[ BlockAxiom
    ( Location
        { locFile = "test/examples/union.tex"
        , locLine = 1
        , locColumn = 1
        }
    )
    ( Just
        [ Word "extensionality" ]
    )
    ( Marker "ext" )
    ( Axiom
        [ AsmSuppose
            ( SymbolicQuantified
                { loc = Location
                    { locFile = "test/examples/union.tex"
                    , locLine = 2
                    , locColumn = 13
                    }
                , quant = Universally
                , vars = NamedVar "a" :| []
                , b = Unbounded
                , suchThat = Nothing
                , stmt = StmtConnected
                    { conn = Equivalence
                    , mloc = Nothing
                    , stmt1 = StmtFormula
                        { formula = FormulaChain
                            ( ChainBase
                                ( ExprVar
                                    ( NamedVar "a" ) :| []
                                ) Positive
                                ( Relation
                                    ( Location
                                        { locFile = "test/examples/union.tex"
                                        , locLine = 2
                                        , locColumn = 35
                                        }
                                    )
                                    ( RelationSymbol
                                        ( Command "in" )
                                        ( ParameterArity 0 )
                                        ( Marker "elem" )
                                    ) []
                                )
                                ( ExprVar
                                    ( NamedVar "A" ) :| []
                                )
                            )
                        }
                    , stmt2 = StmtFormula
                        { formula = FormulaChain
                            ( ChainBase
                                ( ExprVar
                                    ( NamedVar "a" ) :| []
                                ) Positive
                                ( Relation
                                    ( Location
                                        { locFile = "test/examples/union.tex"
                                        , locLine = 2
                                        , locColumn = 48
                                        }
                                    )
                                    ( RelationSymbol
                                        ( Command "in" )
                                        ( ParameterArity 0 )
                                        ( Marker "elem" )
                                    ) []
                                )
                                ( ExprVar
                                    ( NamedVar "B" ) :| []
                                )
                            )
                        }
                    }
                }
            )
        ]
        ( StmtFormula
            { formula = FormulaChain
                ( ChainBase
                    ( ExprVar
                        ( NamedVar "A" ) :| []
                    ) Positive
                    ( Relation
                        ( Location
                            { locFile = "test/examples/union.tex"
                            , locLine = 3
                            , locColumn = 13
                            }
                        )
                        ( RelationSymbol
                            ( Symbol "=" )
                            ( ParameterArity 0 )
                            ( Marker "eq" )
                        ) []
                    )
                    ( ExprVar
                        ( NamedVar "B" ) :| []
                    )
                )
            }
        )
    )
, BlockAxiom
    ( Location
        { locFile = "test/examples/union.tex"
        , locLine = 6
        , locColumn = 1
        }
    ) Nothing
    ( Marker "union_defn" )
    ( Axiom
        [ AsmLetNoun
            ( NamedVar "A" :|
                [ NamedVar "B" ]
            ) NounPhrase ( [] )
            ( Noun
                ( Location
                    { locFile = "test/examples/union.tex"
                    , locLine = 7
                    , locColumn = 19
                    }
                )
                ( LexicalItemSgPl
                    ( SgPl
                        { sg = TokenCons
                            ( Word "set" ) End
                        , pl = TokenCons
                            ( Word "sets" ) End
                        }
                    )
                    ( Marker "set" )
                ) []
            ) ( Nothing ) ( [] ) ( Nothing )
        ]
        ( StmtConnected
            { conn = Equivalence
            , mloc = Nothing
            , stmt1 = StmtFormula
                { formula = FormulaChain
                    ( ChainBase
                        ( ExprVar
                            ( NamedVar "a" ) :| []
                        ) Positive
                        ( Relation
                            ( Location
                                { locFile = "test/examples/union.tex"
                                , locLine = 8
                                , locColumn = 7
                                }
                            )
                            ( RelationSymbol
                                ( Command "in" )
                                ( ParameterArity 0 )
                                ( Marker "elem" )
                            ) []
                        )
                        ( ExprOp
                            ( Location
                                { locFile = "test/examples/union.tex"
                                , locLine = 8
                                , locColumn = 11
                                }
                            )
                            ( MixfixItem
                                ( HoleCons
                                    ( TokenCons
                                        ( Command "union" ) ( HoleCons End )
                                    )
                                )
                                ( Marker "union" ) LeftAssoc
                            )
                            [ ExprVar
                                ( NamedVar "A" )
                            , ExprVar
                                ( NamedVar "B" )
                            ] :| []
                        )
                    )
                }
            , stmt2 = StmtConnected
                { conn = Disjunction
                , mloc = Nothing
                , stmt1 = StmtFormula
                    { formula = FormulaChain
                        ( ChainBase
                            ( ExprVar
                                ( NamedVar "a" ) :| []
                            ) Positive
                            ( Relation
                                ( Location
                                    { locFile = "test/examples/union.tex"
                                    , locLine = 8
                                    , locColumn = 28
                                    }
                                )
                                ( RelationSymbol
