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Article natural-add-def.art

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

17312 bytes
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cons
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constTerm
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var
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refl
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0
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0
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refl
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appTerm
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refl
"_2180"
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refl
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appThm
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"n'"
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var
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appTerm
appTerm
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appTerm
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appThm
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"f"
0
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3
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var
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"A"
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0
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1
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nil
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"Data.Bool.?!"
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0
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0
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cons
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nil
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appTerm
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appTerm
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appTerm
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absTerm
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absTerm
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appTerm
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betaConv
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"Data.Bool.==>"
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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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refl
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appThm
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appTerm
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appThm
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10
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0
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nil
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appTerm
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appThm
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appThm
eqMp
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sym
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refl
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16
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0
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0
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8
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cons
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nil
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"f"
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var
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appTerm
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appTerm
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"Data.Bool.T"
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7
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constTerm
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appTerm
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appTerm
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appTerm
absTerm
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appTerm
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appThm
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0
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0
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9
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8
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nil
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appTerm
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absTerm
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appTerm
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nil
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11
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appTerm
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appTerm
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appThm
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appThm
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sym
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refl
nil
"t"
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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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varTerm
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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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remove
assume
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ref
deductAntisym
deductAntisym
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def
subst
100
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assume
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def
eqMp
appThm
nil
126
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101
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nil
cons
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cons
nil
cons
nil
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cons
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subst
101
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assume
eqMp
appThm
absThm
eqMp
133
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nil
"P"
7
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var
134
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127
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cons
"Q"
7
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var
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cons
nil
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cons
nil
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refl
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115
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appTerm
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varTerm
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appTerm
absTerm
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97
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100
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absTerm
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appTerm
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appTerm
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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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trans
appThm
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appTerm
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appTerm
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refl
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appThm
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absTerm
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appTerm
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appThm
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11
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appTerm
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appTerm
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def
appTerm
refl
97
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appTerm
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appTerm
absTerm
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appTerm
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appThm
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appTerm
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137
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appTerm
