reference documentation

Article list-interval-def.art

path: "vendor/opentheory/data/theories/list-interval-def/list-interval-def.art"

20452 bytes
6
version
"Data.List.interval"
"interval"
"->"
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0
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nil
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0
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1
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"Data.List.list"
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1
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nil
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2
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3
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nil
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cons
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5
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nil
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cons
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7
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var
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nil
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cons
nil
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8
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"Data.Bool./\\"
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0
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"bool"
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nil
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9
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0
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9
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9
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nil
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11
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nil
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cons
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constTerm
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"Data.Bool.!"
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14
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0
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0
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1
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15
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10
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cons
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constTerm
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"m"
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var
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"="
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0
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0
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10
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cons
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constTerm
19
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8
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varTerm
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17
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varTerm
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appTerm
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def
"Number.Natural.zero"
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1
ref
constTerm
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appTerm
appTerm
"Data.List.[]"
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3
ref
constTerm
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def
appTerm
absTerm
appTerm
appTerm
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ref
17
ref
16
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"n"
1
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var
25
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19
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22
remove
"Number.Natural.suc"
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0
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1
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2
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cons
opType
constTerm
26
def
25
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varTerm
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appTerm
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def
appTerm
appTerm
"Data.List.::"
const
0
ref
1
ref
0
ref
3
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4
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cons
opType
nil
cons
cons
opType
constTerm
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appTerm
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20
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remove
21
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appTerm
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appTerm
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appTerm
appTerm
appTerm
absTerm
appTerm
absTerm
appTerm
appTerm
absTerm
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refl
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def
18
ref
0
ref
7
ref
0
ref
7
ref
10
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cons
opType
33
def
nil
cons
cons
opType
constTerm
34
def
20
ref
appTerm
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def
"select"
const
36
def
0
ref
33
ref
7
ref
nil
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cons
opType
constTerm
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def
31
ref
appTerm
appTerm
assume
sym
appThm
31
ref
20
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appTerm
betaConv
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def
trans
"A"
37
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cons
nil
cons
40
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nil
nil
cons
41
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cons
42
def
nil
18
ref
0
ref
0
ref
0
ref
"A"
varType
43
def
10
ref
cons
opType
44
def
10
ref
cons
opType
45
def
0
ref
45
ref
10
ref
cons
opType
nil
cons
cons
opType
constTerm
46
def
"Data.Bool.?"
const
47
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45
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constTerm
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appTerm
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"p"
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var
50
def
50
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varTerm
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0
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nil
cons
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cons
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constTerm
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appTerm
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appTerm
axiom
subst
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appThm
"p"
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var
53
def
53
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varTerm
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38
remove
54
remove
appTerm
appTerm
absTerm
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appTerm
betaConv
trans
47
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0
ref
33
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10
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cons
opType
55
def
constTerm
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refl
"fn"
7
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var
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def
13
ref
18
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0
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5
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0
ref
5
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10
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cons
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nil
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cons
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constTerm
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varTerm
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23
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appTerm
appTerm
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absTerm
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appTerm
appTerm
refl
16
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refl
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25
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59
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28
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appTerm
appTerm
refl
"_16238"
5
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var
62
def
25
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17
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29
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62
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varTerm
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appTerm
appTerm
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def
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27
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appTerm
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appTerm
betaConv
27
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refl
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def
appThm
"n'"
1
ref
var
17
ref
29
ref
64
remove
30
ref
appTerm
appTerm
absTerm
absTerm
27
ref
appTerm
betaConv
trans
appThm
absThm
appThm
appThm
absThm
appThm
nil
"f"
0
ref
5
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37
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cons
opType
var
63
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nil
cons
cons
"e"
5
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var
60
ref
nil
cons
cons
nil
cons
cons
nil
cons
cons
"A"
6
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cons
nil
cons
41
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cons
"f"
0
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43
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0
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1
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52
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cons
opType
66
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nil
cons
67
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cons
opType
68
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var
69
def
"Data.Bool.?!"
