper
U222
X1
X2
X3
proper
X3
proper
U161
X1
X2
U161
proper
X1
proper
X2
proper
cons
X1
X2
cons
proper
X1
proper
X2
active
isNatural
sel
V1
V2
U131
isNatural
V1
V2
active
sel
X1
X2
sel
X1
active
X2
U204
mark
X1
X2
U204
X1
X2
proper
U202
X1
X2
X3
X4
proper
X2
proper
U171
X1
X2
X3
proper
X1
active
isNatural
head
V1
U111
isLNat
V1
proper
U51
X1
X2
proper
X2
active
U121
X
active
X
active
cons
X1
X2
active
X1
active
U212
X1
X2
active
X1
U121
ok
X
U121
X
active
U201
X1
X2
X3
X4
active
X1
U171
mark
X1
X2
X3
U171
X1
X2
X3
proper
U172
X1
X2
X3
U172
proper
X1
proper
X2
proper
X3
U172
mark
X1
X2
X3
U172
X1
X2
X3
U131
mark
X1
X2
U131
X1
X2
active
U181
X1
X2
U181
active
X1
X2
proper
U111
X
U111
proper
X
active
natsFrom
X
natsFrom
active
X
proper
splitAt
X1
X2
proper
X1
active
U151
tt
V2
U152
isLNat
V2
tail
ok
X
tail
X
U32
ok
X1
ok
X2
U32
X1
X2
proper
U131
X1
X2
proper
X1
active
splitAt
0
XS
U191
isLNat
XS
XS
active
isLNat
snd
V1
U81
isPLNat
V1
proper
U22
X1
X2
proper
X2
active
U81
X
U81
active
X
proper
U11
X1
X2
X3
U11
proper
X1
proper
X2
proper
X3
isNatural
ok
X
isNatural
X
proper
isNatural
X
proper
X
active
U172
X1
X2
X3
U172
active
X1
X2
X3
active
U222
X1
X2
X3
active
X1
active
U12
X1
X2
X3
U12
active
X1
X2
X3
active
U191
X1
X2
active
X1
active
sel
X1
X2
sel
active
X1
X2
proper
U32
X1
X2
U32
proper
X1
proper
X2
active
U201
tt
N
X
XS
isNatural
X
proper
U21
X1
X2
X3
proper
X1
U41
mark
X1
X2
U41
X1
X2
active
sel
N
XS
U171
isNatural
N
N
XS
proper
natsFrom
X
proper
X
active
U52
X
active
X
active
splitAt
X1
X2
active
X1
proper
head
X
head
proper
X
pair
ok
X1
ok
X2
pair
X1
X2
active
U152
X
U152
active
X
proper
fst
X
fst
proper
X
proper
cons
X1
X2
proper
X2
active
U21
X1
X2
X3
active
X1
proper
U171
X1
X2
X3
U171
proper
X1
proper
X2
proper
X3
active
tail
cons
N
XS
U211
isNatural
N
XS
proper
U191
X1
X2
proper
X2
proper
U182
X1
X2
U182
proper
X1
proper
X2
active
U203
tt
N
X
XS
U204
splitAt
N
XS
X
proper
U151
X1
X2
proper
X1
proper
U61
X
U61
proper
X
active
isLNat
tail
V1
U91
isLNat
V1
U102
mark
X
U102
X
afterNth
mark
X1
X2
afterNth
X1
X2
proper
U132
X
proper
X
U11
ok
X1
ok
X2
ok
X3
U11
X1
X2
X3
proper
sel
X1
X2
proper
X1
proper
pair
X1
X2
proper
X1
U172
ok
X1
ok
X2
ok
X3
U172
X1
X2
X3
active
U91
X
U91
active
X
active
U204
pair
YS
ZS
X
cons
X
YS
active
U111
X
U111
active
X
proper
U12
X1
X2
X3
proper
X1
top
mark
X
top
proper
X
active
snd
X
active
X
active
U12
tt
N
XS
splitAt
N
XS
U21
mark
X1
X2
X3
U21
X1
X2
X3
active
U41
tt
V2
U42
isLNat
V2
active
sel
X1
X2
active
X2
proper
U221
X1
X2
X3
proper
X1
active
U222
X1
X2
X3
U222
active
X1
X2
X3
head
mark
X
head
X
active
cons
X1
X2
cons
active
X1
X2
proper
U91
X
U91
proper
X
active
U12
X1
X2
X3
active
X1
top
ok
X
active
X
active
splitAt
s
N
cons
X
XS
isNatural
N
U91
mark
X
U91
X
active
fst
X
fst
active
X
proper
U203
X1
X2
X3
X4
U203
proper
X1
proper
X2
proper
