reference documentation

Article list-filter-def.art

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

20016 bytes
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"FILTER"
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"Data.Bool.?"
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refl
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appTerm
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"Data.Bool.==>"
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betaConv
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refl
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appThm
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appThm
eqMp
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sym
109
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"f"
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appTerm
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"Data.Bool.T"
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appTerm
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appTerm
absTerm
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appTerm
betaConv
appThm
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0
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absTerm
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appTerm
betaConv
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nil
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appTerm
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appTerm
axiom
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appThm
eqMp
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appThm
eqMp
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sym
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refl
nil
"t"
2
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var
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nil
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cons
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nil
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appTerm
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appTerm
assume
sym
nil
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axiom
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def
eqMp
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assume
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deductAntisym
deductAntisym
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subst
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assume
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eqMp
appThm
nil
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nil
cons
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cons
nil
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nil
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subst
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assume
eqMp
appThm
absThm
eqMp
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nil
"P"
2
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var
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123
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"Q"
2
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var
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nil
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refl
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appTerm
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varTerm
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appTerm
absTerm
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96
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absTerm
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appTerm
betaConv
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appTerm
betaConv
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refl
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appThm
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absTerm
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appTerm
betaConv
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appThm
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appTerm
betaConv
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appTerm
betaConv
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refl
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appThm
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absTerm
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appTerm
betaConv
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appTerm
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appTerm
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appTerm
refl
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appTerm
absTerm
appTerm
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appTerm
absTerm
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appTerm
betaConv
appThm
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appTerm
refl
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appTerm
betaConv
appThm
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refl
appThm
eqMp
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appThm
eqMp
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assume
eqMp
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refl
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eqMp
sym
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eqMp
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subst
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deductAntisym
eqMp
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assume
eqMp
sym
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eqMp
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92
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absTerm
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absTerm
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appTerm
betaConv
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96
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appTerm
betaConv
