reference documentation

Article real-thm.art

path: "vendor/opentheory/data/theories/real-thm/real-thm.art"

22899 bytes
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absTerm
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ref
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appThm
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53
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def
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appTerm
betaConv
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appTerm
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refl
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appThm
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ref
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ref
appTerm
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appThm
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appThm
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65
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66
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68
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def
appTerm
betaConv
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114
ref
appTerm
betaConv
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refl
119
def
appThm
68
ref
114
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absTerm
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appTerm
betaConv
trans
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appThm
92
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118
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appTerm
betaConv
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ref
53
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appTerm
betaConv
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appTerm
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appTerm
refl
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95
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114
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betaConv
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114
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122
def
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sym
64
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subst
113
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91
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114
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116
ref
appTerm
betaConv
trans
trans
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94
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122
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102
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appThm
eqMp
sym
64
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eqMp
subst
nil
66
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110
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cons
124
def
70
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cons
nil
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cons
85
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107
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109
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104
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106
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cons
nil
cons
cons
123
ref
subst
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def
deductAntisym
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84
remove
74
ref
assume
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sym
105
ref
eqMp
103
remove
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deductAntisym
126
def
subst
nil
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4
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var
127
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13
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17
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15
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appTerm
37
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40
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cons
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def
61
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subst
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subst
13
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62
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129
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def
cons
70
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cons
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def
85
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subst
136
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subst
128
ref
betaConv
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def
128
remove
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eqMp
nil
66
ref
16
ref
nil
cons
138
def
cons
70
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cons
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cons
cons
139
def
126
ref
subst
proveHyp
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ref
85
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subst
nil
66
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cons
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cons
nil
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subst
nil
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19
