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[
    [ BeginEnv "proposition"
    , Label "in_irrefl"
    , Word "for"
    , Word "all"
    , Word "sets"
    , BeginEnv "math"
    , Variable "A"
    , EndEnv "math"
    , Word "we"
    , Word "have"
    , BeginEnv "math"
    , Variable "A"
    , Command "not"
    , Command "in"
    , Variable "A"
    , EndEnv "math"
    , Symbol "."
    , EndEnv "proposition"
    ]
,
    [ BeginEnv "proof"
    , BracketL
    , Word "proof"
    , Word "by"
    , Command "in"
    , Word "-induction"
    , BracketR
    , Word "straightforward"
    , Symbol "."
    , EndEnv "proof"
    ]
]