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appThm
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97
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appTerm
betaConv
trans
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appThm
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appTerm
betaConv
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appTerm
betaConv
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appThm
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appTerm
betaConv
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appThm
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assume
eqMp
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refl
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appThm
eqMp
sym
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eqMp
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proveHyp
deductAntisym
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subst
proveHyp
"A"
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var
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deductAntisym
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subst
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appTerm
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appTerm
betaConv
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0
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constTerm
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betaConv
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nil
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appThm
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assume
eqMp
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appThm
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sym
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eqMp
eqMp
nil
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cons
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cons
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deductAntisym
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subst
eqMp
eqMp
nil
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nil
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nil
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nil
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subst
proveHyp
"A"
75
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nil
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nil
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"P"
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var
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nil
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"x"
75
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var
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nil
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nil
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nil
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subst
eqMp
eqMp
subst
subst
eqMp
nil
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"_16071"
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var
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appTerm
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appTerm
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appTerm
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appTerm
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nil
cons
cons
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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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appTerm
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absTerm
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appTerm
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nil
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cons
nil
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subst
nil
"P"
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var
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167
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appTerm
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appTerm
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appTerm
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absTerm
nil
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nil
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nil
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"A"
55
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nil
cons
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nil
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46
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cons
94
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153
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appTerm
refl
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appThm
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eqMp
sym
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subst
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subst
167
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nil
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201
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nil
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nil
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cons
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nil
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109
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subst
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subst
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betaConv
200
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assume
eqMp
nil
92
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179
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nil
cons
207
def
cons
198
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cons
nil
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cons
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def
150
ref
subst
proveHyp
208
