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Article natural-mult-def.art

path: "vendor/opentheory/data/theories/natural-mult-def/natural-mult-def.art"

17445 bytes
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appTerm
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ref
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appTerm
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ref
appTerm
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18
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trans
"A"
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cons
nil
cons
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nil
nil
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cons
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def
nil
16
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0
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0
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0
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8
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8
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0
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cons
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def
"Data.Bool.?"
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51
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constTerm
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appTerm
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var
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varTerm
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nil
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cons
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var
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8
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cons
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constTerm
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refl
"fn"
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var
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def
11
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16
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0
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3
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0
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3
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cons
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cons
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varTerm
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appTerm
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19
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absTerm
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appTerm
appTerm
refl
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refl
15
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27
remove
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appTerm
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def
appTerm
appTerm
refl
"_2250"
3
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var
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def
26
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15
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varTerm
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appTerm
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appTerm
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def
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21
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appTerm
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appTerm
betaConv
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refl
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appThm
26
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"n'"
1
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var
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32
ref
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remove
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varTerm
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appTerm
appTerm
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appTerm
absTerm
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21
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appTerm
betaConv
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appThm
absThm
appThm
appThm
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appThm
nil
"f"
0
ref
3
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43
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cons
opType
var
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nil
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"e"
3
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var
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nil
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nil
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nil
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cons
"A"
4
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cons
nil
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cons
"f"
0
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0
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1
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cons
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nil
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cons
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var
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def
"Data.Bool.?!"
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0
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0
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74
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8
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cons
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8
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cons
opType
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constTerm
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var
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11
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16
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0
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nil
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constTerm
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appTerm
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"e"
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var
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varTerm
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appTerm
appTerm
14
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15
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83
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67