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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
appThm
eqMp
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eqMp
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subst
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def
deductAntisym
eqMp
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102
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assume
eqMp
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eqMp
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96
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97
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absTerm
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absTerm
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appTerm
betaConv
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100
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appTerm
betaConv
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appThm
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appTerm
betaConv
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trans
appThm
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appTerm
betaConv
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appTerm
betaConv
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appThm
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appTerm
betaConv
trans
trans
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def
appThm
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104
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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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def
proveHyp
deductAntisym
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subst
proveHyp
"A"
57
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cons
nil
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"P"
49
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var
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92
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nil
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"x"
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appTerm
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cons
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appTerm
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113
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subst
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appTerm
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appTerm
betaConv
appThm
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0
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49
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50
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nil
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appTerm
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appTerm
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refl
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appThm
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assume
eqMp
eqMp
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appThm
eqMp
sym
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eqMp
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nil
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cons
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cons
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deductAntisym
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subst
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eqMp
nil
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nil
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cons
97
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proveHyp
"A"
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nil
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"P"
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var
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var
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subst
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nil
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97
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52
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constTerm
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appTerm
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subst
proveHyp
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"P"
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var
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nil
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constTerm
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"y"
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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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appTerm
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appTerm
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appTerm
betaConv
appThm
nil
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appTerm
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appTerm
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appThm
eqMp
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appTerm
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appTerm
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appTerm
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nil
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appTerm
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165
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assume
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eqMp
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deductAntisym
eqMp
eqMp
nil
134
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189
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cons
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cons
nil
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cons
nil
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subst
deductAntisym
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subst
eqMp
eqMp
nil
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177
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cons
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135
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nil
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nil
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subst
proveHyp
eqMp
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134
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cons
135
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177
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cons
nil
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nil
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cons
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subst
deductAntisym
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subst
eqMp
subst
subst
eqMp
nil
96
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6
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11
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20
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appTerm
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appTerm
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appTerm
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nil
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nil
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cons
nil
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204
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cons
nil
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cons
154
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subst
nil
"P"
40
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var
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def
6
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99
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200
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18
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appTerm
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appTerm
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appTerm
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absTerm
nil
cons
cons
nil
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nil