const
70
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0
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0
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66
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10
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cons
opType
71
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10
ref
cons
opType
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constTerm
"fn"
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var
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13
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18
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0
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44
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nil
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constTerm
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23
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"e"
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var
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varTerm
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appTerm
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25
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75
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28
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appTerm
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varTerm
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appTerm
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appTerm
appTerm
absTerm
appTerm
appTerm
absTerm
79
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appTerm
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absTerm
81
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78
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appTerm
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betaConv
76
remove
14
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0
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0
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68
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10
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cons
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10
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cons
opType
constTerm
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absTerm
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77
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appTerm
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betaConv
nil
14
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45
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constTerm
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85
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appTerm
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axiom
nil
"p"
9
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var
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88
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nil
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cons
"q"
9
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var
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86
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nil
cons
cons
nil
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nil
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cons
18
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constTerm
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"Data.Bool.==>"
const
12
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constTerm
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89
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appTerm
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appTerm
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appTerm
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appTerm
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appTerm
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93
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appTerm
absTerm
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absTerm
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93
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appTerm
betaConv
94
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refl
101
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appThm
99
remove
94
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appTerm
betaConv
trans
appThm
nil
18
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0
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12
ref
0
ref
12
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10
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cons
opType
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nil
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cons
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constTerm
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92
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appTerm
100
remove
appTerm
axiom
93
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refl
104
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appThm
101
ref
appThm
eqMp
105
def
sym
106
def
98
remove
refl
90
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18
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0
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102
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0
ref
102
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10
ref
cons
opType
nil
cons
cons
opType
constTerm
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"f"
12
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var
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108
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varTerm
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93
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appTerm
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appTerm
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appTerm
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109
ref
"Data.Bool.T"
const
9
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constTerm
111
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appTerm
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appTerm
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112
def
appTerm
absTerm
113
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94
ref
appTerm
betaConv
appThm
18
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0
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11
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0
ref
11
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10
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cons
opType
114
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nil
cons
cons
opType
constTerm
115
def
96
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appTerm
refl
89
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113
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absTerm
116
def
93