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appTerm
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77
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varTerm
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21
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appTerm
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21
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appTerm
appTerm
absTerm
appTerm
appTerm
absTerm
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appTerm
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absTerm
89
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86
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appTerm
90
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betaConv
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12
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0
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0
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8
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cons
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8
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cons
opType
constTerm
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appTerm
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absTerm
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85
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appTerm
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betaConv
nil
12
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51
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constTerm
95
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93
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appTerm
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axiom
nil
"p"
7
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var
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96
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nil
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"q"
7
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var
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nil
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nil
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nil
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cons
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10
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constTerm
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def
"Data.Bool.==>"
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10
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constTerm
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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
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101
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appTerm
absTerm
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absTerm
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101
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appTerm
betaConv
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refl
109
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appThm
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remove
102
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appTerm
betaConv
trans
appThm
nil
16
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0
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10
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0
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10
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8
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cons
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nil
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cons
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constTerm
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100
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appTerm
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appTerm
axiom
101
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refl
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appThm
109
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appThm
eqMp
113
def
sym
114
def
106
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refl
98
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16
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0
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110
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0
ref
110
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8
ref
cons
opType
nil
cons
cons
opType
constTerm
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"f"
10
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var
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116
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varTerm
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101
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appTerm
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appTerm
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appTerm
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"Data.Bool.T"
const
7
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constTerm
119
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appTerm
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appTerm
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appTerm
absTerm
121
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102
ref
appTerm
betaConv
appThm
16
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0
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9
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0
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9
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8
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cons
opType
122
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nil
cons
cons
opType
constTerm
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104
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appTerm
refl
97
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121
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absTerm
124
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101
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appTerm
betaConv
appThm
nil
111
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11
ref
appTerm
124
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appTerm
axiom
125
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112
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appThm
eqMp
109
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appThm
eqMp
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sym
116
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117
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refl
nil
"t"
7
