[ BlockAxiom
    ( SourcePos
        { sourceName = "test/examples/union.tex"
        , sourceLine = Pos 1
        , sourceColumn = Pos 1
        }
    )
    ( Marker "ext" )
    ( Axiom
        [ Asm
            ( Quantified Universally
                ( Scope
                    ( Connected Equivalence
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( F
                                    ( TermVar
                                        ( NamedVar "A" )
                                    )
                                )
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermVar
                                ( F
                                    ( TermVar
                                        ( NamedVar "B" )
                                    )
                                )
                            ]
                        )
                    )
                )
            )
        ]
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Symbol "=" )
                )
            )
            [ TermVar
                ( NamedVar "A" )
            , TermVar
                ( NamedVar "B" )
            ]
        )
    )
, BlockAxiom
    ( SourcePos
        { sourceName = "test/examples/union.tex"
        , sourceLine = Pos 6
        , sourceColumn = Pos 1
        }
    )
    ( Marker "union_defn" )
    ( Axiom
        [ Asm ( PropositionalConstant IsTop )
        , Asm ( PropositionalConstant IsTop )
        ]
        ( Connected Equivalence
            ( TermSymbol
                ( SymbolPredicate
                    ( PredicateRelation
                        ( Command "in" )
                    )
                )
                [ TermVar
                    ( NamedVar "a" )
                , TermSymbol
                    ( SymbolMixfix
                        [ Nothing
                        , Just
                            ( Command "union" )
                        , Nothing
                        ]
                    )
                    [ TermVar
                        ( NamedVar "A" )
                    , TermVar
                        ( NamedVar "B" )
                    ]
                ]
            )
            ( Connected Disjunction
                ( TermSymbol
                    ( SymbolPredicate
                        ( PredicateRelation
                            ( Command "in" )
                        )
                    )
                    [ TermVar
                        ( NamedVar "a" )
                    , TermVar
                        ( NamedVar "A" )
                    ]
                )
                ( TermSymbol
                    ( SymbolPredicate
                        ( PredicateRelation
                            ( Command "in" )
                        )
                    )
                    [ TermVar
                        ( NamedVar "a" )
                    , TermVar
                        ( NamedVar "B" )
                    ]
                )
            )
        )
    )
, BlockLemma
    ( SourcePos
        { sourceName = "test/examples/union.tex"
        , sourceLine = Pos 11
        , sourceColumn = Pos 1
        }
    )
    ( Marker "union_comm" )
    ( Lemma []
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Symbol "=" )
                )
            )
            [ TermSymbol
                ( SymbolMixfix
                    [ Nothing
                    , Just
                        ( Command "union" )
                    , Nothing
                    ]
                )
                [ TermVar
                    ( NamedVar "A" )
                , TermVar
                    ( NamedVar "B" )
                ]
            , TermSymbol
                ( SymbolMixfix
                    [ Nothing
                    , Just
                        ( Command "union" )
                    , Nothing
                    ]
                )
                [ TermVar
                    ( NamedVar "B" )
                , TermVar
                    ( NamedVar "A" )
                ]
            ]
        )
    )
, BlockLemma
    ( SourcePos
        { sourceName = "test/examples/union.tex"
        , sourceLine = Pos 15
        , sourceColumn = Pos 1
        }
    )
    ( Marker "union_assoc" )
    ( Lemma []
        ( TermSymbol
            ( SymbolPredicate
                ( PredicateRelation
                    ( Symbol "=" )
                )
            )
            [ TermSymbol
                ( SymbolMixfix
                    [ Nothing
                    , Just
                        ( Command "union" )
                    , Nothing
                    ]
                )
                [ TermSymbol
                    ( SymbolMixfix
                        [ Nothing
                        , Just
                            ( Command "union" )
                        , Nothing
                        ]
                    )
                    [ TermVar
                        ( NamedVar "A" )
                    , TermVar
                        ( NamedVar "B" )
                    ]
                , TermVar
                    ( NamedVar "C" )
                ]
            , TermSymbol
                ( SymbolMixfix
                    [ Nothing
                    , Just
                        ( Command "union" )
                    , Nothing
                    ]
                )
                [ TermVar
                    ( NamedVar "A" )
                , TermSymbol
                    ( SymbolMixfix
                        [ Nothing
                        , Just
                            ( Command "union" )
                        , Nothing
                        ]
                    )
                    [ TermVar
                        ( NamedVar "B" )
                    , TermVar
                        ( NamedVar "C" )
                    ]
                ]
            ]
        )
    )
, BlockProof
    ( SourcePos
        { sourceName = "test/examples/union.tex"
        , sourceLine = Pos 18
        , sourceColumn = Pos 1
        }
    )
    ( Have
        ( Quantified Universally
            ( Scope
                ( Connected Implication
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "a" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "union" )
                                , Nothing
                                ]
                            )
                            [ TermSymbol
                                ( SymbolMixfix
                                    [ Nothing
                                    , Just
