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[
[ BeginEnv "datatype"
, Label "propform"
, Word "define"
, BeginEnv "math"
, Command "propform"
, EndEnv "math"
, Word "inductively"
, Word "as"
, Word "follows"
, Symbol "."
, BeginEnv "enumerate"
, Command "item"
, BeginEnv "math"
, Command "propbot"
, Command "in"
, Command "propform"
, EndEnv "math"
, Symbol "."
, Command "item"
, BeginEnv "math"
, Command "propvar"
, InvisibleBraceL
, Variable "n"
, InvisibleBraceR
, Command "in"
, Command "propform"
, EndEnv "math"
, Word "for"
, BeginEnv "math"
, Variable "n"
, Command "in"
, VisibleBraceL
, Command "emptyset"
, VisibleBraceR
, EndEnv "math"
, Symbol "."
, Command "item"
, BeginEnv "math"
, ParenL
, Variable "p"
, Command "propto"
, Variable "q"
, ParenR
, Command "in"
, Command "propform"
, EndEnv "math"
, Word "for"
, BeginEnv "math"
, Variable "p"
, Command "in"
, Command "propform"
, EndEnv "math"
, Word "and"
, BeginEnv "math"
, Variable "q"
, Command "in"
, Command "propform"
, EndEnv "math"
, Symbol "."
, EndEnv "enumerate"
, EndEnv "datatype"
]
,
[ BeginEnv "proposition"
, Label "propform_bot_test"
, BeginEnv "math"
, Command "propbot"
, Command "in"
, Command "propform"
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
]
,
[ BeginEnv "proposition"
, Label "propform_var_test"
, Word "if"
, BeginEnv "math"
, Command "emptyset"
, Command "in"
, VisibleBraceL
, Command "emptyset"
, VisibleBraceR
, EndEnv "math"
, Symbol ","
, Word "then"
, BeginEnv "math"
, Command "propvar"
, InvisibleBraceL
, Command "emptyset"
, InvisibleBraceR
, Command "in"
, Command "propform"
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
]
,
[ BeginEnv "proposition"
, Label "propform_imp_test"
, BeginEnv "math"
, ParenL
, Command "propbot"
, Command "propto"
, Command "propbot"
, ParenR
, Command "in"
, Command "propform"
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
]
,
[ BeginEnv "proposition"
, Label "propform_distinct_test"
, BeginEnv "math"
, Command "propbot"
, Command "neq"
, ParenL
, Command "propbot"
, Command "propto"
, Command "propbot"
, ParenR
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
]
,
[ BeginEnv "proposition"
, Label "propform_injective_test"
, Word "if"
, BeginEnv "math"
, Command "propvar"
, InvisibleBraceL
, Variable "x"
, InvisibleBraceR
, Symbol "="
, Command "propvar"
, InvisibleBraceL
, Variable "y"
, InvisibleBraceR
, EndEnv "math"
, Symbol ","
, Word "then"
, BeginEnv "math"
, Variable "x"
, Symbol "="
, Variable "y"
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
]
]
|