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var
127
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101
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nil
cons
128
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cons
nil
cons
nil
cons
cons
99
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127
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varTerm
129
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appTerm
119
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appTerm
assume
sym
nil
119
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axiom
130
def
eqMp
129
remove
assume
130
ref
deductAntisym
deductAntisym
131
def
subst
101
ref
assume
132
def
eqMp
appThm
nil
127
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102
ref
nil
cons
133
def
cons
nil
cons
nil
cons
cons
131
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subst
102
ref
assume
eqMp
appThm
absThm
eqMp
134
def
nil
"P"
7
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var
135
def
128
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cons
"Q"
7
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var
136
def
133
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cons
nil
cons
cons
nil
cons
cons
99
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refl
137
def
116
ref
117
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135
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varTerm
138
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appTerm
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136
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varTerm
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def
appTerm
absTerm
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def
97
ref
98
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101
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absTerm
absTerm
142
def
appTerm
betaConv
142
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138
ref
appTerm
betaConv
140
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refl
143
def
appThm
98
ref
138
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absTerm
140
ref
appTerm
betaConv
trans
trans
appThm
120
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142
ref
appTerm
betaConv
142
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119
ref
appTerm
betaConv
119
ref
refl
144
def
appThm
98
ref
119
ref
absTerm
119
ref
appTerm
betaConv
trans
trans
appThm
99
ref
11
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138
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appTerm
145
def
140
ref
appTerm
146
def
appTerm
refl
98
ref
115
remove
116
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139
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102
ref
appTerm
absTerm
appTerm
120
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appTerm
absTerm
140
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appTerm
betaConv
appThm
123
remove
145
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appTerm
refl
124
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138
ref
appTerm
betaConv
appThm
125
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138
ref
refl
appThm
eqMp
143
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appThm
eqMp
146
remove
assume
eqMp
147
def
142
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refl
appThm
eqMp
sym
130
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eqMp
148
def
subst
149
def
deductAntisym
eqMp
113
remove
103
ref
assume
eqMp
sym
132
ref
eqMp
137
ref
118
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97
ref
98
ref
102
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absTerm
150
def
absTerm
151
def
appTerm
betaConv
151
ref
101
ref
appTerm
betaConv
109
remove
appThm
150
ref
102
ref
appTerm
betaConv
trans
trans
appThm
120
remove
151
ref
appTerm
betaConv
151
ref
119
ref
appTerm
betaConv
144
remove
appThm
150
ref
119
ref
appTerm
betaConv
trans
trans
152
def
appThm
126
remove
105
remove
assume
eqMp
151
ref
refl
153
def
appThm
eqMp
sym
130
ref
eqMp
154
def
proveHyp
deductAntisym
155
def
subst
proveHyp
"A"
58
remove
cons
nil
cons
156
def
"P"
50
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var
157
def
93
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nil
cons
cons
"x"
49
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var
158
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85
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nil
cons
cons
nil
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cons
nil
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cons
nil
97
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95
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varTerm
159
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appTerm
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nil
cons
161
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cons
98
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159
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varTerm
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appTerm
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nil
cons
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cons
nil
cons
cons
nil
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cons
165
def
114
ref
subst
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134
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deductAntisym
166
def
subst
99
ref
163
ref
appTerm
refl
158
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119
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absTerm
167
def
162
ref
appTerm
betaConv
appThm
56
ref
16
remove
0
remove
50
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51
ref
nil
cons
cons
opType
constTerm
57
ref
appTerm
167
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appTerm
absTerm
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def
159
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appTerm
betaConv
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def
nil
52
ref
95
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appTerm
168
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appTerm
axiom
159
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refl
170
def
appThm
171
def
160
ref
assume
eqMp
eqMp
162
ref
refl
appThm
eqMp
sym
130
ref
eqMp
eqMp
nil
135
ref
161
remove
cons
136
ref
164
ref
cons
nil
cons
cons
nil
cons
cons
148
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subst
deductAntisym
eqMp
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def
subst
eqMp
eqMp
nil
97
ref
92
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nil
cons
cons
98
ref
90
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nil
cons
cons
nil
cons
cons
nil
cons
cons
155
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subst
proveHyp
"A"
76
ref
nil
cons
cons
nil
cons
"P"
91