                                    ( Command "in" )
                                    ( ParameterArity 0 )
                                    ( Marker "elem" )
                                ) []
                            )
                            ( ExprVar
                                ( NamedVar "A" ) :| []
                            )
                        )
                    }
                , stmt2 = StmtFormula
                    { formula = FormulaChain
                        ( ChainBase
                            ( ExprVar
                                ( NamedVar "a" ) :| []
                            ) Positive
                            ( Relation
                                ( Location
                                    { locFile = "test/examples/union.tex"
                                    , locLine = 8
                                    , locColumn = 40
                                    }
                                )
                                ( RelationSymbol
                                    ( Command "in" )
                                    ( ParameterArity 0 )
                                    ( Marker "elem" )
                                ) []
                            )
                            ( ExprVar
                                ( NamedVar "B" ) :| []
                            )
                        )
                    }
                }
            }
        )
    )
, BlockClaim Proposition
    ( Location
        { locFile = "test/examples/union.tex"
        , locLine = 11
        , locColumn = 1
        }
    ) Nothing
    ( Marker "union_comm" )
    ( Claim []
        ( StmtFormula
            { formula = FormulaChain
                ( ChainBase
                    ( ExprOp
                        ( Location
                            { locFile = "test/examples/union.tex"
                            , locLine = 12
                            , locColumn = 6
                            }
                        )
                        ( MixfixItem
                            ( HoleCons
                                ( TokenCons
                                    ( Command "union" ) ( HoleCons End )
                                )
                            )
                            ( Marker "union" ) LeftAssoc
                        )
                        [ ExprVar
                            ( NamedVar "A" )
                        , ExprVar
                            ( NamedVar "B" )
                        ] :| []
                    ) Positive
                    ( Relation
                        ( Location
                            { locFile = "test/examples/union.tex"
                            , locLine = 12
                            , locColumn = 16
                            }
                        )
                        ( RelationSymbol
                            ( Symbol "=" )
                            ( ParameterArity 0 )
                            ( Marker "eq" )
                        ) []
                    )
                    ( ExprOp
                        ( Location
                            { locFile = "test/examples/union.tex"
                            , locLine = 12
                            , locColumn = 18
                            }
                        )
                        ( MixfixItem
                            ( HoleCons
                                ( TokenCons
                                    ( Command "union" ) ( HoleCons End )
                                )
                            )
                            ( Marker "union" ) LeftAssoc
                        )
                        [ ExprVar
                            ( NamedVar "B" )
                        , ExprVar
                            ( NamedVar "A" )
                        ] :| []
                    )
                )
            }
        )
    )
, BlockClaim Proposition
    ( Location
        { locFile = "test/examples/union.tex"
        , locLine = 15
        , locColumn = 1
        }
    ) Nothing
    ( Marker "union_assoc" )
    ( Claim []
        ( StmtFormula
            { formula = FormulaChain
                ( ChainBase
                    ( ExprOp
                        ( Location
                            { locFile = "test/examples/union.tex"
                            , locLine = 16
                            , locColumn = 7
                            }
                        )
                        ( MixfixItem
                            ( HoleCons
                                ( TokenCons
                                    ( Command "union" ) ( HoleCons End )
                                )
                            )
                            ( Marker "union" ) LeftAssoc
                        )
                        [ ExprOp
                            ( Location
                                { locFile = "test/examples/union.tex"
                                , locLine = 16
                                , locColumn = 7
                                }
                            )
                            ( MixfixItem
                                ( HoleCons
                                    ( TokenCons
                                        ( Command "union" ) ( HoleCons End )
                                    )
                                )
                                ( Marker "union" ) LeftAssoc
                            )
                            [ ExprVar
                                ( NamedVar "A" )
                            , ExprVar
                                ( NamedVar "B" )
                            ]
                        , ExprVar
                            ( NamedVar "C" )
                        ] :| []
                    ) Positive
                    ( Relation
                        ( Location
                            { locFile = "test/examples/union.tex"
                            , locLine = 16
                            , locColumn = 26
                            }
                        )
                        ( RelationSymbol
                            ( Symbol "=" )
                            ( ParameterArity 0 )
                            ( Marker "eq" )
                        ) []
                    )
                    ( ExprOp
                        ( Location
                            { locFile = "test/examples/union.tex"
                            , locLine = 16
                            , locColumn = 28
                            }
                        )
                        ( MixfixItem
                            ( HoleCons
                                ( TokenCons
                                    ( Command "union" ) ( HoleCons End )
                                )
                            )
                            ( Marker "union" ) LeftAssoc
                        )
                        [ ExprVar
                            ( NamedVar "A" )
                        , ExprOp
                            ( Location
                                { locFile = "test/examples/union.tex"
                                , locLine = 16
                                , locColumn = 37
                                }
                            )