X3
proper
X4
U81
ok
X
U81
X
active
U171
X1
X2
X3
active
X1
proper
U12
X1
X2
X3
proper
X2
proper
natsFrom
X
natsFrom
proper
X
take
ok
X1
ok
X2
take
X1
X2
U201
ok
X1
ok
X2
ok
X3
ok
X4
U201
X1
X2
X3
X4
active
isNatural
head
V1
isLNat
V1
active
U91
X
active
X
active
U102
X
active
X
proper
isPLNat
X
proper
X
proper
U171
X1
X2
X3
proper
X2
proper
U11
X1
X2
X3
proper
X1
proper
U161
X1
X2
proper
X1
U41
ok
X1
ok
X2
U41
X1
X2
U71
mark
X
U71
X
proper
U132
X
U132
proper
X
active
U161
X1
X2
U161
active
X1
X2
proper
U101
X1
X2
U101
proper
X1
proper
X2
top
ok
X
top
active
X
proper
snd
X
proper
X
proper
U111
X
proper
X
U181
mark
X1
X2
U181
X1
X2
proper
U211
X1
X2
proper
X2
proper
s
X
s
proper
X
active
isLNat
snd
V1
isPLNat
V1
active
U132
X
U132
active
X
proper
U182
X1
X2
proper
X1
proper
U142
X
U142
proper
X
sel
mark
X1
X2
sel
X1
X2
active
U51
X1
X2
U51
active
X1
X2
active
U101
X1
X2
U101
active
X1
X2
sel
X1
mark
X2
sel
X1
X2
proper
cons
X1
X2
proper
X1
active
splitAt
0
XS
isLNat
XS
isLNat
ok
X
isLNat
X
pair
X1
mark
X2
pair
X1
X2
active
U101
tt
V2
U102
isLNat
V2
proper
take
X1
X2
take
proper
X1
proper
X2
U202
mark
X1
X2
X3
X4
U202
X1
X2
X3
X4
active
head
X
active
X
U182
ok
X1
ok
X2
U182
X1
X2
proper
U191
X1
X2
proper
X1
active
U221
tt
N
XS
isLNat
XS
active
U21
tt
X
Y
isLNat
Y
active
pair
X1
X2
pair
active
X1
X2
proper
U221
X1
X2
X3
proper
X2
cons
mark
X1
X2
cons
X1
X2
U151
mark
X1
X2
U151
X1
X2
isPLNat
ok
X
isPLNat
X
U131
ok
X1
ok
X2
U131
X1
X2
active
U32
X1
X2
active
X1
active
afterNth
X1
X2
active
X1
proper
U42
X
U42
proper
X
active
U212
X1
X2
U212
active
X1
X2
active
U211
X1
X2
active
X1
natsFrom
ok
X
natsFrom
X
active
U131
tt
V2
U132
isLNat
V2
active
U161
tt
N
cons
N
natsFrom
s
N
U182
mark
X1
X2
U182
X1
X2
proper
U204
X1
X2
U204
proper
X1
proper
X2
active
U172
X1
X2
X3
active
X1
U61
ok
X
U61
X
active
tail
X
active
X
active
take
N
XS
isNatural
N
active
U102
X
U102
active
X
proper
U151
X1
X2
proper
X2
active
splitAt
X1
X2
splitAt
X1
active
X2
active
U111
X
active
X
U31
mark
X1
X2
X3
U31
X1
X2
X3
active
U11
X1
X2
X3
U11
active
X1
X2
X3
proper
fst
X
proper
X
proper
U101
X1
X2
proper
X2
active
head
cons
N
XS
isNatural
N
active
afterNth
N
XS
isNatural
N
fst
ok
X
fst
X
active
U151
X1
X2
U151
active
X1
X2
proper
U203
X1
X2
X3
X4
proper
X2
proper
U221
X1
X2
X3
U221
proper
X1
proper
X2
proper
X3
U101
mark
X1
X2
U101
X1
X2
proper
U212
X1
X2
U212
proper
X1
proper
X2
active
U31
tt
N
XS
U32
isLNat
XS
N
proper
U203
X1
X2
X3
X4
proper
X1
active
U22
X1
X2
active
X1
active
U172
tt
N
XS
afterNth
N
XS
s
ok
X
s
X
proper
U172
X1
X2
X3
proper
X3
U21
ok
X1
ok
X2
ok
X3
U21
X1
X2
X3
U111
ok
X
U111
X
pair
mark
X1
X2
pair
X1
X2
proper
U31
X1
X2
X3
U31
proper
X1
proper
X2
proper
X3
active
U204
X1
X2
U204
active
X1
X2
active
natsFrom
X
active
X
proper
sel
X1
X2
sel
proper
X1
proper
X2
proper
U81
X
proper
X
U11
mark