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appTerm
betaConv
appThm
nil
103
remove
13
ref
appTerm
116
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appTerm
axiom
117
def
104
remove
appThm
eqMp
101
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appThm
eqMp
118
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sym
108
ref
109
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refl
nil
"t"
9
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var
119
def
93
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nil
cons
120
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cons
nil
cons
nil
cons
cons
91
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119
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varTerm
121
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appTerm
111
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appTerm
assume
sym
nil
111
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axiom
122
def
eqMp
121
remove
assume
122
ref
deductAntisym
deductAntisym
123
def
subst
93
ref
assume
124
def
eqMp
appThm
nil
119
ref
94
ref
nil
cons
125
def
cons
nil
cons
nil
cons
cons
123
ref
subst
94
ref
assume
eqMp
appThm
absThm
eqMp
126
def
nil
"P"
9
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var
127
def
120
remove
cons
"Q"
9
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var
128
def
125
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cons
nil
cons
cons
nil
cons
cons
91
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refl
129
def
108
ref
109
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127
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varTerm
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appTerm
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def
128
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varTerm
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def
appTerm
absTerm
133
def
89
ref
90
ref
93
ref
absTerm
absTerm
134
def
appTerm
betaConv
134
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130
ref
appTerm
betaConv
132
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refl
135
def
appThm
90
ref
130
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absTerm
132
ref
appTerm
betaConv
trans
trans
appThm
112
ref
134
ref
appTerm
betaConv
134
ref
111
ref
appTerm
betaConv
111
ref
refl
136
def
appThm
90
ref
111
ref
absTerm
111
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appTerm
betaConv
trans
trans
appThm
91
ref
13
ref
130
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appTerm
137
def
132
ref
appTerm
138
def
appTerm
refl
90
ref
107
remove
108
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131
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94
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appTerm
absTerm
appTerm
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appTerm
absTerm
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ref
appTerm
betaConv
appThm
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137
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appTerm
refl
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130
ref
appTerm
betaConv
appThm
117
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130
ref
refl
appThm
eqMp
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appThm
eqMp
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remove
assume
eqMp
139
def
134
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refl
appThm
eqMp
sym
122
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eqMp
140
def
subst
141
def
deductAntisym
eqMp
105
remove
95
ref
assume
eqMp
sym
124
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eqMp
129
ref
110
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89
ref
90
ref
94
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absTerm
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absTerm
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appTerm
betaConv
143
ref
93
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appTerm
betaConv
101
remove
appThm
142
ref
94
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appTerm
betaConv
trans
trans
appThm
112
remove
143
ref
appTerm
betaConv
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ref
111
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appTerm
betaConv
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appThm
142
ref
111
ref
appTerm
betaConv
trans
trans
144
def
appThm
118
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97
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assume
eqMp
143
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refl
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appThm
eqMp
sym
122
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eqMp
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def
proveHyp
deductAntisym
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def
subst
proveHyp
"A"
52
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cons
nil
cons
148
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"P"
44
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var
149
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85
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nil
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cons
"x"
43
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var
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77
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nil
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cons
nil
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nil
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varTerm
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appTerm
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nil
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cons
90
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varTerm
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appTerm
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nil
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cons
nil
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nil
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106
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subst
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126
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deductAntisym
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subst
91
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155
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appTerm
refl
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111
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absTerm
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154
ref
appTerm
betaConv
appThm
50
ref
18
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0
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44
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45
ref
nil
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cons
opType
constTerm
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appTerm
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appTerm