                            ( MixfixItem
                                ( HoleCons
                                    ( TokenCons
                                        ( Command "union" ) ( HoleCons End )
                                    )
                                )
                                ( Marker "union" ) LeftAssoc
                            )
                            [ ExprVar
                                ( NamedVar "B" )
                            , ExprVar
                                ( NamedVar "C" )
                            ]
                        ] :| []
                    )
                )
            }
        )
    )
, BlockProof
    ( Location
        { locFile = "test/examples/union.tex"
        , locLine = 18
        , locColumn = 1
        }
    )
    ( Have
        ( Location
            { locFile = "test/examples/union.tex"
            , locLine = 19
            , locColumn = 5
            }
        ) Nothing
        ( SymbolicQuantified
            { loc = Location
                { locFile = "test/examples/union.tex"
                , locLine = 19
                , locColumn = 5
                }
            , quant = Universally
            , vars = NamedVar "a" :| []
            , b = Unbounded
            , suchThat = Nothing
            , stmt = StmtConnected
                { conn = Implication
                , mloc = Just
                    ( Location
                        { locFile = "test/examples/union.tex"
                        , locLine = 19
                        , locColumn = 25
                        }
                    )
                , stmt1 = StmtFormula
                    { formula = FormulaChain
                        ( ChainBase
                            ( ExprVar
                                ( NamedVar "a" ) :| []
                            ) Positive
                            ( Relation
                                ( Location
                                    { locFile = "test/examples/union.tex"
                                    , locLine = 19
                                    , locColumn = 30
                                    }
                                )
                                ( RelationSymbol
                                    ( Command "in" )
                                    ( ParameterArity 0 )
                                    ( Marker "elem" )
                                ) []
                            )
                            ( ExprOp
                                ( Location
                                    { locFile = "test/examples/union.tex"
                                    , locLine = 19
                                    , locColumn = 35
                                    }
                                )
                                ( MixfixItem
                                    ( HoleCons
                                        ( TokenCons
                                            ( Command "union" ) ( HoleCons End )
                                        )
                                    )
                                    ( Marker "union" ) LeftAssoc
                                )
                                [ ExprOp
                                    ( Location
                                        { locFile = "test/examples/union.tex"
                                        , locLine = 19
                                        , locColumn = 35
                                        }
                                    )
                                    ( MixfixItem
                                        ( HoleCons
                                            ( TokenCons
                                                ( Command "union" ) ( HoleCons End )
                                            )
                                        )
                                        ( Marker "union" ) LeftAssoc
                                    )
                                    [ ExprVar
                                        ( NamedVar "A" )
                                    , ExprVar
                                        ( NamedVar "B" )
                                    ]
                                , ExprVar
                                    ( NamedVar "C" )
                                ] :| []
                            )
                        )
                    }
                , stmt2 = StmtFormula
                    { formula = FormulaChain
                        ( ChainBase
                            ( ExprVar
                                ( NamedVar "a" ) :| []
                            ) Positive
                            ( Relation
                                ( Location
                                    { locFile = "test/examples/union.tex"
                                    , locLine = 19
                                    , locColumn = 63
                                    }
                                )
                                ( RelationSymbol
                                    ( Command "in" )
                                    ( ParameterArity 0 )
                                    ( Marker "elem" )
                                ) []
                            )
                            ( ExprOp
                                ( Location
                                    { locFile = "test/examples/union.tex"
                                    , locLine = 19
                                    , locColumn = 67
                                    }
                                )
                                ( MixfixItem
                                    ( HoleCons
                                        ( TokenCons
                                            ( Command "union" ) ( HoleCons End )
                                        )
                                    )
                                    ( Marker "union" ) LeftAssoc
                                )
                                [ ExprVar
                                    ( NamedVar "A" )
                                , ExprOp
                                    ( Location
                                        { locFile = "test/examples/union.tex"
                                        , locLine = 19
                                        , locColumn = 76
                                        }
                                    )
                                    ( MixfixItem
                                        ( HoleCons
                                            ( TokenCons
                                                ( Command "union" ) ( HoleCons End )
                                            )
                                        )
                                        ( Marker "union" ) LeftAssoc
                                    )
                                    [ ExprVar
                                        ( NamedVar "B" )
                                    , ExprVar
                                        ( NamedVar "C" )
                                    ]
                                ] :| []
                            )
                        )
                    }
                }
            }