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30
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appTerm
37
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appTerm
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absTerm
nil
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cons
nil
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nil
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134
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subst
19
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nil
62
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65
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66
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nil
cons
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def
cons
70
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cons
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cons
143
def
85
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subst
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108
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subst
140
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betaConv
144
def
140
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assume
eqMp
nil
66
ref
29
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nil
cons
145
def
cons
70
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cons
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cons
cons
146
def
126
ref
subst
proveHyp
146
ref
85
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subst
146
remove
108
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subst
36
ref
"Number.Real.sup"
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131
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131
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varTerm
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127
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opType
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var
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def
42
ref
"Data.Bool.~"
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41
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opType
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52
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176
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186
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20
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0
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172
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42
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183
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178
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def
assume
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deductAntisym
absThm
appThm
nil
187
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172
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188
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eqMp
nil
66
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187
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185
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cons
68
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186
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nil
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126
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"A"
171
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nil
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189
def
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nil
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"P"
174
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var
185
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171
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176
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68
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181
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193
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108
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subst
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191
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refl
54
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181
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appTerm
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appThm
56
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60
remove
49
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assume
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eqMp
181
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eqMp
sym
64
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eqMp
nil
109
ref
190
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cons
111
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192
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cons
123
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deductAntisym
eqMp
194
def
subst
eqMp
eqMp
subst
subst
12
ref
refl
195
def
"_17353"
1
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var
196
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nil
13
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196
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133
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52
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182
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197
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179
