[ BlockDefn
    ( SourcePos
        { sourceName = "test/examples/proofdefinefunction.tex"
        , sourceLine = Pos 3
        , sourceColumn = Pos 1
        }
    )
    ( Marker "apply" )
    ( DefnOp
        ( SymbolPattern
            [ Just
                ( Command "apply" )
            , Just InvisibleBraceL
            , Nothing
            , Just InvisibleBraceR
            , Just InvisibleBraceL
            , Nothing
            , Just InvisibleBraceR
            ]
            [ NamedVar "f"
            , NamedVar "x"
            ]
        )
        ( ExprVar
            ( NamedVar "x" )
        )
    )
, BlockDefn
    ( SourcePos
        { sourceName = "test/examples/proofdefinefunction.tex"
        , sourceLine = Pos 8
        , sourceColumn = Pos 1
        }
    )
    ( Marker "dom" )
    ( DefnOp
        ( SymbolPattern
            [ Just
                ( Command "dom" )
            , Just InvisibleBraceL
            , Nothing
            , Just InvisibleBraceR
            ]
            [ NamedVar "f" ]
        )
        ( ExprVar
            ( NamedVar "f" )
        )
    )
, BlockDefn
    ( SourcePos
        { sourceName = "test/examples/proofdefinefunction.tex"
        , sourceLine = Pos 13
        , sourceColumn = Pos 1
        }
    )
    ( Marker "rightunique" )
    ( Defn []
        ( DefnAdj Nothing
            ( NamedVar "f" )
            ( Adj
                [ Just
                    ( Word "right-unique" )
                ] []
            )
        )
        ( StmtFormula
            ( FormulaChain
                ( ChainBase
                    ( ExprVar
                        ( NamedVar "f" ) :| []
                    ) Positive
                    ( RelationSymbol
                        ( Symbol "=" )
                    )
                    ( ExprVar
                        ( NamedVar "f" ) :| []
                    )
                )
            )
        )
    )
, BlockDefn
    ( SourcePos
        { sourceName = "test/examples/proofdefinefunction.tex"
        , sourceLine = Pos 18
        , sourceColumn = Pos 1
        }
    )
    ( Marker "relation" )
    ( Defn []
        ( DefnNoun
            ( NamedVar "f" )
            ( Noun
                ( SgPl
                    { sg =
                        [ Just
                            ( Word "relation" )
                        ]
                    , pl =
                        [ Just
                            ( Word "relations" )
                        ]
                    }
                ) []
            )
        )
        ( StmtFormula
            ( FormulaChain
                ( ChainBase
                    ( ExprVar
                        ( NamedVar "f" ) :| []
                    ) Positive
                    ( RelationSymbol
                        ( Symbol "=" )
                    )
                    ( ExprVar
                        ( NamedVar "f" ) :| []
                    )
                )
            )
        )
    )
, BlockLemma
    ( SourcePos
        { sourceName = "test/examples/proofdefinefunction.tex"
        , sourceLine = Pos 22
        , sourceColumn = Pos 1
        }
    )
    ( Marker "definefunctiontest" )
    ( Lemma []
        ( StmtConnected Implication
            ( StmtFormula
                ( FormulaChain
                    ( ChainBase
                        ( ExprVar
                            ( NamedVar "x" ) :| []
                        ) Positive
                        ( RelationSymbol
                            ( Command "in" )
                        )
                        ( ExprVar
                            ( NamedVar "y" ) :| []
                        )
                    )
                )
            )
            ( StmtFormula
                ( FormulaChain
                    ( ChainBase
                        ( ExprVar
                            ( NamedVar "x" ) :| []
                        ) Positive
                        ( RelationSymbol
                            ( Command "in" )
                        )
                        ( ExprVar
                            ( NamedVar "y" ) :| []
                        )
                    )
                )
            )
        )
    )
, BlockProof
    ( SourcePos
        { sourceName = "test/examples/proofdefinefunction.tex"
        , sourceLine = Pos 25
        , sourceColumn = Pos 1
        }
    )
    ( DefineFunction
        ( NamedVar "f" )
        ( NamedVar "z" )
        ( ExprVar
            ( NamedVar "z" )
        )
        ( NamedVar "z" )
        ( ExprVar
            ( NamedVar "x" )
        ) ( Qed JustificationEmpty )
    )
]