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109
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subst
208
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160
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168
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appTerm
209
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betaConv
210
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sym
nil
130
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170
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nil
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nil
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cons
nil
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nil
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cons
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143
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subst
nil
"P"
15
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var
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nil
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cons
nil
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nil
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"A"
4
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nil
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cons
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subst
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subst
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nil
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refl
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23
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appTerm
betaConv
appThm
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assume
23
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refl
215
def
appThm
eqMp
eqMp
absThm
eqMp
proveHyp
nil
92
ref
185
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nil
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cons
93
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nil
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cons
nil
cons
cons
nil
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cons
160
ref
subst
proveHyp
212
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132
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136
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146
ref
appTerm
betaConv
146
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133
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appTerm
betaConv
138
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appThm
145
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135
ref
appTerm
betaConv
trans
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appThm
147
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appThm
142
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148
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appThm
eqMp
sym
125
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eqMp
216
def
subst
nil
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192
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nil
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nil
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nil
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subst
18
ref
nil
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nil
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nil
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nil
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cons
126
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nil
151
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nil
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cons
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subst
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nil
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nil
cons
cons
nil
cons
nil
cons
cons
126
ref
subst
nil
"P"
20
remove
var
217
def
188
remove
nil
cons
cons
nil
cons
nil
cons
cons
"A"
7
remove
cons
nil
cons
218
def
46
ref
cons
203
ref
subst
subst
29
ref
nil
122
ref
187
remove
nil
cons
cons
nil
cons
nil
cons
cons
126
ref
subst
186
remove
refl
174
remove
23
ref
appTerm
betaConv
appThm
175
ref
32
ref
appTerm
219
def
betaConv
177
ref
30
ref
appTerm
220
def
betaConv
nil
92
ref
211
remove
cons
93
ref
220
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
150
ref
subst
72
remove
nil
cons
221
def
151
ref
177
remove
nil
cons
cons
155
ref
30
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
166
ref
subst
eqMp
eqMp
nil
92
ref
176
remove
nil
cons
cons
93
ref
219
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
150
ref
subst
proveHyp
218
remove
217
remove
175
remove
nil
cons
cons
"x"
6
ref
var
32
ref
nil
cons
cons
nil
cons
cons
nil
cons
cons
166
ref
subst
eqMp
eqMp
215
ref
appThm
eqMp
eqMp
absThm
eqMp
eqMp
absThm
eqMp
eqMp
absThm
eqMp
proveHyp
eqMp
eqMp
202
ref
199
ref
195
ref
nil
cons
cons
222
def
"x"
55
remove
var
223
def
168
ref
nil
cons
cons
nil
cons
cons
nil
cons
cons
94
ref
49
remove
152
ref
appTerm
224
def
appTerm
225
def
refl
18
ref
14
ref
117
remove
constTerm
226
def
93
ref
95
ref
26
ref
155
ref
95
ref
23
ref
156
ref
appTerm
appTerm
97
ref
appTerm
absTerm
appTerm
appTerm
97
ref
appTerm
absTerm
appTerm
absTerm
227
def
152
remove
appTerm
betaConv
appThm
nil
50
remove
227
remove
appTerm
axiom
164
remove
appThm
eqMp
228
def
sym
nil
"P"
11
remove
var
229
def
131
ref
95
ref
26
ref
155
ref
95
ref
157
remove
appTerm
230
def
135
ref
appTerm
absTerm
231
def
appTerm
232
def
appTerm
135
ref
appTerm
233
def
absTerm
nil
cons
cons
nil
cons
nil
cons
cons
"A"
3
ref
cons
nil
cons
234
def
46
remove
cons
203
remove
subst
subst
131
ref
nil
122
ref
233
remove
nil
cons
cons
nil
cons
nil
cons
cons
126
ref
subst
nil
92
ref
232
remove
nil
cons
235
def
cons
236
def
93
ref
135
ref
nil
cons
237
def
cons
nil
cons
238
def
cons
nil
cons
cons
239
def
109
ref
subst
239
ref
160
ref
subst
nil
92
ref
158
remove
cons
238
ref
cons
nil
cons
cons
150
ref
subst
231
ref
156
ref
appTerm
240
def
betaConv
nil
236
ref
93
ref
240