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"y"
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198
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199
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197
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200
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appTerm
51
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200
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51
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181
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201
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absTerm
202
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181
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appTerm
203
def
betaConv
50
ref
46
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202
ref
appTerm
204
def
absTerm
205
def
51
ref
appTerm
206
def
betaConv
nil
20
ref
57
remove
constTerm
205
ref
appTerm
207
def
axiom
nil
66
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207
remove
nil
cons
cons
68
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206
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nil
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nil
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cons
nil
cons
cons
126
ref
subst
proveHyp
"A"
199
remove
cons
nil
cons
"P"
45
remove
var
205
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nil
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cons
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44
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var
51
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nil
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cons
nil
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nil
cons
cons
194
ref
subst
eqMp
eqMp
nil
66
ref
204
remove
nil
cons
cons
68
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203
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nil
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cons
nil
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nil
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cons
126
ref
subst
proveHyp
"A"
170
remove
cons
nil
cons
208
def
47
ref
202
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nil
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cons
52
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181
ref
nil
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cons
nil
cons
209
def
cons
nil
cons
cons
194
ref
subst
eqMp
eqMp
subst
210
def
subst
absThm
appThm
trans
appThm
211
def
166
remove
195
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var
212
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ref
refl
213
def
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1
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214
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refl
215
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13
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214
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varTerm
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def
nil
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nil
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nil
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cons
210
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subst
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216
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appTerm
212
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varTerm
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refl
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appThm
appThm
217
def
nil
13
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158
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cons
nil
cons
218
def
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210
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subst
nil
62
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162
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cons
nil
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nil
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cons
65
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subst
159
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trans
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nil
62
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112
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cons
nil
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nil
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62
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42
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10
ref
63
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appTerm
53
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appTerm
appTerm
63
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appTerm
absTerm
219
def
63
ref
appTerm
220
def
betaConv
nil
20
ref
97
remove
constTerm
221
def
219
ref
appTerm
222
def
axiom
nil
66
ref
222
remove
nil
cons
cons
68
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220
remove
nil
cons
cons
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cons
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nil
cons
cons
126
ref
subst
proveHyp
"A"
3
ref
cons
nil
cons
223
def
"P"
7
remove
var
224
def
219
remove
nil
cons
cons
"x"
2
remove
var
225
def
63
ref
nil
cons
cons
nil
cons
226
def
cons
nil
cons
cons
194
ref
subst
eqMp