X1
X2
X3
U11
X1
X2
X3
active
U171
tt
N
XS
U172
isLNat
XS
N
XS
U161
mark
X1
X2
U161
X1
X2
active
take
X1
X2
active
X2
active
isPLNat
pair
V1
V2
U141
isLNat
V1
V2
active
U181
X1
X2
active
X1
active
U201
tt
N
X
XS
U202
isNatural
X
N
X
XS
active
pair
X1
X2
active
X1
active
U131
X1
X2
U131
active
X1
X2
active
U61
X
active
X
afterNth
X1
mark
X2
afterNth
X1
X2
U22
ok
X1
ok
X2
U22
X1
X2
U121
mark
X
U121
X
active
isLNat
take
V1
V2
isNatural
V1
snd
ok
X
snd
X
U203
ok
X1
ok
X2
ok
X3
ok
X4
U203
X1
X2
X3
X4
active
U202
X1
X2
X3
X4
U202
active
X1
X2
X3
X4
U171
ok
X1
ok
X2
ok
X3
U171
X1
X2
X3
active
U203
X1
X2
X3
X4
active
X1
active
s
X
active
X
active
U141
X1
X2
active
X1
active
snd
pair
X
Y
isLNat
X
proper
U121
X
U121
proper
X
active
snd
X
snd
active
X
proper
U222
X1
X2
X3
proper
X1
active
natsFrom
N
isNatural
N
U42
mark
X
U42
X
active
isLNat
cons
V1
V2
U51
isNatural
V1
V2
proper
U202
X1
X2
X3
X4
proper
X3
active
sel
N
XS
isNatural
N
U81
mark
X
U81
X
U203
mark
X1
X2
X3
X4
U203
X1
X2
X3
X4
proper
splitAt
X1
X2
splitAt
proper
X1
proper
X2
U211
mark
X1
X2
U211
X1
X2
active
U161
tt
N
natsFrom
s
N
proper
head
X
proper
X
proper
U201
X1
X2
X3
X4
proper
X3
proper
U201
X1
X2
X3
X4
proper
X1
active
U11
tt
N
XS
isLNat
XS
U32
mark
X1
X2
U32
X1
X2
proper
tail
X
proper
X
proper
U181
X1
X2
proper
X2
active
U52
X
U52
active
X
active
isLNat
fst
V1
U61
isPLNat
V1
proper
take
X1
X2
proper
X1
proper
U31
X1
X2
X3
proper
X2
active
isNatural
sel
V1
V2
isNatural
V1
active
U221
tt
N
XS
U222
isLNat
XS
N
XS
proper
U42
X
proper
X
active
isPLNat
splitAt
V1
V2
isNatural
V1
active
U222
tt
N
XS
fst
splitAt
N
XS
U12
ok
X1
ok
X2
ok
X3
U12
X1
X2
X3
s
mark
X
s
X
proper
U211
X1
X2
proper
X1
proper
U131
X1
X2
proper
X2
proper
U204
X1
X2
proper
X2
U71
ok
X
U71
X
proper
U191
X1
X2
U191
proper
X1
proper
X2
proper
U152
X
proper
X
proper
splitAt
X1
X2
proper
X2
active
U42
X
active
X
active
U211
tt
XS
U212
isLNat
XS
XS
active
isLNat
natsFrom
V1
U71
isNatural
V1
active
U42
X
U42
active
X
active
head
cons
N
XS
U31
isNatural
N
N
XS
U101
ok
X1
ok
X2
U101
X1
X2
proper
U41
X1
X2
proper
X1
U111
mark
X
U111
X
fst
mark
X
fst
X
proper
U201
X1
X2
X3
X4
proper
X2
proper
U222
X1
X2
X3
proper
X2
U31
ok
X1
ok
X2
ok
X3
U31
X1
X2
X3
proper
U102
X
U102
proper
X
proper
U21
X1
X2
X3
proper
X3
U12
mark
X1
X2
X3
U12
X1
X2
X3
active
natsFrom
N
U161
isNatural
N
N
proper
U202
X1
X2
X3
X4
proper
X1
proper
U81
X
U81
proper
X
proper
sel
X1
X2
proper
X2
active
U161
X1
X2
active
X1
active
splitAt
X1
X2
active
X2
afterNth
ok
X1
ok
X2
afterNth
X1
X2
active
U51
tt
V2
isLNat
V2
proper
U101
X1
X2
proper
X1
proper
U61
X
proper
X
active
U101
X1
X2
active
X1
active
U202
tt
N
X
XS
U203
isLNat
XS
N
X
XS
proper
U204
X1
X2
proper
X1
proper
snd
X
snd
proper
X
active
U222
tt
N
XS
splitAt
N
XS
splitAt
mark
X1
X2
splitAt
X1
X2
proper
afterNth
X1
X2
proper
X2
proper
U182
X1
X2