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151
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appTerm
betaConv
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nil
46
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87
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appTerm
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appTerm
axiom
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refl
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appThm
163
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152
ref
assume
eqMp
eqMp
154
ref
refl
appThm
eqMp
sym
122
ref
eqMp
eqMp
nil
127
ref
153
remove
cons
128
ref
156
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cons
nil
cons
cons
nil
cons
cons
140
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subst
deductAntisym
eqMp
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def
subst
eqMp
eqMp
nil
89
ref
84
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nil
cons
cons
90
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82
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nil
cons
cons
nil
cons
cons
nil
cons
cons
147
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subst
proveHyp
"A"
68
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nil
cons
cons
nil
cons
"P"
83
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var
81
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nil
cons
cons
"x"
68
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var
78
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nil
cons
cons
nil
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cons
nil
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cons
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subst
eqMp
eqMp
nil
89
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80
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nil
cons
cons
90
ref
47
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72
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constTerm
79
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appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
147
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subst
proveHyp
"A"
67
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cons
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"P"
71
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var
79
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nil
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cons
nil
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nil
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cons
nil
89
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70
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45
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constTerm
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nil
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cons
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90
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48
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151
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appTerm
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nil
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cons
nil
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nil
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106
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subst
nil
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90
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13
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150
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87
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"y"
43
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var
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92
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13
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155
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appTerm
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172
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varTerm
173
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appTerm
appTerm
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74
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appTerm
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appTerm
absTerm
appTerm
absTerm
appTerm
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appTerm
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nil
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cons
nil
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nil
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147
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subst
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appTerm
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refl
50
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13
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51
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appTerm
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appTerm
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appTerm
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appTerm
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appTerm
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appTerm
appTerm
absTerm
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def
151
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appTerm
betaConv
appThm
nil
46
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165
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appTerm
180
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appTerm
axiom
162
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appThm
eqMp
nil
89
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178
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176
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appTerm
nil
cons
cons
90
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92
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166
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appTerm
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appTerm
nil
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nil
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nil
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cons
147
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subst
proveHyp
177
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nil
89
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93
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appTerm
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appTerm
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nil
cons
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cons
90
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95
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cons
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nil
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106
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subst