eqMp
subst
227
def
trans
appThm
sym
137
remove
sym
16
remove
assume
eqMp
132
ref
127
ref
17
remove
nil
cons
cons
228
def
13
ref
15
ref
nil
cons
cons
nil
cons
229
def
cons
nil
cons
cons
42
ref
179
ref
48
ref
appTerm
230
def
appTerm
231
def
refl
50
remove
221
ref
68
ref
9
ref
46
ref
52
ref
9
ref
201
remove
appTerm
73
ref
appTerm
absTerm
appTerm
appTerm
73
ref
appTerm
absTerm
appTerm
absTerm
232
def
48
remove
appTerm
betaConv
appThm
nil
58
remove
179
remove
appTerm
232
remove
appTerm
axiom
59
remove
appThm
eqMp
233
def
sym
nil
224
ref
111
ref
9
ref
46
ref
52
ref
9
ref
191
remove
appTerm
234
def
116
ref
appTerm
absTerm
235
def
appTerm
236
def
appTerm
116
ref
appTerm
237
def
absTerm
nil
cons
cons
nil
cons
nil
cons
cons
223
ref
40
ref
cons
61
ref
subst
subst
111
ref
nil
62
ref
237
remove
nil
cons
cons
nil
cons
nil
cons
cons
65
ref
subst
nil
66
ref
236
remove
nil
cons
238
def
cons
239
def
68
ref
116
ref
nil
cons
240
def
cons
nil
cons
241
def
cons
nil
cons
cons
242
def
85
ref
subst
242
ref
108
ref
subst
nil
66
ref
192
remove
cons
241
ref
cons
nil
cons
cons
126
ref
subst
235
ref
181
remove
appTerm
243
def
betaConv
nil
239
ref
68
ref
243
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
ref
subst
208
remove
47
remove
235
remove
nil
cons
cons
209
remove
cons
nil
cons
cons
194
ref
subst
eqMp
eqMp
eqMp
eqMp
nil
109
ref
238
remove
cons
244
def
111
ref
240
ref
cons
nil
cons
245
def
cons
nil
cons
cons
123
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
eqMp
246
def
subst
proveHyp
nil
124
remove
68
ref
112
remove
cons
nil
cons
cons
nil
cons
cons
108
ref
subst
proveHyp
144
remove
sym
29
remove
assume
eqMp
132
ref
127
ref
30
ref
nil
cons
cons
247
def
13
ref
27
ref
nil
cons
cons
nil
cons
248
def
cons
nil
cons
cons
246
ref
subst
proveHyp
eqMp
249
def
eqMp
nil
66
ref
10
ref
173
ref
41
remove
0
ref
148
ref
0
ref
148
ref
3
ref
cons
opType
250
def
nil
cons
251
def
cons
opType
constTerm
252
def
155
ref
appTerm
177
remove
148
ref
constTerm
253
def
appTerm
appTerm
appTerm
254
def
10
ref
12
ref
19
ref
21
ref
13
ref
9
ref
180
remove
0
ref
1
ref
251
remove
cons
opType
constTerm
255
def
15
ref
appTerm
256
def
155
ref
appTerm
appTerm
257
def
28
ref
appTerm
absTerm
appTerm
absTerm
appTerm
appTerm
258
def
255
remove
158
remove
appTerm
155
remove
appTerm
appTerm
appTerm
nil
cons
cons
164
remove
cons
nil
cons
cons
126
ref
subst
proveHyp
nil
168
remove
218
remove
cons
nil
cons
cons
167
ref
9
ref
10
ref
173
remove
252
remove
167
ref
varTerm
259
def
appTerm
253
remove
appTerm
appTerm
appTerm
260
def
10
remove
12
remove
19
ref
21
ref
13
ref
9
ref
256
remove
259
ref
appTerm
261
def
appTerm
28
remove
appTerm
absTerm
appTerm
262
def
absTerm
appTerm
appTerm
263
def
261
remove
appTerm
appTerm
appTerm
26
ref
149
remove
259
ref
appTerm
264
def
appTerm
appTerm
265
def
absTerm
266
def
259
ref
appTerm
267
def
betaConv
13
ref
20
ref
0
ref
250
ref
3
ref
cons
opType
constTerm
268
def
266
ref
appTerm
269
def
absTerm
270
def
15
ref
appTerm
271
def
betaConv
nil
268
ref
167
ref
21
ref
13
ref
265
ref
absTerm
272
def
appTerm
273
def
absTerm
274
def
appTerm
275
def
axiom
nil
66
ref
275
remove
nil
cons
276
def
cons
277
def
68
ref
21
ref
270
ref
appTerm
nil
cons
278
def
cons
nil
cons
cons
nil
cons
cons
279
def
126
ref
subst
proveHyp
279
ref
85
ref
subst
279
remove
108
ref
subst
nil
127
ref
270
remove
nil
cons
cons
280
def
nil
cons
nil
cons
cons
134
ref
subst
13
ref
nil
62
ref
269
remove
nil
cons
281
def
cons
nil
cons
nil
cons
cons
65
ref
subst
nil
"P"
250
remove
var
282
def
266
remove
nil
cons
cons
283
def
nil
cons
nil
cons
cons
"A"
151
remove
cons
nil
cons
284
def
40
remove
cons
61
remove
subst
subst
167
ref
nil
62
ref
265
remove
nil
cons
cons
nil
cons
nil
cons
cons
65
ref
subst
272
ref
15
ref
appTerm
285
def
betaConv
274
ref
259
ref
appTerm
286
def
betaConv
nil
277
remove
68
ref
286
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
ref
subst
284
ref
282
ref
274
remove
nil
cons
cons
"x"
148
remove
var
259
ref
nil
cons
cons
nil
cons
287
def
cons
nil
cons
cons
194
ref
subst
eqMp
eqMp
nil
66
ref
273
remove
nil
cons
cons
68
ref
285
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
ref
subst
proveHyp
132
ref
127
ref
272
remove
nil
cons
cons
229
ref
cons
nil
cons
cons
194
ref
subst
eqMp
eqMp
eqMp
absThm
eqMp
eqMp
absThm
eqMp
eqMp
nil
109
ref
276
remove
cons
111
ref
278
ref
cons
nil
cons
cons
nil
cons
cons
123
ref
subst
deductAntisym
eqMp
eqMp
nil
66
ref
278
remove
cons
68
ref
271
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
ref
subst
proveHyp
132
ref
280
remove
229
ref
cons
nil
cons
cons
194
ref
subst
eqMp
eqMp
nil
66
ref
281
remove
cons
68
ref
267
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
ref
subst
proveHyp
284
ref
283
remove
287
ref
cons
nil
cons
cons
194
ref
subst
eqMp
eqMp
subst
eqMp
eqMp
nil
109
ref
162
remove
cons
111
ref
163
remove
cons
nil
cons
cons
nil
cons
cons
123
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
nil
66
ref
21
ref
13
ref
22
ref
26
ref
156
ref
appTerm
appTerm
absTerm
appTerm
nil
cons
cons
68
ref
21
ref
19
ref
35
remove
25
ref
156
ref
appTerm
288
def
27
ref
appTerm
appTerm
absTerm
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
108
ref
subst
proveHyp
nil
127
ref
"m'"
1
ref
var
289
def
9
ref
21
ref
13
ref
22
remove
26
remove
289
ref
varTerm
290
def
appTerm
291
def
appTerm
292
def
absTerm
293
def
appTerm
294
def
appTerm
288
remove
290
ref
appTerm
295
def
appTerm
296
def
absTerm
nil
cons
cons
nil
cons
nil
cons
cons
134
remove
subst
289
remove
nil
62
ref
296
remove
nil
cons
cons
nil
