[ BeginEnv "proposition"
, Label "first_proposition"
, BeginEnv "math"
, Variable "a"
, Symbol "="
, Variable "a"
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
, BeginEnv "proposition"
, Label "second_proposition"
, BeginEnv "math"
, Variable "b"
, Symbol "="
, Variable "b"
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
, BeginEnv "proposition"
, Label "third_proposition"
, BeginEnv "math"
, Variable "c"
, Symbol "="
, Variable "c"
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
, BeginEnv "proof"
, Word "follows"
, Word "by"
, Ref
    ( "first_proposition" :| [] )
, Symbol "."
, EndEnv "proof"
, BeginEnv "proposition"
, Label "fourth_proposition"
, BeginEnv "math"
, Variable "e"
, Symbol "="
, Variable "e"
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
, BeginEnv "proof"
, Word "for"
, Word "all"
, BeginEnv "math"
, Variable "d"
, EndEnv "math"
, Word "we"
, Word "have"
, BeginEnv "math"
, Variable "d"
, Symbol "="
, Variable "d"
, EndEnv "math"
, Word "by"
, Ref
    ( "first_proposition" :| [] )
, Symbol "."
, EndEnv "proof"
, BeginEnv "proposition"
, Label "fifth_proposition"
, BeginEnv "math"
, Variable "f"
, Symbol "="
, Variable "f"
, EndEnv "math"
, Symbol "."
, EndEnv "proposition"
]