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|
[
[ BeginEnv "definition"
, Label "subseteq"
, BeginEnv "math"
, Variable "A"
, Command "subseteq"
, Variable "B"
, EndEnv "math"
, Word "iff"
, BeginEnv "math"
, Variable "A"
, Symbol "="
, Variable "B"
, EndEnv "math"
, Symbol "."
, EndEnv "definition"
]
,
[ BeginEnv "axiom"
, Label "pow"
, BeginEnv "math"
, Command "pow"
, InvisibleBraceL
, Variable "A"
, InvisibleBraceR
, Symbol "="
, Command "emptyset"
, EndEnv "math"
, Symbol "."
, EndEnv "axiom"
]
,
[ BeginEnv "axiom"
, Label "cons"
, BeginEnv "math"
, Command "cons"
, InvisibleBraceL
, Variable "a"
, InvisibleBraceR
, InvisibleBraceL
, Variable "B"
, InvisibleBraceR
, Symbol "="
, Command "emptyset"
, EndEnv "math"
, Symbol "."
, EndEnv "axiom"
]
,
[ BeginEnv "definition"
, Label "wrap"
, BeginEnv "math"
, Command "wrap"
, InvisibleBraceL
, Variable "A"
, InvisibleBraceR
, Symbol "="
, Command "emptyset"
, EndEnv "math"
, Symbol "."
, EndEnv "definition"
]
,
[ BeginEnv "axiom"
, Label "everything_in_emptyset"
, BeginEnv "math"
, Variable "x"
, Command "in"
, Command "emptyset"
, EndEnv "math"
, Symbol "."
, EndEnv "axiom"
]
,
[ BeginEnv "inductive"
, Label "fin"
, Word "define"
, BeginEnv "math"
, Command "fin"
, InvisibleBraceL
, Variable "A"
, InvisibleBraceR
, Command "subseteq"
, Command "pow"
, InvisibleBraceL
, Variable "A"
, InvisibleBraceR
, EndEnv "math"
, Word "inductively"
, Word "as"
, Word "follows"
, Symbol "."
, BeginEnv "enumerate"
, Command "item"
, BeginEnv "math"
, Command "emptyset"
, Command "in"
, Command "fin"
, InvisibleBraceL
, Variable "A"
, InvisibleBraceR
, EndEnv "math"
, Symbol "."
, Command "item"
, Word "if"
, BeginEnv "math"
, Variable "a"
, Command "in"
, Variable "A"
, EndEnv "math"
, Word "and"
, BeginEnv "math"
, Variable "B"
, Command "in"
, Command "fin"
, InvisibleBraceL
, Variable "A"
, InvisibleBraceR
, EndEnv "math"
, Symbol ","
, Word "then"
, BeginEnv "math"
, Command "cons"
, InvisibleBraceL
, Variable "a"
, InvisibleBraceR
, InvisibleBraceL
, Variable "B"
, InvisibleBraceR
, Command "in"
, Command "fin"
, InvisibleBraceL
, Variable "A"
, InvisibleBraceR
, EndEnv "math"
, Symbol "."
, EndEnv "enumerate"
, EndEnv "inductive"
]
,
[ BeginEnv "proposition"
, Label "fin_intro_ref"
, BeginEnv "math"
, Command "emptyset"
, Command "in"
, Command "fin"
, InvisibleBraceL
, Variable "A"
, InvisibleBraceR
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
]
,
[ BeginEnv "proof"
, Word "follows"
, Word "by"
, Ref
( "fin_intro_1" :| [] )
, Symbol "."
, EndEnv "proof"
]
,
[ BeginEnv "inductive"
, Label "acc"
, Word "define"
, BeginEnv "math"
, Command "acc"
, InvisibleBraceL
, Variable "R"
, InvisibleBraceR
, Command "subseteq"
, Command "wrap"
, InvisibleBraceL
, Variable "R"
, InvisibleBraceR
, EndEnv "math"
, Word "inductively"
, Word "as"
, Word "follows"
, Symbol "."
, BeginEnv "enumerate"
, Command "item"
, Word "if"
, BeginEnv "math"
, Variable "x"
, Command "in"
, Command "wrap"
, InvisibleBraceL
, Command "acc"
, InvisibleBraceL
, Variable "R"
, InvisibleBraceR
, InvisibleBraceR
, EndEnv "math"
, Symbol ","
, Word "then"
, BeginEnv "math"
, Variable "x"
, Command "in"
, Command "acc"
, InvisibleBraceL
, Variable "R"
, InvisibleBraceR
, EndEnv "math"
, Symbol "."
, EndEnv "enumerate"
, EndEnv "inductive"
]
]
|