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cons
47
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98
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159
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appTerm
refl
168
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appThm
170
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eqMp
sym
208
def
subst
subst
6
ref
nil
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nil
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nil
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nil
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nil
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cons
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nil
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113
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165
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subst
6
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14
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18
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appTerm
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27
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21
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appTerm
72
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appTerm
appTerm
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appTerm
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appTerm
appTerm
absTerm
18
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appTerm
211
def
betaConv
211
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assume
eqMp
nil
96
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199
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nil
cons
212
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cons
204
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cons
nil
cons
cons
213
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154
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subst
proveHyp
213
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113
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subst
213
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165
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subst
44
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sym
nil
134
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194
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nil
cons
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135
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nil
cons
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cons
nil
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nil
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215
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147
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subst
nil
"P"
13
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var
216
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24
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nil
cons
cons
nil
cons
nil
cons
cons
"A"
2
remove
cons
nil
cons
217
def
46
ref
cons
208
ref
subst
218
def
subst
15
ref
nil
126
ref
23
remove
nil
cons
cons
nil
cons
nil
cons
cons
130
ref
subst
22
remove
refl
65
remove
21
ref
appTerm
betaConv
appThm
194
remove
assume
70
ref
appThm
eqMp
eqMp
absThm
eqMp
proveHyp
nil
96
ref
25
remove
nil
cons
cons
97
ref
37
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
165
ref
subst
proveHyp
215
remove
136
remove
140
remove
150
ref
appTerm
betaConv
150
remove
137
remove
appTerm
betaConv
142
remove
appThm
149
remove
139
ref
appTerm
betaConv
trans
trans
appThm
151
remove
appThm
146
remove
152
remove
appThm
eqMp
sym
129
remove
eqMp
219
def
subst
nil
216
ref
36
remove
nil
cons
cons
nil
cons
nil
cons
cons
218
ref
subst
26
ref
nil
126
ref
35
remove
nil
cons
cons
nil
cons
nil
cons
cons
130
ref
subst
nil
216
ref
34
remove
nil
cons
cons
nil
cons
nil
cons
cons
218
remove
subst
15
ref
nil
126
ref
33
remove
nil
cons
cons
nil
cons
nil
cons
cons
130
ref
subst
31
remove
refl
196
remove
21
ref
appTerm
betaConv
appThm
197
ref
28
ref
appTerm
220
def
betaConv
nil
96
ref
214
remove
cons
97
ref
220
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
154
ref
subst
217
remove
216
remove
197
remove
nil
cons
cons
"x"
1
remove
var
28
ref
nil
cons
cons
nil
cons
cons
nil
cons
cons
171
ref
subst
eqMp
eqMp
70
remove
appThm
eqMp
eqMp
absThm
eqMp
eqMp
absThm
eqMp
proveHyp
eqMp
eqMp
45
ref
205
ref
38
remove
nil
cons
cons
"x"
5
ref
var
221
def
18
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
98
remove
176
ref
appTerm
222
def
refl
55
remove
12
ref
121
remove
constTerm
223
def
97
ref
99
ref
94
ref
157
ref
99
ref
186
remove
appTerm
101
ref
appTerm
absTerm
appTerm
appTerm
101
ref
appTerm
absTerm
appTerm
absTerm
224
def
158
remove
appTerm
betaConv
appThm
nil
54
remove
224
remove
appTerm
axiom
169
remove
appThm
eqMp
225
def
sym
nil
"P"
9
remove
var
226
def
135
ref
99
ref
94
ref
157
ref
99
ref
162
remove
appTerm
227
def
139
ref
appTerm
absTerm
228
def
appTerm
229
def
appTerm
139
ref
appTerm
230
def
absTerm
nil
cons
cons
nil
cons
nil
cons
cons
"A"
8
remove
cons
nil
cons
231
def
46
remove
cons
208
remove
subst
subst
135
ref
nil
126
remove
230
remove
nil
cons
cons
nil
cons
nil
cons
cons
130
remove
subst
nil
96
ref
229
remove
nil
cons
232
def
cons
233
def
97
ref
139
ref
nil
cons
234
def
cons
nil
cons
235
def
cons
nil
cons
cons
236
def
113
ref
subst
236
ref
165
ref
subst
nil
96
ref
163
remove
cons
235
ref
cons
nil
cons
cons
154
ref
subst
228
ref
161
ref
appTerm
237
def
betaConv
nil
233
ref
97
ref
237
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
154
ref
subst
155
remove
156
remove
228
remove
nil
cons
cons
157
ref
161
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
171
ref
subst
eqMp
eqMp
eqMp
eqMp
nil
134
ref
232
remove
cons
238
def
135
ref
234
ref
cons
nil
cons
239
def
cons
nil
cons
cons
147
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
eqMp
subst
proveHyp
eqMp
nil
134
ref
212
remove
cons
135
ref
203
remove
cons
nil
cons
240
def
cons
nil
cons
cons
147
ref
subst
deductAntisym
eqMp
eqMp
eqMp
nil
134
ref
209
remove
cons
240
ref
cons
nil
cons
cons
147
ref
subst
deductAntisym
eqMp
eqMp
absThm
eqMp
nil
96
ref
12
remove
60
remove
constTerm
221
ref
99
ref
200
ref
221
remove
varTerm
appTerm
appTerm
202
ref
appTerm
absTerm
appTerm
nil
cons
cons
97
ref
99
ref
201
remove
appTerm
202
remove
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
154
ref
subst
proveHyp
45
remove
205
remove
200
remove
nil
cons
cons
240
remove
cons
nil
cons
cons
nil
233
remove
97
ref
99
ref
176
remove
appTerm
241
def
139
ref
appTerm
nil
cons
242
def
cons
nil
cons
cons
nil
cons
cons
243
def
113
ref
subst
243
remove
165
ref
subst
nil
96
ref
177
remove
cons
244
def
235
remove
cons
nil
cons
cons
245
def
113
remove
subst
245
remove
165
remove
subst
236
remove
154
ref
subst
97
ref
99
remove
94
remove
157
remove
227
remove
101
ref
appTerm
absTerm
appTerm
appTerm
101
remove
appTerm
absTerm
246
def
139
remove
appTerm
247
def
betaConv
nil
244
remove
97
ref
223
remove
246
ref
appTerm
248
def
nil
cons
249
def
cons
nil
cons
cons
nil
cons
cons
250
def
154
ref
subst
225
remove
nil
96
ref
222
remove
248
ref
appTerm
nil
cons
cons
97
ref
241
remove
248
remove
appTerm
nil
cons
cons
nil
cons
cons
nil
cons
cons
154
ref
subst
proveHyp
250
remove
192
remove
subst
eqMp
eqMp
nil
96
remove
249
remove
cons
97
remove
247
remove
nil
cons
cons
nil
cons
cons
nil
cons
cons
154
remove
subst
proveHyp
231
remove
226
remove
246
remove
nil
cons
cons
"x"
7
remove
var
234
remove
cons
nil
cons
cons
nil
cons
cons
171
remove
subst
eqMp
eqMp
eqMp
eqMp
nil
193
remove
239
remove
cons
nil
cons
cons
147
ref
subst
deductAntisym
eqMp
eqMp
nil
238
remove
135
ref
242
remove
cons
nil
cons
cons
nil
cons
cons
147
ref
subst
deductAntisym
eqMp
subst
eqMp
eqMp
proveHyp
eqMp
eqMp
defineConstList
251
def
pop
252
def
pop
251
ref
nil
134
remove
14
ref
15
ref
17
ref
252
remove
hdTl
pop
5
remove
constTerm
253
def
19
remove
appTerm
21
ref
appTerm
appTerm
21
ref
appTerm
absTerm
appTerm
254
def
nil
cons
cons
135
remove
14
ref
26
remove
14
remove
15
remove
17
remove
253
ref
29
remove
appTerm
21
ref
appTerm
appTerm
27
remove
253
remove
28
remove
appTerm
21
remove
appTerm
appTerm
appTerm
absTerm
appTerm
absTerm
appTerm
255
def
nil
cons
cons
nil
cons
cons
nil
cons
cons
256
def
219
remove
subst
proveHyp
nil
255
remove
thm
251
remove
256
remove
147
remove
subst
proveHyp
nil
254
remove
thm