[ BeginEnv "definition"
, Label "apply"
, BeginEnv "math"
, Command "apply"
, InvisibleBraceL
, Variable "f"
, InvisibleBraceR
, InvisibleBraceL
, Variable "x"
, InvisibleBraceR
, Symbol "="
, Variable "x"
, EndEnv "math"
, Symbol "."
, EndEnv "definition"
, BeginEnv "definition"
, Label "dom"
, BeginEnv "math"
, Command "dom"
, InvisibleBraceL
, Variable "f"
, InvisibleBraceR
, Symbol "="
, Variable "f"
, EndEnv "math"
, Symbol "."
, EndEnv "definition"
, BeginEnv "definition"
, Label "rightunique"
, BeginEnv "math"
, Variable "f"
, EndEnv "math"
, Word "is"
, Word "right-unique"
, Word "iff"
, BeginEnv "math"
, Variable "f"
, Symbol "="
, Variable "f"
, EndEnv "math"
, Symbol "."
, EndEnv "definition"
, BeginEnv "definition"
, Label "relation"
, BeginEnv "math"
, Variable "f"
, EndEnv "math"
, Word "is"
, Word "a"
, Word "relation"
, Word "iff"
, BeginEnv "math"
, Variable "f"
, Symbol "="
, Variable "f"
, EndEnv "math"
, Symbol "."
, EndEnv "definition"
, BeginEnv "proposition"
, Label "definefunctiontest"
, Word "if"
, BeginEnv "math"
, Variable "x"
, Command "in"
, Variable "y"
, EndEnv "math"
, Symbol ","
, Word "then"
, BeginEnv "math"
, Variable "x"
, Command "in"
, Variable "y"
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
, BeginEnv "proof"
, Word "let"
, BeginEnv "math"
, Variable "f"
, ParenL
, Variable "z"
, ParenR
, Symbol "="
, Variable "z"
, EndEnv "math"
, Word "for"
, BeginEnv "math"
, Variable "z"
, Command "in"
, Variable "x"
, EndEnv "math"
, Symbol "."
, EndEnv "proof"
]