        ) JustificationEmpty
        ( Have
            ( Location
                { locFile = "test/examples/union.tex"
                , locLine = 20
                , locColumn = 5
                }
            ) Nothing
            ( SymbolicQuantified
                { loc = Location
                    { locFile = "test/examples/union.tex"
                    , locLine = 20
                    , locColumn = 5
                    }
                , quant = Universally
                , vars = NamedVar "a" :| []
                , b = Unbounded
                , suchThat = Nothing
                , stmt = StmtConnected
                    { conn = Implication
                    , mloc = Just
                        ( Location
                            { locFile = "test/examples/union.tex"
                            , locLine = 20
                            , locColumn = 25
                            }
                        )
                    , stmt1 = StmtFormula
                        { formula = FormulaChain
                            ( ChainBase
                                ( ExprVar
                                    ( NamedVar "a" ) :| []
                                ) Positive
                                ( Relation
                                    ( Location
                                        { locFile = "test/examples/union.tex"
                                        , locLine = 20
                                        , locColumn = 30
                                        }
                                    )
                                    ( RelationSymbol
                                        ( Command "in" )
                                        ( ParameterArity 0 )
                                        ( Marker "elem" )
                                    ) []
                                )
                                ( ExprOp
                                    ( Location
                                        { locFile = "test/examples/union.tex"
                                        , locLine = 20
                                        , locColumn = 34
                                        }
                                    )
                                    ( MixfixItem
                                        ( HoleCons
                                            ( TokenCons
                                                ( Command "union" ) ( HoleCons End )
                                            )
                                        )
                                        ( Marker "union" ) LeftAssoc
                                    )
                                    [ ExprVar
                                        ( NamedVar "A" )
                                    , ExprOp
                                        ( Location
                                            { locFile = "test/examples/union.tex"
                                            , locLine = 20
                                            , locColumn = 43
                                            }
                                        )
                                        ( MixfixItem
                                            ( HoleCons
                                                ( TokenCons
                                                    ( Command "union" ) ( HoleCons End )
                                                )
                                            )
                                            ( Marker "union" ) LeftAssoc
                                        )
                                        [ ExprVar
                                            ( NamedVar "B" )
                                        , ExprVar
                                            ( NamedVar "C" )
                                        ]
                                    ] :| []
                                )
                            )
                        }
                    , stmt2 = StmtFormula
                        { formula = FormulaChain
                            ( ChainBase
                                ( ExprVar
                                    ( NamedVar "a" ) :| []
                                ) Positive
                                ( Relation
                                    ( Location
                                        { locFile = "test/examples/union.tex"
                                        , locLine = 20
                                        , locColumn = 63
                                        }
                                    )
                                    ( RelationSymbol
                                        ( Command "in" )
                                        ( ParameterArity 0 )
                                        ( Marker "elem" )
                                    ) []
                                )
                                ( ExprOp
                                    ( Location
                                        { locFile = "test/examples/union.tex"
                                        , locLine = 20
                                        , locColumn = 68
                                        }
                                    )
                                    ( MixfixItem
                                        ( HoleCons
                                            ( TokenCons
                                                ( Command "union" ) ( HoleCons End )
                                            )
                                        )
                                        ( Marker "union" ) LeftAssoc
                                    )
                                    [ ExprOp
                                        ( Location
                                            { locFile = "test/examples/union.tex"
                                            , locLine = 20
                                            , locColumn = 68
                                            }
                                        )
                                        ( MixfixItem
                                            ( HoleCons
                                                ( TokenCons
                                                    ( Command "union" ) ( HoleCons End )
                                                )
                                            )
                                            ( Marker "union" ) LeftAssoc
                                        )
                                        [ ExprVar
                                            ( NamedVar "A" )
                                        , ExprVar
                                            ( NamedVar "B" )
                                        ]
                                    , ExprVar
                                        ( NamedVar "C" )
                                    ] :| []
                                )
                            )
                        }
                    }
                }
            ) JustificationEmpty ( Qed Nothing JustificationEmpty )
        )
    )
    ( Location
        { locFile = "test/examples/union.tex"
        , locLine = 21
        , locColumn = 1
        }
    )
]