184
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158
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subst
106
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158
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181
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assume
124
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eqMp
eqMp
141
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deductAntisym
eqMp
eqMp
nil
127
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182
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cons
128
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183
remove
cons
nil
cons
cons
nil
cons
cons
140
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subst
deductAntisym
eqMp
185
def
subst
eqMp
eqMp
nil
127
ref
170
ref
cons
186
def
128
ref
175
remove
nil
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cons
nil
cons
cons
nil
cons
cons
140
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subst
proveHyp
eqMp
nil
127
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167
remove
cons
128
ref
170
ref
cons
nil
cons
cons
nil
cons
cons
140
ref
subst
deductAntisym
eqMp
subst
eqMp
subst
subst
eqMp
nil
89
ref
56
ref
"_16237"
7
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var
187
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13
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58
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187
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varTerm
188
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23
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appTerm
189
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appTerm
60
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appTerm
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appTerm
16
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25
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58
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188
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28
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appTerm
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appTerm
17
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29
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27
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appTerm
30
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appTerm
appTerm
192
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absTerm
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appTerm
absTerm
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appTerm
195
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appTerm
196
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absTerm
197
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appTerm
198
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nil
cons
cons
90
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56
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187
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13
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16
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17
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19
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189
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21
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appTerm
appTerm
199
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24
ref
appTerm
200
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absTerm
201
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appTerm
202
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appTerm
16
ref
17
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16
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25
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19
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191
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21
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appTerm
appTerm
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192
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absTerm
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appTerm
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absTerm
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appTerm
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appTerm
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absTerm
210
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appTerm
211
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nil
cons
212
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cons
nil
cons
213
def
cons
nil
cons
cons
147
ref
subst
nil
"P"
33
remove
var
214
def
187
ref
92
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197
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188
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appTerm
215
def
appTerm
211
ref
appTerm
216
def
absTerm
nil
cons
cons
nil
cons
nil
cons
cons
42
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91
ref
152
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appTerm
refl
161
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appThm
163
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eqMp
sym
217
def
subst
218
def
subst
187
ref
nil
119
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216
remove
nil
cons
cons
nil
cons
nil
cons
cons
123
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subst
nil
89
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215
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nil
cons
219
def
cons
213
ref
cons
nil
cons
cons
220
def
106
ref
subst
220
remove
158
ref
subst
215
ref
betaConv
215
remove
assume
eqMp
nil
89
ref
196
remove
nil
cons
221
def
cons
213
remove
cons
nil
cons
cons
222
def
147
ref
subst
proveHyp
222
ref
106
ref
subst
222
remove
158
ref
subst
210
ref
188
ref
appTerm
223
def
betaConv
224
def
sym
nil
127
ref
190
ref
nil
cons
cons
128
ref
195
remove
nil
cons
225
def
cons
nil
cons
cons
nil
cons
cons
226
def
140
ref
subst
nil
"P"
15
remove
var
227
def
201
remove
nil
cons
cons
nil
cons
nil
cons
cons
"A"
2
remove
cons
nil
cons
228
def
41
ref
cons
217
ref
subst
229
def
subst
17
ref
nil
119
ref
200
remove
nil
cons
cons
nil
cons
nil
cons
cons
123
ref
subst
199
remove
refl
60
remove
21
ref
appTerm
betaConv
appThm
190
remove
assume
21
ref
refl
230
def
appThm
eqMp
eqMp
absThm
eqMp
proveHyp
nil
89
ref
202
remove
nil
cons
cons
90
ref
208
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
158
ref
subst
proveHyp
226
remove
129
remove
133
remove
143
ref
appTerm
betaConv
143
remove
130
remove
appTerm
betaConv
135
remove
appThm
142
remove
132
ref
appTerm
betaConv
trans
trans
appThm
144
remove
appThm
139
remove
145
remove
appThm
eqMp
sym
122
remove
eqMp
231
def
subst
nil
227
ref
207
remove
nil
cons
cons
nil
cons
nil
cons
cons
229
ref
subst
17
ref
nil
119
ref
206
remove
nil
cons
cons
nil
cons
nil
cons
cons
123
ref
subst
nil
227
ref
205
remove
nil
cons
cons
nil
cons
nil
cons
cons
229
remove
subst
25
ref
nil
119
ref
204
remove
nil
cons
cons
nil
cons
nil
cons
cons
123
ref
subst
203