cons
nil
cons
cons
65
ref
subst
nil
66
ref
294
remove
nil
cons
297
def
cons
298
def
68
ref
295
remove
nil
cons
299
def
cons
nil
cons
300
def
cons
nil
cons
cons
301
def
85
ref
subst
301
remove
108
ref
subst
211
remove
217
remove
213
remove
"_17363"
1
remove
var
302
def
215
remove
nil
13
ref
302
remove
varTerm
303
def
nil
cons
cons
nil
cons
nil
cons
cons
304
def
210
remove
subst
appThm
25
ref
303
remove
appTerm
290
ref
appTerm
refl
appThm
304
remove
nil
62
ref
292
remove
nil
cons
cons
nil
cons
nil
cons
cons
65
remove
subst
293
ref
15
ref
appTerm
305
def
betaConv
nil
298
remove
68
ref
305
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
ref
subst
132
ref
127
ref
293
remove
nil
cons
cons
229
remove
cons
nil
cons
cons
194
ref
subst
eqMp
eqMp
eqMp
subst
trans
absThm
appThm
nil
62
ref
53
remove
nil
cons
cons
nil
cons
nil
cons
cons
133
remove
62
remove
42
ref
46
ref
52
ref
63
ref
absTerm
appTerm
appTerm
63
ref
appTerm
absTerm
306
def
63
remove
appTerm
307
def
betaConv
nil
221
ref
306
ref
appTerm
308
def
axiom
nil
66
ref
308
remove
nil
cons
cons
68
ref
307
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
ref
subst
proveHyp
223
ref
224
ref
306
remove
nil
cons
cons
226
remove
cons
nil
cons
cons
194
ref
subst
eqMp
eqMp
subst
subst
trans
appThm
227
remove
trans
appThm
sym
249
remove
eqMp
nil
66
ref
254
remove
258
remove
21
ref
13
ref
257
remove
291
remove
appTerm
absTerm
appTerm
appTerm
appTerm
nil
cons
cons
300
remove
cons
nil
cons
cons
126
ref
subst
proveHyp
nil
19
ref
290
remove
nil
cons
cons
169
remove
cons
nil
cons
cons
19
remove
9
ref
260
remove
263
remove
262
remove
appTerm
appTerm
appTerm
25
remove
264
remove
appTerm
27
ref
appTerm
appTerm
absTerm
309
def
27
remove
appTerm
310
def
betaConv
167
remove
21
ref
309
ref
appTerm
311
def
absTerm
312
def
259
remove
appTerm
313
def
betaConv
nil
268
remove
312
ref
appTerm
314
def
axiom
nil
66
ref
314
remove
nil
cons
cons
68
ref
313
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
ref
subst
proveHyp
284
remove
282
remove
312
remove
nil
cons
cons
287
remove
cons
nil
cons
cons
194
ref
subst
eqMp
eqMp
nil
66
ref
311
remove
nil
cons
cons
68
ref
310
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
ref
subst
proveHyp
132
ref
127
ref
309
remove
nil
cons
cons
248
remove
cons
nil
cons
cons
194
ref
subst
eqMp
eqMp
subst
eqMp
eqMp
nil
109
ref
297
remove
cons
111
ref
299
remove
cons
nil
cons
cons
nil
cons
cons
123
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
eqMp
eqMp
132
ref
127
remove
36
remove
nil
cons
cons
13
ref
156
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
246
remove
subst
proveHyp
eqMp
nil
109
ref
145
remove
cons
111
ref
69
remove
cons
nil
cons
315
def
cons
nil
cons
cons
123
ref
subst
deductAntisym
eqMp
eqMp
eqMp
nil
109
ref
142
remove
cons
315
ref
cons
nil
cons
cons
123
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
nil
66
ref
21
ref
13
remove
9
ref
30
remove
15
remove
appTerm
appTerm
37
ref
appTerm
absTerm
appTerm
nil
cons
cons
68
ref
9
ref
31
remove
appTerm
37
ref
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
ref
subst
proveHyp
132
ref
247
remove
315
ref
cons
nil
cons
cons
nil
239
remove
68
ref
9
ref
230
ref
appTerm
316
def
116
ref
appTerm
nil
cons
317
def
cons
nil
cons
cons
nil
cons
cons
318
def
85
ref
subst
318
remove
108
ref
subst
nil
66
ref
230
remove
nil
cons
319
def
cons
320
def
241
remove
cons
nil
cons
cons
321
def
85
ref
subst
321
remove
108
ref
subst
242
remove
126
ref
subst
68
ref
9
ref
46
remove
52
remove
234
remove
73
ref
appTerm
absTerm
appTerm
appTerm
73
ref
appTerm
absTerm
322
def
116
remove
appTerm
323
def
betaConv
nil
320
remove
68
ref
221
remove
322
ref
appTerm
324
def
nil
cons
325
def
cons
nil
cons
cons
nil
cons
cons
326
def
126
ref
subst
233
remove
nil
66
ref
231
remove
324
ref
appTerm
nil
cons
cons
68
ref
316
remove
324
remove
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
ref
subst
proveHyp
326
remove
nil
66
ref
42
remove
72
remove
appTerm
73
remove
appTerm
327
def
nil
cons
328
def
cons
68
ref
74
remove
nil
cons
329
def
cons
nil
cons
cons
nil
cons
cons
330
def
85
ref
subst
330
remove
108
ref
subst
85
remove
108
remove
327
remove
assume
105
remove
eqMp
eqMp
125
remove
deductAntisym
eqMp
eqMp
nil
109
ref
328
remove
cons
111
ref
329
remove
cons
nil
cons
cons
nil
cons
cons
123
ref
subst
deductAntisym
eqMp
subst
eqMp
eqMp
nil
66
ref
325
remove
cons
68
ref
323
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
ref
subst
proveHyp
223
remove
224
remove
322
remove
nil
cons
cons
225
remove
240
remove
cons
nil
cons
cons
nil
cons
cons
194
remove
subst
eqMp
eqMp
eqMp
eqMp
nil
109
ref
319
remove
cons
245
remove
cons
nil
cons
cons
123
ref
subst
deductAntisym
eqMp
eqMp
nil
244
remove
111
remove
317
remove
cons
nil
cons
cons
nil
cons
cons
123
ref
subst
deductAntisym
eqMp
331
def
subst
eqMp
eqMp
eqMp
nil
109
ref
138
remove
cons
315
ref
cons
nil
cons
cons
123
ref
subst
deductAntisym
eqMp
eqMp
eqMp
nil
109
ref
135
remove
cons
315
ref
cons
nil
cons
cons
123
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
nil
66
remove
21
remove
130
remove
appTerm
nil
cons
cons
68
remove
9
remove
18
remove
appTerm
37
remove
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
126
remove
subst
proveHyp
132
remove
228
remove
315
ref
cons
nil
cons
cons
331
remove
subst
eqMp
eqMp
proveHyp
proveHyp
eqMp
nil
109
remove
67
remove
cons
315
remove
cons
nil
cons
cons
123
remove
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
nil
20
remove
0
remove
5
remove
3
remove
cons
opType
constTerm
39
remove
appTerm
thm