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|
[
[ BeginEnv "signature"
, Label "example_cons"
, BeginEnv "math"
, Command "cons"
, InvisibleBraceL
, Variable "y"
, InvisibleBraceR
, InvisibleBraceL
, Variable "X"
, InvisibleBraceR
, EndEnv "math"
, Word "is"
, Word "a"
, Word "set"
, Symbol "."
, EndEnv "signature"
]
,
[ BeginEnv "signature"
, Label "example_pair"
, BeginEnv "math"
, ParenL
, Variable "x"
, Symbol ","
, Variable "y"
, ParenR
, EndEnv "math"
, Word "is"
, Word "a"
, Word "set"
, Symbol "."
, EndEnv "signature"
]
,
[ BeginEnv "axiom"
, Label "cons"
, BeginEnv "math"
, Variable "x"
, Command "in"
, Command "cons"
, InvisibleBraceL
, Variable "y"
, InvisibleBraceR
, InvisibleBraceL
, Variable "X"
, InvisibleBraceR
, EndEnv "math"
, Word "iff"
, BeginEnv "math"
, Variable "x"
, Symbol "="
, Variable "y"
, EndEnv "math"
, Word "or"
, BeginEnv "math"
, Variable "x"
, Command "in"
, Variable "X"
, EndEnv "math"
, Symbol "."
, EndEnv "axiom"
]
,
[ BeginEnv "definition"
, Label "times"
, BeginEnv "math"
, Variable "A"
, Command "times"
, Variable "B"
, Symbol "="
, VisibleBraceL
, ParenL
, Variable "a"
, Symbol ","
, Variable "b"
, ParenR
, Command "mid"
, Variable "a"
, Command "in"
, Variable "A"
, Symbol ","
, Variable "b"
, Command "in"
, Variable "B"
, VisibleBraceR
, EndEnv "math"
, Symbol "."
, EndEnv "definition"
]
,
[ BeginEnv "definition"
, Label "unit"
, BeginEnv "math"
, Command "unit"
, Symbol "="
, VisibleBraceL
, Command "emptyset"
, VisibleBraceR
, EndEnv "math"
, Symbol "."
, EndEnv "definition"
]
,
[ BeginEnv "proposition"
, Label "pair_emptyset_in_times_unit"
, BeginEnv "math"
, ParenL
, Command "emptyset"
, Symbol ","
, Command "emptyset"
, ParenR
, Command "in"
, Command "unit"
, Command "times"
, Command "unit"
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
]
,
[ BeginEnv "definition"
, Label "suc"
, BeginEnv "math"
, Command "suc"
, InvisibleBraceL
, Variable "a"
, InvisibleBraceR
, Symbol "="
, VisibleBraceL
, Variable "y"
, Command "mid"
, Command "exists"
, Variable "x"
, Command "in"
, Variable "a"
, Symbol "."
, Variable "y"
, Symbol "="
, VisibleBraceL
, Variable "x"
, VisibleBraceR
, VisibleBraceR
, EndEnv "math"
, Symbol "."
, EndEnv "definition"
]
,
[ BeginEnv "proposition"
, Label "times_replacement_test"
, BeginEnv "math"
, Variable "A"
, Command "times"
, Variable "B"
, Symbol "="
, VisibleBraceL
, ParenL
, Variable "a"
, Symbol ","
, Variable "b"
, ParenR
, Command "mid"
, Variable "a"
, Command "in"
, Variable "A"
, Symbol ","
, Variable "b"
, Command "in"
, Variable "B"
, VisibleBraceR
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
]
,
[ BeginEnv "proof"
, Word "follows"
, Word "by"
, Ref
( "times" :| [] )
, Symbol "."
, EndEnv "proof"
]
]
|