remove
refl
193
remove
21
ref
appTerm
betaConv
appThm
194
ref
27
ref
appTerm
232
def
betaConv
nil
89
ref
225
remove
cons
90
ref
232
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
147
ref
subst
228
remove
227
remove
194
remove
nil
cons
cons
"x"
1
ref
var
27
ref
nil
cons
cons
nil
cons
cons
nil
cons
cons
164
ref
subst
eqMp
eqMp
230
ref
appThm
eqMp
eqMp
absThm
eqMp
eqMp
absThm
eqMp
proveHyp
eqMp
eqMp
40
ref
214
ref
210
ref
nil
cons
cons
233
def
"x"
7
ref
var
234
def
188
ref
nil
cons
cons
nil
cons
cons
nil
cons
cons
91
remove
169
ref
appTerm
235
def
refl
50
remove
14
ref
114
remove
constTerm
236
def
90
ref
92
ref
87
ref
150
ref
92
ref
179
remove
appTerm
94
ref
appTerm
absTerm
appTerm
appTerm
94
ref
appTerm
absTerm
appTerm
absTerm
237
def
151
remove
appTerm
betaConv
appThm
nil
49
remove
237
remove
appTerm
axiom
162
remove
appThm
eqMp
238
def
sym
nil
"P"
11
remove
var
239
def
128
ref
92
ref
87
ref
150
ref
92
ref
155
remove
appTerm
240
def
132
ref
appTerm
absTerm
241
def
appTerm
242
def
appTerm
132
ref
appTerm
243
def
absTerm
nil
cons
cons
nil
cons
nil
cons
cons
"A"
10
remove
cons
nil
cons
244
def
41
remove
cons
217
remove
subst
subst
128
ref
nil
119
ref
243
remove
nil
cons
cons
nil
cons
nil
cons
cons
123
ref
subst
nil
89
ref
242
remove
nil
cons
245
def
cons
246
def
90
ref
132
ref
nil
cons
247
def
cons
nil
cons
248
def
cons
nil
cons
cons
249
def
106
ref
subst
249
ref
158
ref
subst
nil
89
ref
156
remove
cons
248
ref
cons
nil
cons
cons
147
ref
subst
241
ref
154
ref
appTerm
250
def
betaConv
nil
246
ref
90
ref
250
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
147
ref
subst
148
remove
149
remove
241
remove
nil
cons
cons
150
ref
154
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
164
ref
subst
eqMp
eqMp
eqMp
eqMp
nil
127
ref
245
remove
cons
251
def
128
ref
247
ref
cons
nil
cons
252
def
cons
nil
cons
cons
140
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
eqMp
253
def
subst
proveHyp
eqMp
nil
127
ref
221
remove
cons
128
ref
212
ref
cons
nil
cons
254
def
cons
nil
cons
cons
140
ref
subst
deductAntisym
eqMp
eqMp
eqMp
nil
127
ref
219
remove
cons
254
ref
cons
nil
cons
cons
140
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
nil
89
ref
14
remove
55
remove
constTerm
255
def
234
ref
92
ref
197
ref
234
ref
varTerm
256
def
appTerm
appTerm
211
ref
appTerm
absTerm
appTerm
nil
cons
cons
90
ref
92
ref
198
remove
appTerm
211
ref
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
147
ref
subst
proveHyp
40
ref
214
ref
197
remove
nil
cons
cons
254
remove
cons
nil
cons
cons
nil
246
remove
90
ref
92
ref
169
remove
appTerm
257
def
132
ref
appTerm
nil
cons
258
def
cons
nil
cons
cons
nil
cons
cons
259
def
106
ref
subst
259
remove
158
ref
subst
nil
89
ref
170
remove
cons
260
def
248
remove
cons
nil
cons
cons
261
def
106
ref
subst
261
remove
158
ref
subst
249
remove
147
ref
subst
90
ref
92
ref
87
remove
150
remove
240
remove
94
ref
appTerm
absTerm
appTerm
appTerm
94
remove
appTerm
absTerm
262
def
132
remove
appTerm
263
def
betaConv
nil
260
remove
90
ref
236
remove
262
ref
appTerm
264
def
nil
cons
265
def
cons
nil
cons
cons
nil
cons
cons
266
def
147
ref
subst
238
remove
nil
89
ref
235
remove
264
ref
appTerm
nil
cons
cons
90
ref
257
remove
264
remove
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
147
ref
subst
proveHyp
266
remove
185
remove
subst
eqMp
eqMp
nil
89
ref
265
remove
cons
90
ref
263
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
147
ref
subst
proveHyp
244
remove
239
remove
262
remove
nil
cons
cons
"x"
9
remove
var
247
remove
cons
nil
cons
cons
nil
cons
cons
164
remove
subst
eqMp
eqMp
eqMp
eqMp
nil
186
remove
252
remove
cons
nil
cons
cons
140
ref
subst
deductAntisym
eqMp
eqMp
nil
251
remove
128
ref
258
remove
cons
nil
cons
cons
nil
cons
cons
140
ref
subst
deductAntisym
eqMp
267
def
subst
eqMp
eqMp
proveHyp
nil
89
ref
212
remove
cons
90
ref
56
remove
31
ref
appTerm
268
def
nil
cons
269
def
cons
nil
cons
270
def
cons
nil
cons
cons
147
ref
subst
nil
214
ref
187
ref
92
ref
223
ref
appTerm
268
ref
appTerm
271
def
absTerm
nil
cons
cons
nil
cons
nil
cons
cons
218
remove
subst
187
remove
nil
119
remove
271
remove
nil
cons
cons
nil
cons
nil
cons
cons
123
remove
subst
nil
89
ref
223
ref
nil
cons
272
def
cons
270
ref
cons
nil
cons
cons
273
def
106
ref
subst
273
remove
158
ref
subst
224
remove
223
remove
assume
eqMp
nil
89
ref
209
ref
nil
cons
274
def
cons
270
ref
cons
nil
cons
cons
275
def
147
ref
subst
proveHyp
275
ref
106
ref
subst
275
remove
158
ref
subst
"_16235"
1
ref
var
276
def
"_16236"
1
remove
var
277
def
188
remove
277
ref
varTerm
appTerm
278
def
276
remove
varTerm
appTerm
absTerm
absTerm
279
def
refl
nil
89
ref
34
remove
279
ref
appTerm
279
ref
appTerm
nil
cons
cons
270
ref
cons
nil
cons
cons
147
ref
subst
proveHyp
nil
8
remove
279
ref
nil
cons
cons
nil
cons
nil
cons
cons
nil
89
ref
35
remove
279
ref
appTerm
280
def
nil
cons
281
def
cons
270
remove
cons
nil
cons
cons
282
def
106
remove
subst
282
remove
158
remove
subst
39
remove
sym
13
remove
refl
61
ref
17
ref
19
ref
refl
283
def
280
remove
assume
284
def
230
remove
appThm
279
ref
21
ref
appTerm
betaConv
trans
285
def
nil
25
ref
23
ref
nil
cons
cons
nil
cons
nil
cons
cons
65
ref
subst
appThm
277
ref
278
ref
21
ref
appTerm
absTerm
286
def
23
ref
appTerm
betaConv
trans
appThm
24
ref
refl
appThm
absThm
appThm
appThm
61
ref
17
ref
61
remove
25
ref
283
remove
285
remove
28
ref
refl
appThm
286
remove
28
ref
appTerm
betaConv
trans
appThm
29
ref
refl
284
remove
30
ref
refl
appThm
279
remove
30
ref
appTerm
betaConv
trans
65
remove
appThm
277
remove
278
remove
30
ref
appTerm
absTerm
27
ref
appTerm
betaConv
trans
appThm
appThm
absThm
appThm
absThm
appThm
appThm
sym
209
remove
assume
eqMp
eqMp
40
ref
214
remove
31
remove
nil
cons
cons
234
ref
20
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
253
remove
subst
proveHyp
eqMp
nil
127
ref
281
remove
cons
128
ref
269
remove
cons
nil
cons
287
def
cons
nil
cons
cons
140
ref
subst
deductAntisym
eqMp
subst
eqMp
eqMp
nil
127
ref
274
remove
cons
287
ref
cons
nil
cons
cons
140
ref
subst
deductAntisym
eqMp
eqMp
eqMp
nil
127
ref
272
remove
cons
287
ref
cons
nil
cons
cons
140
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
nil
89
remove
255
remove
234
remove
92
ref
210
remove
256
remove
appTerm
appTerm
268
ref
appTerm
absTerm
appTerm
nil
cons
cons
90
remove
92
remove
211
remove
appTerm
268
remove
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
147
remove
subst
proveHyp
40
remove
233
remove
287
remove
cons
nil
cons
cons
267
remove
subst
eqMp
eqMp
proveHyp
eqMp
eqMp
defineConstList
288
def
pop
289
def
pop
288
ref
nil
127
remove
16
ref
17
ref
19
ref
289
remove
hdTl
pop
7
remove
constTerm
290
def
21
remove
appTerm
291
def
23
remove
appTerm
appTerm
24
remove
appTerm
absTerm
appTerm
292
def
nil
cons
cons
128
remove
16
ref
17
remove
16
remove
25
remove
19
remove
291
remove
28
remove
appTerm
appTerm
29
remove
290
remove
30
remove
appTerm
27
remove
appTerm
appTerm
appTerm
absTerm
appTerm
absTerm
appTerm
293
def
nil
cons
cons
nil
cons
cons
nil
cons
cons
294
def
231
remove
subst
proveHyp
nil
293
remove
thm
288
remove
294
remove
140
remove
subst
proveHyp
nil
292
remove
thm