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var
89
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nil
cons
cons
"x"
76
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var
86
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nil
cons
cons
nil
cons
cons
nil
cons
cons
172
ref
subst
eqMp
eqMp
nil
97
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88
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nil
cons
cons
98
ref
53
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80
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constTerm
87
ref
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
155
ref
subst
proveHyp
"A"
75
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cons
nil
cons
"P"
79
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var
87
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nil
cons
cons
nil
cons
nil
cons
cons
nil
97
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78
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51
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constTerm
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159
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appTerm
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nil
cons
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cons
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98
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54
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159
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appTerm
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nil
cons
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cons
nil
cons
cons
nil
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cons
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def
114
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subst
179
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166
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subst
nil
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98
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11
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appTerm
95
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158
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95
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"y"
49
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var
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100
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11
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163
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appTerm
159
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180
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varTerm
181
def
appTerm
appTerm
appTerm
82
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162
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appTerm
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appTerm
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def
appTerm
absTerm
appTerm
absTerm
appTerm
183
def
appTerm
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def
nil
cons
cons
nil
cons
cons
nil
cons
cons
185
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155
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subst
99
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appTerm
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def
refl
56
ref
11
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54
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57
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appTerm
appTerm
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100
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11
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appTerm
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def
appTerm
57
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appTerm
appTerm
appTerm
182
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appTerm
absTerm
appTerm
absTerm
appTerm
appTerm
absTerm
188
def
159
ref
appTerm
betaConv
appThm
nil
52
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173
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appTerm
188
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appTerm
axiom
170
ref
appThm
eqMp
nil
97
ref
186
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184
ref
appTerm
nil
cons
cons
98
ref
100
ref
174
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appTerm
184
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appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
155
ref
subst
proveHyp
185
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nil
97
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99
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101
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appTerm
102
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appTerm
189
def
nil
cons
190
def
cons
98
ref
103
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nil
cons
191
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cons
nil
cons
cons
nil
cons
cons
192
def
114
ref
subst
192
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166
ref
subst
114
ref
166
ref
189
remove
assume
132
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eqMp
eqMp
149
remove
deductAntisym
eqMp
eqMp
nil
135
ref
190
remove
cons
136
ref
191
remove
cons
nil
cons
cons
nil
cons
cons
148
ref
subst
deductAntisym
eqMp
193
def
subst
eqMp
eqMp
nil
135
ref
178
ref
cons
194
def
136
ref
183
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
148
ref
subst
proveHyp
eqMp
nil
135
ref
175
remove
cons
136
ref
178
ref
cons
nil
cons
cons
nil
cons
cons
148
ref
subst
deductAntisym
eqMp
subst
eqMp
subst
subst
eqMp
nil
97
ref
62
ref
6
ref
11
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64
ref
20
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appTerm
66
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appTerm
195
def
appTerm
196
def
14
ref
26
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64
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30
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appTerm
15
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33
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absTerm
197
def
appTerm
absTerm
198
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appTerm
199
def
appTerm
200
def
absTerm
201
def
appTerm
202
def
nil
cons
cons
98
ref
62
remove
39
ref
appTerm
203
def
nil
cons
204
def
cons
nil
cons
205
def
cons
nil
cons
cons
155
ref
subst
nil
"P"
41
remove
var
206
def
6
ref
100
ref
201
ref
18
ref
appTerm
207
def
appTerm
203
ref
appTerm
208
def
absTerm
nil
cons
cons
nil
cons
nil
cons
cons
48
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99
ref
160
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appTerm
refl
169
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appThm
