[ BlockDefn ( Location { locFile = "test/examples/geometry.tex" , locLine = 1 , locColumn = 1 } ) Nothing ( Marker "collinear" ) ( Defn [] ( DefnAdj Nothing ( NamedVar "a" ) ( Adj ( Location { locFile = "test/examples/geometry.tex" , locLine = 2 , locColumn = 12 } ) ( LexicalItem ( TokenCons ( Word "collinear" ) ( TokenCons ( Word "with" ) ( HoleCons ( TokenCons ( Word "and" ) ( HoleCons End ) ) ) ) ) ( Marker "collinear" ) ) [ NamedVar "b" , NamedVar "c" ] ) ) ( StmtConnected { conn = Disjunction , mloc = Nothing , stmt1 = StmtConnected { conn = Disjunction , mloc = Nothing , stmt1 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 2 , locColumn = 44 } ) ( PrefixPredicate "Betw" 3 ) ( Marker "betw" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "c" ) ] ) } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 2 , locColumn = 64 } ) ( PrefixPredicate "Betw" 3 ) ( Marker "betw" ) ( ExprVar ( NamedVar "b" ) :| [ ExprVar ( NamedVar "c" ) , ExprVar ( NamedVar "a" ) ] ) } } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 2 , locColumn = 84 } ) ( PrefixPredicate "Betw" 3 ) ( Marker "betw" ) ( ExprVar ( NamedVar "c" ) :| [ ExprVar ( NamedVar "a" ) , ExprVar ( NamedVar "b" ) ] ) } } ) ) , BlockAxiom ( Location { locFile = "test/examples/geometry.tex" , locLine = 5 , locColumn = 1 } ) ( Just [ Word "reflexivity" , Word "of" , Word "congruence" ] ) ( Marker "cong_refl_swap" ) ( Axiom [ AsmLetNoun ( NamedVar "a" :| [ NamedVar "b" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 6 , locColumn = 19 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 7 , locColumn = 11 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "a" ) ] ) } ) ) , BlockAxiom ( Location { locFile = "test/examples/geometry.tex" , locLine = 10 , locColumn = 1 } ) ( Just [ Word "pseudotransitivity" , Word "of" , Word "congruence" ] ) ( Marker "cong_pseudotransitive" ) ( Axiom [ AsmLetNoun ( NamedVar "a" :| [ NamedVar "b" , NamedVar "c" , NamedVar "d" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 11 , locColumn = 25 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( StmtConnected { conn = Implication , mloc = Just ( Location { locFile = "test/examples/geometry.tex" , locLine = 12 , locColumn = 5 } ) , stmt1 = StmtConnected { conn = Conjunction , mloc = Nothing , stmt1 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 12 , locColumn = 9 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "c" ) :| [ ExprVar ( NamedVar "d" ) , ExprVar ( NamedVar "a" ) , ExprVar ( NamedVar "b" ) ] ) } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 12 , locColumn = 33 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "c" ) :| [ ExprVar ( NamedVar "d" ) , ExprVar ( NamedVar "e" ) , ExprVar ( NamedVar "f" ) ] ) } } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 12 , locColumn = 58 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "e" ) , ExprVar ( NamedVar "f" ) ] ) } } ) ) , BlockAxiom ( Location { locFile = "test/examples/geometry.tex" , locLine = 15 , locColumn = 1 } ) ( Just [ Word "identity" , Word "of" , Word "congruence" ] ) ( Marker "cong_id" ) ( Axiom [ AsmLetNoun ( NamedVar "a" :| [ NamedVar "b" , NamedVar "c" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 16 , locColumn = 22 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( StmtConnected { conn = Implication , mloc = Just ( Location { locFile = "test/examples/geometry.tex" , locLine = 17 , locColumn = 5 } ) , stmt1 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 17 , locColumn = 9 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "c" ) , ExprVar ( NamedVar "c" ) ] ) } , stmt2 = StmtFormula { formula = FormulaChain ( ChainBase ( ExprVar ( NamedVar "a" ) :| [] ) Positive ( Relation ( Location { locFile = "test/examples/geometry.tex" , locLine = 17 , locColumn = 36 } ) ( RelationSymbol ( Symbol "=" ) ( ParameterArity 0 ) ( Marker "eq" ) ) [] ) ( ExprVar ( NamedVar "b" ) :| [] ) ) } } ) ) , BlockAxiom ( Location { locFile = "test/examples/geometry.tex" , locLine = 21 , locColumn = 1 } ) ( Just [ Word "segment" , Word "construction" ] ) ( Marker "segment_construction" ) ( Axiom [] ( StmtExists { loc = Location { locFile = "test/examples/geometry.tex" , locLine = 22 , locColumn = 5 } , np = NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 22 , locColumn = 20 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( [ NamedVar "c" ] ) ( [] ) ( Just ( StmtConnected { conn = Conjunction , mloc = Nothing , stmt1 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 22 , locColumn = 41 } ) ( PrefixPredicate "Betw" 3 ) ( Marker "betw" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "c" ) ] ) } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 22 , locColumn = 62 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "b" ) :| [ ExprVar ( NamedVar "c" ) , ExprVar ( NamedVar "d" ) , ExprVar ( NamedVar "e" ) ] ) } } ) ) } ) ) , BlockDefn ( Location { locFile = "test/examples/geometry.tex" , locLine = 26 , locColumn = 1 } ) Nothing ( Marker "ofs" ) ( Defn [ AsmLetNoun ( NamedVar "x" :| [ NamedVar "y" , NamedVar "z" , NamedVar "r" , NamedVar "u" , NamedVar "v" , NamedVar "w" , NamedVar "p" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 27 , locColumn = 30 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( DefnSymbolicPredicate ( PrefixPredicate "OFS" 8 ) ( Marker "ofs" ) ( NamedVar "x" :| [ NamedVar "y" , NamedVar "z" , NamedVar "r" , NamedVar "u" , NamedVar "v" , NamedVar "w" , NamedVar "p" ] ) ) ( StmtConnected { conn = Conjunction , mloc = Nothing , stmt1 = StmtFormula { formula = Connected ( Location { locFile = "test/examples/geometry.tex" , locLine = 29 , locColumn = 6 } ) Conjunction ( FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 29 , locColumn = 6 } ) ( PrefixPredicate "Betw" 3 ) ( Marker "betw" ) ( ExprVar ( NamedVar "x" ) :| [ ExprVar ( NamedVar "y" ) , ExprVar ( NamedVar "z" ) ] ) ) ( FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 30 , locColumn = 13 } ) ( PrefixPredicate "Betw" 3 ) ( Marker "betw" ) ( ExprVar ( NamedVar "u" ) :| [ ExprVar ( NamedVar "v" ) , ExprVar ( NamedVar "w" ) ] ) ) } , stmt2 = StmtFormula { formula = Connected ( Location { locFile = "test/examples/geometry.tex" , locLine = 32 , locColumn = 6 } ) Conjunction ( Connected ( Location { locFile = "test/examples/geometry.tex" , locLine = 32 , locColumn = 6 } ) Conjunction ( Connected ( Location { locFile = "test/examples/geometry.tex" , locLine = 32 , locColumn = 6 } ) Conjunction ( FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 32 , locColumn = 6 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "x" ) :| [ ExprVar ( NamedVar "y" ) , ExprVar ( NamedVar "u" ) , ExprVar ( NamedVar "v" ) ] ) ) ( FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 33 , locColumn = 13 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "y" ) :| [ ExprVar ( NamedVar "z" ) , ExprVar ( NamedVar "v" ) , ExprVar ( NamedVar "w" ) ] ) ) ) ( FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 34 , locColumn = 13 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "x" ) :| [ ExprVar ( NamedVar "r" ) , ExprVar ( NamedVar "u" ) , ExprVar ( NamedVar "p" ) ] ) ) ) ( FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 35 , locColumn = 13 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "y" ) :| [ ExprVar ( NamedVar "r" ) , ExprVar ( NamedVar "v" ) , ExprVar ( NamedVar "p" ) ] ) ) } } ) ) , BlockAxiom ( Location { locFile = "test/examples/geometry.tex" , locLine = 39 , locColumn = 1 } ) ( Just [ Word "five" , Word "segment" , Word "axiom" ] ) ( Marker "five_segment" ) ( Axiom [ AsmLetNoun ( NamedVar "a" :| [ NamedVar "b" , NamedVar "c" , NamedVar "d" , NamedVar "a_" , NamedVar "b_" , NamedVar "c_" , NamedVar "d_" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 40 , locColumn = 34 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( StmtConnected { conn = Implication , mloc = Just ( Location { locFile = "test/examples/geometry.tex" , locLine = 41 , locColumn = 5 } ) , stmt1 = StmtConnected { conn = Conjunction , mloc = Nothing , stmt1 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 41 , locColumn = 9 } ) ( PrefixPredicate "OFS" 8 ) ( Marker "ofs" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "c" ) , ExprVar ( NamedVar "d" ) , ExprVar ( NamedVar "a_" ) , ExprVar ( NamedVar "b_" ) , ExprVar ( NamedVar "c_" ) , ExprVar ( NamedVar "d_" ) ] ) } , stmt2 = StmtFormula { formula = FormulaChain ( ChainBase ( ExprVar ( NamedVar "a" ) :| [] ) Positive ( Relation ( Location { locFile = "test/examples/geometry.tex" , locLine = 42 , locColumn = 8 } ) ( RelationSymbol ( Command "neq" ) ( ParameterArity 0 ) ( Marker "neq" ) ) [] ) ( ExprVar ( NamedVar "b" ) :| [] ) ) } } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 42 , locColumn = 22 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "c" ) :| [ ExprVar ( NamedVar "d" ) , ExprVar ( NamedVar "c_" ) , ExprVar ( NamedVar "d_" ) ] ) } } ) ) , BlockAxiom ( Location { locFile = "test/examples/geometry.tex" , locLine = 46 , locColumn = 1 } ) ( Just [ Word "identity" , Word "of" , Word "betweenness" ] ) ( Marker "betw_id" ) ( Axiom [ AsmLetNoun ( NamedVar "a" :| [ NamedVar "b" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 47 , locColumn = 18 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( StmtConnected { conn = Implication , mloc = Just ( Location { locFile = "test/examples/geometry.tex" , locLine = 48 , locColumn = 5 } ) , stmt1 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 48 , locColumn = 9 } ) ( PrefixPredicate "Betw" 3 ) ( Marker "betw" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "a" ) ] ) } , stmt2 = StmtFormula { formula = FormulaChain ( ChainBase ( ExprVar ( NamedVar "a" ) :| [] ) Positive ( Relation ( Location { locFile = "test/examples/geometry.tex" , locLine = 48 , locColumn = 33 } ) ( RelationSymbol ( Symbol "=" ) ( ParameterArity 0 ) ( Marker "eq" ) ) [] ) ( ExprVar ( NamedVar "b" ) :| [] ) ) } } ) ) , BlockAxiom ( Location { locFile = "test/examples/geometry.tex" , locLine = 52 , locColumn = 1 } ) ( Just [ Word "inner" , Word "pasch" ] ) ( Marker "innerpasch" ) ( Axiom [ AsmLetNoun ( NamedVar "x" :| [ NamedVar "y" , NamedVar "z" , NamedVar "u" , NamedVar "v" , NamedVar "w" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 53 , locColumn = 26 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( StmtConnected { conn = Implication , mloc = Just ( Location { locFile = "test/examples/geometry.tex" , locLine = 54 , locColumn = 5 } ) , stmt1 = StmtConnected { conn = Conjunction , mloc = Nothing , stmt1 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 54 , locColumn = 9 } ) ( PrefixPredicate "Betw" 3 ) ( Marker "betw" ) ( ExprVar ( NamedVar "x" ) :| [ ExprVar ( NamedVar "u" ) , ExprVar ( NamedVar "z" ) ] ) } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 54 , locColumn = 30 } ) ( PrefixPredicate "Betw" 3 ) ( Marker "betw" ) ( ExprVar ( NamedVar "y" ) :| [ ExprVar ( NamedVar "v" ) , ExprVar ( NamedVar "z" ) ] ) } } , stmt2 = StmtExists { loc = Location { locFile = "test/examples/geometry.tex" , locLine = 54 , locColumn = 51 } , np = NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 54 , locColumn = 66 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( [ NamedVar "w" ] ) ( [] ) ( Just ( StmtConnected { conn = Conjunction , mloc = Nothing , stmt1 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 55 , locColumn = 16 } ) ( PrefixPredicate "Betw" 3 ) ( Marker "betw" ) ( ExprVar ( NamedVar "u" ) :| [ ExprVar ( NamedVar "w" ) , ExprVar ( NamedVar "y" ) ] ) } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 55 , locColumn = 37 } ) ( PrefixPredicate "Betw" 3 ) ( Marker "betw" ) ( ExprVar ( NamedVar "v" ) :| [ ExprVar ( NamedVar "w" ) , ExprVar ( NamedVar "x" ) ] ) } } ) ) } } ) ) , BlockAxiom ( Location { locFile = "test/examples/geometry.tex" , locLine = 66 , locColumn = 1 } ) ( Just [ Word "upper" , Word "dimension" ] ) ( Marker "upperdim" ) ( Axiom [ AsmLetNoun ( NamedVar "x" :| [ NamedVar "y" , NamedVar "z" , NamedVar "u" , NamedVar "v" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 67 , locColumn = 24 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( StmtConnected { conn = Implication , mloc = Just ( Location { locFile = "test/examples/geometry.tex" , locLine = 68 , locColumn = 5 } ) , stmt1 = StmtConnected { conn = Conjunction , mloc = Nothing , stmt1 = StmtConnected { conn = Conjunction , mloc = Nothing , stmt1 = StmtConnected { conn = Conjunction , mloc = Nothing , stmt1 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 68 , locColumn = 9 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "x" ) :| [ ExprVar ( NamedVar "u" ) , ExprVar ( NamedVar "x" ) , ExprVar ( NamedVar "v" ) ] ) } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 68 , locColumn = 33 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "y" ) :| [ ExprVar ( NamedVar "u" ) , ExprVar ( NamedVar "y" ) , ExprVar ( NamedVar "v" ) ] ) } } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 69 , locColumn = 10 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "z" ) :| [ ExprVar ( NamedVar "u" ) , ExprVar ( NamedVar "z" ) , ExprVar ( NamedVar "v" ) ] ) } } , stmt2 = StmtFormula { formula = FormulaChain ( ChainBase ( ExprVar ( NamedVar "u" ) :| [] ) Positive ( Relation ( Location { locFile = "test/examples/geometry.tex" , locLine = 69 , locColumn = 36 } ) ( RelationSymbol ( Command "neq" ) ( ParameterArity 0 ) ( Marker "neq" ) ) [] ) ( ExprVar ( NamedVar "v" ) :| [] ) ) } } , stmt2 = StmtVerbPhrase { args = TermExpr ( ExprVar ( NamedVar "x" ) ) :| [] , verb = VPAdj ( Adj ( Location { locFile = "test/examples/geometry.tex" , locLine = 70 , locColumn = 17 } ) ( LexicalItem ( TokenCons ( Word "collinear" ) ( TokenCons ( Word "with" ) ( HoleCons ( TokenCons ( Word "and" ) ( HoleCons End ) ) ) ) ) ( Marker "collinear" ) ) [ TermExpr ( ExprVar ( NamedVar "y" ) ) , TermExpr ( ExprVar ( NamedVar "z" ) ) ] :| [] ) } } ) ) , BlockClaim Lemma ( Location { locFile = "test/examples/geometry.tex" , locLine = 82 , locColumn = 1 } ) ( Just [ Word "reflexivity" , Word "of" , Word "congruence" ] ) ( Marker "cong_refl" ) ( Claim [ AsmLetNoun ( NamedVar "a" :| [ NamedVar "b" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 83 , locColumn = 19 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 84 , locColumn = 11 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "a" ) , ExprVar ( NamedVar "b" ) ] ) } ) ) , BlockClaim Lemma ( Location { locFile = "test/examples/geometry.tex" , locLine = 88 , locColumn = 1 } ) ( Just [ Word "symmetry" , Word "of" , Word "congruence" ] ) ( Marker "cong_sym" ) ( Claim [ AsmLetNoun ( NamedVar "a" :| [ NamedVar "b" , NamedVar "c" , NamedVar "d" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 89 , locColumn = 25 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) , AsmSuppose ( StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 90 , locColumn = 14 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "c" ) , ExprVar ( NamedVar "d" ) ] ) } ) ] ( StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 91 , locColumn = 11 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "c" ) :| [ ExprVar ( NamedVar "d" ) , ExprVar ( NamedVar "a" ) , ExprVar ( NamedVar "b" ) ] ) } ) ) , BlockClaim Lemma ( Location { locFile = "test/examples/geometry.tex" , locLine = 95 , locColumn = 1 } ) ( Just [ Word "transitivity" , Word "of" , Word "congruence" ] ) ( Marker "cong_transitive" ) ( Claim [ AsmLetNoun ( NamedVar "a" :| [ NamedVar "b" , NamedVar "c" , NamedVar "d" , NamedVar "e" , NamedVar "f" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 96 , locColumn = 31 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( StmtConnected { conn = Implication , mloc = Just ( Location { locFile = "test/examples/geometry.tex" , locLine = 97 , locColumn = 5 } ) , stmt1 = StmtConnected { conn = Conjunction , mloc = Nothing , stmt1 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 97 , locColumn = 9 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "c" ) , ExprVar ( NamedVar "d" ) ] ) } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 97 , locColumn = 33 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "c" ) :| [ ExprVar ( NamedVar "d" ) , ExprVar ( NamedVar "e" ) , ExprVar ( NamedVar "f" ) ] ) } } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 98 , locColumn = 11 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "e" ) , ExprVar ( NamedVar "f" ) ] ) } } ) ) , BlockClaim Lemma ( Location { locFile = "test/examples/geometry.tex" , locLine = 102 , locColumn = 1 } ) Nothing ( Marker "cong_shuffle_left" ) ( Claim [ AsmLetNoun ( NamedVar "a" :| [ NamedVar "b" , NamedVar "c" , NamedVar "d" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 103 , locColumn = 25 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( StmtConnected { conn = Implication , mloc = Just ( Location { locFile = "test/examples/geometry.tex" , locLine = 104 , locColumn = 5 } ) , stmt1 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 104 , locColumn = 9 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "c" ) , ExprVar ( NamedVar "d" ) ] ) } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 105 , locColumn = 11 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "b" ) :| [ ExprVar ( NamedVar "a" ) , ExprVar ( NamedVar "c" ) , ExprVar ( NamedVar "d" ) ] ) } } ) ) , BlockClaim Lemma ( Location { locFile = "test/examples/geometry.tex" , locLine = 109 , locColumn = 1 } ) Nothing ( Marker "cong_shuffle_right" ) ( Claim [ AsmLetNoun ( NamedVar "a" :| [ NamedVar "b" , NamedVar "c" , NamedVar "d" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 110 , locColumn = 25 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( StmtConnected { conn = Implication , mloc = Just ( Location { locFile = "test/examples/geometry.tex" , locLine = 111 , locColumn = 5 } ) , stmt1 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 111 , locColumn = 9 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "c" ) , ExprVar ( NamedVar "d" ) ] ) } , stmt2 = StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 112 , locColumn = 11 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "b" ) :| [ ExprVar ( NamedVar "a" ) , ExprVar ( NamedVar "d" ) , ExprVar ( NamedVar "c" ) ] ) } } ) ) , BlockClaim Lemma ( Location { locFile = "test/examples/geometry.tex" , locLine = 116 , locColumn = 1 } ) ( Just [ Word "zero" , Word "segments" , Word "are" , Word "congruent" ] ) ( Marker "cong_zero" ) ( Claim [ AsmLetNoun ( NamedVar "a" :| [ NamedVar "b" ] ) NounPhrase ( [] ) ( Noun ( Location { locFile = "test/examples/geometry.tex" , locLine = 117 , locColumn = 18 } ) ( LexicalItemSgPl ( SgPl { sg = TokenCons ( Word "point" ) End , pl = TokenCons ( Word "points" ) End } ) ( Marker "point" ) ) [] ) ( Nothing ) ( [] ) ( Nothing ) ] ( StmtFormula { formula = FormulaPredicate ( Location { locFile = "test/examples/geometry.tex" , locLine = 118 , locColumn = 11 } ) ( PrefixPredicate "Cong" 4 ) ( Marker "cong" ) ( ExprVar ( NamedVar "a" ) :| [ ExprVar ( NamedVar "a" ) , ExprVar ( NamedVar "b" ) , ExprVar ( NamedVar "b" ) ] ) } ) ) ]