                                        ( Command "union" )
                                    , Nothing
                                    ]
                                )
                                [ TermVar
                                    ( F
                                        ( TermVar
                                            ( NamedVar "A" )
                                        )
                                    )
                                , TermVar
                                    ( F
                                        ( TermVar
                                            ( NamedVar "B" )
                                        )
                                    )
                                ]
                            , TermVar
                                ( F
                                    ( TermVar
                                        ( NamedVar "C" )
                                    )
                                )
                            ]
                        ]
                    )
                    ( TermSymbol
                        ( SymbolPredicate
                            ( PredicateRelation
                                ( Command "in" )
                            )
                        )
                        [ TermVar
                            ( B
                                ( NamedVar "a" )
                            )
                        , TermSymbol
                            ( SymbolMixfix
                                [ Nothing
                                , Just
                                    ( Command "union" )
                                , Nothing
                                ]
                            )
                            [ TermVar
                                ( F
                                    ( TermVar
                                        ( NamedVar "A" )
                                    )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Nothing
                                    , Just
                                        ( Command "union" )
                                    , Nothing
                                    ]
                                )
                                [ TermVar
                                    ( F
                                        ( TermVar
                                            ( NamedVar "B" )
                                        )
                                    )
                                , TermVar
                                    ( F
                                        ( TermVar
                                            ( NamedVar "C" )
                                        )
                                    )
                                ]
                            ]
                        ]
                    )
                )
            )
        ) JustificationEmpty
        ( Have
            ( Quantified Universally
                ( Scope
                    ( Connected Implication
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Nothing
                                    , Just
                                        ( Command "union" )
                                    , Nothing
                                    ]
                                )
                                [ TermVar
                                    ( F
                                        ( TermVar
                                            ( NamedVar "A" )
                                        )
                                    )
                                , TermSymbol
                                    ( SymbolMixfix
                                        [ Nothing
                                        , Just
                                            ( Command "union" )
                                        , Nothing
                                        ]
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( NamedVar "B" )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( NamedVar "C" )
                                            )
                                        )
                                    ]
                                ]
                            ]
                        )
                        ( TermSymbol
                            ( SymbolPredicate
                                ( PredicateRelation
                                    ( Command "in" )
                                )
                            )
                            [ TermVar
                                ( B
                                    ( NamedVar "a" )
                                )
                            , TermSymbol
                                ( SymbolMixfix
                                    [ Nothing
                                    , Just
                                        ( Command "union" )
                                    , Nothing
                                    ]
                                )
                                [ TermSymbol
                                    ( SymbolMixfix
                                        [ Nothing
                                        , Just
                                            ( Command "union" )
                                        , Nothing
                                        ]
                                    )
                                    [ TermVar
                                        ( F
                                            ( TermVar
                                                ( NamedVar "A" )
                                            )
                                        )
                                    , TermVar
                                        ( F
                                            ( TermVar
                                                ( NamedVar "B" )
                                            )
                                        )
                                    ]
                                , TermVar
                                    ( F
                                        ( TermVar
                                            ( NamedVar "C" )
                                        )
                                    )
                                ]
                            ]
                        )
                    )
                )
            ) JustificationEmpty ( Qed JustificationEmpty )
        )
    )
]