171
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eqMp
sym
209
def
subst
subst
6
ref
nil
127
ref
208
remove
nil
cons
cons
nil
cons
nil
cons
cons
131
ref
subst
nil
97
ref
207
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nil
cons
210
def
cons
205
ref
cons
nil
cons
cons
211
def
114
ref
subst
211
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166
ref
subst
6
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196
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14
ref
15
ref
64
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18
ref
67
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appTerm
appTerm
72
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32
ref
18
ref
21
ref
appTerm
73
ref
appTerm
appTerm
73
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appTerm
absTerm
appTerm
absTerm
appTerm
appTerm
absTerm
18
ref
appTerm
212
def
betaConv
212
remove
assume
eqMp
nil
97
ref
200
remove
nil
cons
213
def
cons
205
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cons
nil
cons
cons
214
def
155
ref
subst
proveHyp
214
ref
114
ref
subst
214
remove
166
ref
subst
45
remove
sym
nil
135
ref
195
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nil
cons
cons
136
ref
199
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nil
cons
215
def
cons
nil
cons
cons
nil
cons
cons
216
def
148
ref
subst
nil
"P"
13
remove
var
217
def
24
remove
nil
cons
cons
nil
cons
nil
cons
cons
"A"
2
remove
cons
nil
cons
218
def
47
ref
cons
209
ref
subst
219
def
subst
15
ref
nil
127
ref
23
remove
nil
cons
cons
nil
cons
nil
cons
cons
131
ref
subst
22
remove
refl
66
remove
21
ref
appTerm
betaConv
appThm
195
remove
assume
71
ref
appThm
eqMp
eqMp
absThm
eqMp
proveHyp
nil
97
ref
25
remove
nil
cons
cons
98
ref
38
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
166
ref
subst
proveHyp
216
remove
137
remove
141
remove
151
ref
appTerm
betaConv
151
remove
138
remove
appTerm
betaConv
143
remove
appThm
150
remove
140
ref
appTerm
betaConv
trans
trans
appThm
152
remove
appThm
147
remove
153
remove
appThm
eqMp
sym
130
remove
eqMp
220
def
subst
nil
217
ref
37
remove
nil
cons
cons
nil
cons
nil
cons
cons
219
ref
subst
26
ref
nil
127
ref
36
remove
nil
cons
cons
nil
cons
nil
cons
cons
131
ref
subst
nil
217
ref
35
remove
nil
cons
cons
nil
cons
nil
cons
cons
219
remove
subst
15
ref
nil
127
ref
34
remove
nil
cons
cons
nil
cons
nil
cons
cons
131
ref
subst
31
remove
refl
197
remove
21
ref
appTerm
betaConv
appThm
198
ref
28
ref
appTerm
221
def
betaConv
nil
97
ref
215
remove
cons
98
ref
221
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
155
ref
subst
218
remove
217
remove
198
remove
nil
cons
cons
"x"
1
remove
var
28
ref
nil
cons
cons
nil
cons
cons
nil
cons
cons
172
ref
subst
eqMp
eqMp
71
remove
appThm
eqMp
eqMp
absThm
eqMp
eqMp
absThm
eqMp
proveHyp
eqMp
eqMp
46
ref
206
ref
39
remove
nil
cons
cons
"x"
5
ref
var
222
def
18
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
99
remove
177
ref
appTerm
223
def
refl
56
remove
12
ref
122
remove
constTerm
224
def
98
ref
100
ref
95
ref
158
ref
100
ref
187
remove
appTerm
102
ref
appTerm
absTerm
appTerm
appTerm
102
ref
appTerm
absTerm
appTerm
absTerm
225
def
159
remove
appTerm
betaConv
appThm
nil
55
remove
225
remove
appTerm
axiom
170
remove
appThm
eqMp
226
def
sym
nil
"P"
9
remove
var
227
def
136
ref
100
ref
95
ref
158
ref
100
ref
163
remove
appTerm
228
def
140
ref
appTerm
absTerm
229
def
appTerm
230
def
appTerm
140
ref
appTerm
231
def
absTerm
nil
cons
cons
nil
cons
nil
cons
cons
"A"
8
remove
cons
nil
cons
232
def
47
remove
cons
209
remove
subst
subst
136
ref
nil
127
remove
231
remove
nil
cons
cons
nil
cons
nil
cons
cons
131
remove
subst
nil
97
ref
230
remove
nil
cons
233
def
cons
234
def
98
ref
140
ref
nil
cons
235
def
cons
nil
cons
236
def
cons
nil
cons
cons
237
def
114
ref
subst
237
ref
166
ref
subst
nil
97
ref
164
remove
cons
236
ref
cons
nil
cons
cons
155
ref
subst
229
ref
162
ref
appTerm
238
def
betaConv
nil
234
ref
98
ref
238
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
155
ref
subst
156
remove
157
remove
229
remove
nil
cons
cons
158
ref
162
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
172
ref
subst
eqMp
eqMp
eqMp
eqMp
nil
135
ref
233
remove
cons
239
def
136
ref
235
ref
cons
nil
cons
240
def
cons
nil
cons
cons
148
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
eqMp
subst
proveHyp
eqMp
nil
135
ref
213
remove
cons
136
ref
204
remove
cons
nil
cons
241
def
cons
nil
cons
cons
148
ref
subst
deductAntisym
eqMp
eqMp
eqMp
nil
135
ref
210
remove
cons
241
ref
cons
nil
cons
cons
148
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
nil
97
ref
12
remove
61
remove
constTerm
222
ref
100
ref
201
ref
222
remove
varTerm
appTerm
appTerm
203
ref
appTerm
absTerm
appTerm
nil
cons
cons
98
ref
100
ref
202
remove
appTerm
203
remove
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
155
ref
subst
proveHyp
46
remove
206
remove
201
remove
nil
cons
cons
241
remove
cons
nil
cons
cons
nil
234
remove
98
ref
100
ref
177
remove
appTerm
242
def
140
ref
appTerm
nil
cons
243
def
cons
nil
cons
cons
nil
cons
cons
244
def
114
ref
subst
244
remove
166
ref
subst
nil
97
ref
178
remove
cons
245
def
236
remove
cons
nil
cons
cons
246
def
114
remove
subst
246
remove
166
remove
subst
237
remove
155
ref
subst
98
ref
100
remove
95
remove
158
remove
228
remove
102
ref
appTerm
absTerm
appTerm
appTerm
102
remove
appTerm
absTerm
247
def
140
remove
appTerm
248
def
betaConv
nil
245
remove
98
ref
224
remove
247
ref
appTerm
249
def
nil
cons
250
def
cons
nil
cons
cons
nil
cons
cons
251
def
155
ref
subst
226
remove
nil
97
ref
223
remove
249
ref
appTerm
nil
cons
cons
98
ref
242
remove
249
remove
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
155
ref
subst
proveHyp
251
remove
193
remove
subst
eqMp
eqMp
nil
97
remove
250
remove
cons
98
remove
248
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
155
remove
subst
proveHyp
232
remove
227
remove
247
remove
nil
cons
cons
"x"
7
remove
var
235
remove
cons
nil
cons
cons
nil
cons
cons
172
remove
subst
eqMp
eqMp
eqMp
eqMp
nil
194
remove
240
remove
cons
nil
cons
cons
148
ref
subst
deductAntisym
eqMp
eqMp
nil
239
remove
136
ref
243
remove
cons
nil
cons
cons
nil
cons
cons
148
ref
subst
deductAntisym
eqMp
subst
eqMp
eqMp
proveHyp
eqMp
eqMp
defineConstList
252
def
pop
253
def
pop
252
ref
nil
135
remove
14
ref
15
ref
17
ref
253
remove
hdTl
pop
5
remove
constTerm
254
def
19
ref
appTerm
21
ref
appTerm
appTerm
19
remove
appTerm
absTerm
appTerm
255
def
nil
cons
cons
136
remove
14
ref
26
remove
14
remove
15
remove
17
remove
254
ref
29
remove
appTerm
21
ref
appTerm
appTerm
32
remove
254
remove
28
remove
appTerm
21
ref
appTerm
appTerm
21
remove
appTerm
appTerm
absTerm
appTerm
absTerm
appTerm
256
def
nil
cons
cons
nil
cons
cons
nil
cons
cons
257
def
220
remove
subst
proveHyp
nil
256
remove
thm
252
remove
257
remove
148
remove
subst
proveHyp
nil
255
remove
thm