proper
X2
active
U181
tt
Y
isLNat
Y
U221
mark
X1
X2
X3
U221
X1
X2
X3
take
X1
mark
X2
take
X1
X2
active
U41
X1
X2
U41
active
X1
X2
take
mark
X1
X2
take
X1
X2
proper
pair
X1
X2
proper
X2
U132
mark
X
U132
X
proper
U212
X1
X2
proper
X2
proper
U172
X1
X2
X3
proper
X1
active
U191
X1
X2
U191
active
X1
X2
U201
mark
X1
X2
X3
X4
U201
X1
X2
X3
X4
proper
U141
X1
X2
proper
X2
active
U51
X1
X2
active
X1
U181
ok
X1
ok
X2
U181
X1
X2
active
take
X1
X2
take
X1
active
X2
proper
U11
X1
X2
X3
proper
X3
proper
isNatural
X
isNatural
proper
X
active
isLNat
afterNth
V1
V2
U41
isNatural
V1
V2
active
U31
X1
X2
X3
U31
active
X1
X2
X3
proper
U181
X1
X2
U181
proper
X1
proper
X2
proper
U22
X1
X2
proper
X1
U191
mark
X1
X2
U191
X1
X2
U142
mark
X
U142
X
active
U31
X1
X2
X3
active
X1
proper
U12
X1
X2
X3
U12
proper
X1
proper
X2
proper
X3
active
afterNth
X1
X2
afterNth
X1
active
X2
active
U11
tt
N
XS
U12
isLNat
XS
N
XS
active
U141
tt
V2
isLNat
V2
proper
s
X
proper
X
active
fst
pair
X
Y
isLNat
X
sel
ok
X1
ok
X2
sel
X1
X2
proper
U51
X1
X2
proper
X1
proper
U202
X1
X2
X3
X4
proper
X4
proper
U41
X1
X2
proper
X2
proper
U71
X
U71
proper
X
proper
U203
X1
X2
X3
X4
proper
X4
U161
ok
X1
ok
X2
U161
X1
X2
proper
U41
X1
X2
U41
proper
X1
proper
X2
U141
mark
X1
X2
U141
X1
X2
proper
pair
X1
X2
pair
proper
X1
proper
X2
active
U41
tt
V2
isLNat
V2
proper
U181
X1
X2
proper
X1
U211
ok
X1
ok
X2
U211
X1
X2
active
U221
X1
X2
X3
active
X1
U61
mark
X
U61
X
active
U211
X1
X2
U211
active
X1
X2
active
U61
X
U61
active
X
active
isPLNat
pair
V1
V2
isLNat
V1
active
U171
X1
X2
X3
U171
active
X1
X2
X3
proper
U201
X1
X2
X3
X4
U201
proper
X1
proper
X2
proper
X3
proper
X4
proper
U203
X1
X2
X3
X4
proper
X3
proper
U212
X1
X2
proper
X1
tail
mark
X
tail
X
active
U203
tt
N
X
XS
splitAt
N
XS
active
U202
X1
X2
X3
X4
active
X1
splitAt
ok
X1
ok
X2
splitAt
X1
X2
active
U81
X
active
X
proper
U11
X1
X2
X3
proper
X2
active
U172
tt
N
XS
head
afterNth
N
XS
active
fst
X
active
X
natsFrom
mark
X
natsFrom
X
proper
U201
X1
X2
X3
X4
proper
X4
proper
U102
X
proper
X
proper
U91
X
proper
X
proper
U152
X
U152
proper
X
active
U21
X1
X2
X3
U21
active
X1
X2
X3
proper
afterNth
X1
X2
afterNth
proper
X1
proper
X2
active
U191
tt
XS
pair
nil
XS
proper
U21
X1
X2
X3
proper
X2
U222
ok
X1
ok
X2
ok
X3
U222
X1
X2
X3
active
isLNat
afterNth
V1
V2
isNatural
V1
active
isLNat
fst
V1
isPLNat
V1
proper
U52
X
proper
X
proper
take
X1
X2
proper
X2
active
U204
pair
YS
ZS
X
pair
cons
X
YS
ZS
proper
afterNth
X1
X2
proper
X1
proper
U32
X1
X2
proper
X2
proper
U12
X1
X2
X3
proper
X3
active
U132
X
active
X
active
isLNat
natsFrom
V1
isNatural
V1
U22
mark
X1
X2
U22
X1
X2
proper
U222
X1
X2
X3
U222
proper
X1
proper
X2
proper
X3
active
s
X
s
active
X
active
afterNth
X1
X2
afterNth
active
X1
X2
active
isNatural
s
V1
isNatural
V1
true
top
ok
X
top
active
X
top
mark
X
top
proper
X
true
Failed!
NaTT
certifiable-1.6