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
150
ref
subst
221
remove
151
remove
231
remove
nil
cons
cons
155
ref
156
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
166
ref
subst
eqMp
eqMp
eqMp
eqMp
nil
130
ref
235
remove
cons
241
def
131
ref
237
ref
cons
nil
cons
242
def
cons
nil
cons
cons
143
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
eqMp
243
def
subst
proveHyp
eqMp
nil
130
ref
207
remove
cons
131
ref
197
ref
cons
nil
cons
244
def
cons
nil
cons
cons
143
ref
subst
deductAntisym
eqMp
eqMp
eqMp
nil
130
ref
205
remove
cons
244
ref
cons
nil
cons
cons
143
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
nil
92
ref
14
remove
57
remove
constTerm
245
def
223
ref
95
ref
180
ref
223
ref
varTerm
246
def
appTerm
appTerm
196
ref
appTerm
absTerm
appTerm
nil
cons
cons
93
ref
95
ref
181
remove
appTerm
196
ref
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
150
ref
subst
proveHyp
202
ref
199
ref
180
remove
nil
cons
cons
244
remove
cons
nil
cons
cons
nil
236
remove
93
ref
95
ref
224
ref
appTerm
247
def
135
ref
appTerm
nil
cons
248
def
cons
nil
cons
cons
nil
cons
cons
249
def
109
ref
subst
249
remove
160
ref
subst
nil
92
ref
224
remove
nil
cons
250
def
cons
251
def
238
remove
cons
nil
cons
cons
252
def
109
ref
subst
252
remove
160
ref
subst
239
remove
150
ref
subst
93
ref
95
ref
26
ref
155
remove
230
remove
97
ref
appTerm
absTerm
appTerm
appTerm
97
ref
appTerm
absTerm
253
def
135
remove
appTerm
254
def
betaConv
nil
251
remove
93
ref
226
remove
253
ref
appTerm
255
def
nil
cons
256
def
cons
nil
cons
cons
nil
cons
cons
257
def
150
ref
subst
228
remove
nil
92
ref
225
remove
255
ref
appTerm
nil
cons
cons
93
ref
247
remove
255
remove
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
150
ref
subst
proveHyp
257
remove
nil
92
ref
94
remove
96
remove
appTerm
97
remove
appTerm
258
def
nil
cons
259
def
cons
93
ref
98
remove
nil
cons
260
def
cons
nil
cons
cons
nil
cons
cons
261
def
109
ref
subst
261
remove
160
ref
subst
109
ref
160
ref
258
remove
assume
127
remove
eqMp
eqMp
144
remove
deductAntisym
eqMp
eqMp
nil
130
ref
259
remove
cons
131
ref
260
remove
cons
nil
cons
cons
nil
cons
cons
143
ref
subst
deductAntisym
eqMp
subst
eqMp
eqMp
nil
92
ref
256
remove
cons
93
ref
254
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
150
ref
subst
proveHyp
234
remove
229
remove
253
remove
nil
cons
cons
"x"
2
remove
var
237
remove
cons
nil
cons
cons
nil
cons
cons
166
remove
subst
eqMp
eqMp
eqMp
eqMp
nil
130
ref
250
remove
cons
242
remove
cons
nil
cons
cons
143
ref
subst
deductAntisym
eqMp
eqMp
nil
241
remove
131
ref
248
remove
cons
nil
cons
cons
nil
cons
cons
143
ref
subst
deductAntisym
eqMp
262
def
subst
eqMp
eqMp
proveHyp
nil
92
ref
197
remove
cons
93
ref
48
remove
0
remove
38
ref
3
remove
cons
opType
constTerm
36
ref
appTerm
263
def
nil
cons
264
def
cons
nil
cons
265
def
cons
nil
cons
cons
150
ref
subst
nil
199
remove
167
ref
95
ref
209
ref
appTerm
263
ref
appTerm
266
def
absTerm
nil
cons
cons
nil
cons
nil
cons
cons
204
remove
subst
167
remove
nil
122
remove
266
remove
nil
cons
cons
nil
cons
nil
cons
cons
126
remove
subst
nil
92
ref
209
ref
nil
cons
267
def
cons
265
ref
cons
nil
cons
cons
268
def
109
ref
subst
268
remove
160
ref
subst
210
remove
209
remove
assume
eqMp
nil
92
ref
194
ref
nil
cons
269
def
cons
265
ref
cons
nil
cons
cons
270
def
150
ref
subst
proveHyp
270
ref
109
ref
subst
270
remove
160
ref
subst
"_16069"
4
remove
var
271
def
"_16070"
6
remove
var
272
def
168
remove
272
ref
varTerm
appTerm
273
def
271
remove
varTerm
appTerm
absTerm
absTerm
274
def
refl
nil
92
ref
39
remove
274
ref
appTerm
274
ref
appTerm
nil
cons
cons
265
ref
cons
nil
cons
cons
150
ref
subst
proveHyp
nil
10
remove
274
ref
nil
cons
cons
nil
cons
nil
cons
cons
nil
92
ref
40
remove
274
ref
appTerm
275
def
nil
cons
276
def
cons
265
remove
cons
nil
cons
cons
277
def
109
remove
subst
277
remove
160
remove
subst
44
remove
sym
13
remove
refl
17
ref
refl
278
def
18
ref
21
ref
refl
279
def
275
remove
assume
215
remove
appThm
274
remove
23
ref
appTerm
betaConv
trans
280
def
25
ref
refl
281
def
appThm
272
remove
273
remove
23
ref
appTerm
absTerm
282
def
25
ref
appTerm
betaConv
trans
appThm
281
remove
appThm
absThm
appThm
appThm
278
remove
18
ref
63
remove
27
ref
64
remove
29
ref
279
remove
280
ref
33
ref
refl
appThm
282
ref
33
ref
appTerm
betaConv
trans
appThm
34
ref
refl
31
ref
refl
280
remove
70
remove
appThm
282
remove
32
ref
appTerm
betaConv
trans
283
def
appThm
appThm
283
remove
appThm
appThm
absThm
appThm
absThm
appThm
absThm
appThm
appThm
sym
194
remove
assume
eqMp
eqMp
45
remove
"P"
38
remove
var
36
remove
nil
cons
cons
"x"
9
ref
var
22
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
243
remove
subst
proveHyp
eqMp
nil
130
ref
276
remove
cons
131
ref
264
remove
cons
nil
cons
284
def
cons
nil
cons
cons
143
ref
subst
deductAntisym
eqMp
subst
eqMp
eqMp
nil
130
ref
269
remove
cons
284
ref
cons
nil
cons
cons
143
ref
subst
deductAntisym
eqMp
eqMp
eqMp
nil
130
ref
267
remove
cons
284
ref
cons
nil
cons
cons
143
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
nil
92
remove
245
remove
223
remove
95
ref
195
remove
246
remove
appTerm
appTerm
263
ref
appTerm
absTerm
appTerm
nil
cons
cons
93
remove
95
remove
196
remove
appTerm
263
remove
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
150
remove
subst
proveHyp
202
remove
222
remove
284
remove
cons
nil
cons
cons
262
remove
subst
eqMp
eqMp
proveHyp
eqMp
eqMp
defineConstList
285
def
pop
286
def
pop
285
ref
nil
130
remove
17
ref
18
ref
21
ref
286
remove
hdTl
pop
9
remove
constTerm
23
remove
appTerm
287
def
25
ref
appTerm
appTerm
25
remove
appTerm
absTerm
appTerm
288
def
nil
cons
cons
131
remove
17
remove
18
remove
26
remove
27
remove
28
remove
29
remove
21
remove
287
ref
33
remove
appTerm
appTerm
34
remove
31
remove
287
remove
32
remove
appTerm
289
def
appTerm
appTerm
289
remove
appTerm
appTerm
absTerm
appTerm
absTerm
appTerm
absTerm
appTerm
290
def
nil
cons
cons
nil
cons
cons
nil
cons
cons
291
def
216
remove
subst
proveHyp
nil
290
remove
thm
285
remove
291
remove
143
remove
subst
proveHyp
nil
288
remove
thm