[ BlockDefn ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 1 , sourceColumn = Pos 1 } ) ( Marker "collinear" ) ( DefnPredicate [] ( PredicateAdj [ Just ( Word "collinear" ) , Just ( Word "with" ) , Nothing , Just ( Word "and" ) , Nothing ] ) ( NamedVar "a" :| [ NamedVar "b" , NamedVar "c" ] ) ( Connected Disjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Betw" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "c" ) ] ) ( Connected Disjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Betw" ) ) [ TermVar ( NamedVar "b" ) , TermVar ( NamedVar "c" ) , TermVar ( NamedVar "a" ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Betw" ) ) [ TermVar ( NamedVar "c" ) , TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) ] ) ) ) ) , BlockAxiom ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 5 , sourceColumn = Pos 1 } ) ( Marker "cong_refl_swap" ) ( Axiom [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "a" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "b" ) ] ) ] ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "a" ) ] ) ) , BlockAxiom ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 10 , sourceColumn = Pos 1 } ) ( Marker "cong_pseudotransitive" ) ( Axiom [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "a" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "b" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "c" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "d" ) ] ) ] ( Connected Implication ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "c" ) , TermVar ( NamedVar "d" ) , TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "c" ) , TermVar ( NamedVar "d" ) , TermVar ( NamedVar "e" ) , TermVar ( NamedVar "f" ) ] ) ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "e" ) , TermVar ( NamedVar "f" ) ] ) ) ) , BlockAxiom ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 15 , sourceColumn = Pos 1 } ) ( Marker "cong_id" ) ( Axiom [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "a" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "b" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "c" ) ] ) ] ( Connected Implication ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "c" ) , TermVar ( NamedVar "c" ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Symbol "=" ) ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) ] ) ) ) , BlockAxiom ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 21 , sourceColumn = Pos 1 } ) ( Marker "segment_construction" ) ( Axiom [] ( Quantified Existentially ( Scope ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( B ( NamedVar "c" ) ) ] ) ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Betw" ) ) [ TermVar ( F ( TermVar ( NamedVar "a" ) ) ) , TermVar ( F ( TermVar ( NamedVar "b" ) ) ) , TermVar ( B ( NamedVar "c" ) ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( F ( TermVar ( NamedVar "b" ) ) ) , TermVar ( B ( NamedVar "c" ) ) , TermVar ( F ( TermVar ( NamedVar "d" ) ) ) , TermVar ( F ( TermVar ( NamedVar "e" ) ) ) ] ) ) ) ) ) ) , BlockDefn ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 26 , sourceColumn = Pos 1 } ) ( Marker "ofs" ) ( DefnPredicate [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "x" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "y" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "z" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "r" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "u" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "v" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "w" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "p" ) ] ) ] ( PredicateSymbol "OFS" ) ( NamedVar "x" :| [ NamedVar "y" , NamedVar "z" , NamedVar "r" , NamedVar "u" , NamedVar "v" , NamedVar "w" , NamedVar "p" ] ) ( Connected Conjunction ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Betw" ) ) [ TermVar ( NamedVar "x" ) , TermVar ( NamedVar "y" ) , TermVar ( NamedVar "z" ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Betw" ) ) [ TermVar ( NamedVar "u" ) , TermVar ( NamedVar "v" ) , TermVar ( NamedVar "w" ) ] ) ) ( Connected Conjunction ( Connected Conjunction ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "x" ) , TermVar ( NamedVar "y" ) , TermVar ( NamedVar "u" ) , TermVar ( NamedVar "v" ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "y" ) , TermVar ( NamedVar "z" ) , TermVar ( NamedVar "v" ) , TermVar ( NamedVar "w" ) ] ) ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "x" ) , TermVar ( NamedVar "r" ) , TermVar ( NamedVar "u" ) , TermVar ( NamedVar "p" ) ] ) ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "y" ) , TermVar ( NamedVar "r" ) , TermVar ( NamedVar "v" ) , TermVar ( NamedVar "p" ) ] ) ) ) ) , BlockAxiom ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 39 , sourceColumn = Pos 1 } ) ( Marker "five_segment" ) ( Axiom [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "a" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "b" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "c" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "d" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "aprime" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "bprime" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "cprime" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "dprime" ) ] ) ] ( Connected Implication ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "OFS" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "c" ) , TermVar ( NamedVar "d" ) , TermVar ( NamedVar "aprime" ) , TermVar ( NamedVar "bprime" ) , TermVar ( NamedVar "cprime" ) , TermVar ( NamedVar "dprime" ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "neq" ) ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) ] ) ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "c" ) , TermVar ( NamedVar "d" ) , TermVar ( NamedVar "cprime" ) , TermVar ( NamedVar "dprime" ) ] ) ) ) , BlockAxiom ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 46 , sourceColumn = Pos 1 } ) ( Marker "betw_id" ) ( Axiom [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "a" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "b" ) ] ) ] ( Connected Implication ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Betw" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "a" ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Symbol "=" ) ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) ] ) ) ) , BlockAxiom ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 52 , sourceColumn = Pos 1 } ) ( Marker "innerpasch" ) ( Axiom [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "x" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "y" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "z" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "u" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "v" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "w" ) ] ) ] ( Connected Implication ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Betw" ) ) [ TermVar ( NamedVar "x" ) , TermVar ( NamedVar "u" ) , TermVar ( NamedVar "z" ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Betw" ) ) [ TermVar ( NamedVar "y" ) , TermVar ( NamedVar "v" ) , TermVar ( NamedVar "z" ) ] ) ) ( Quantified Existentially ( Scope ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( B ( NamedVar "w" ) ) ] ) ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Betw" ) ) [ TermVar ( F ( TermVar ( NamedVar "u" ) ) ) , TermVar ( B ( NamedVar "w" ) ) , TermVar ( F ( TermVar ( NamedVar "y" ) ) ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Betw" ) ) [ TermVar ( F ( TermVar ( NamedVar "v" ) ) ) , TermVar ( B ( NamedVar "w" ) ) , TermVar ( F ( TermVar ( NamedVar "x" ) ) ) ] ) ) ) ) ) ) ) , BlockAxiom ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 66 , sourceColumn = Pos 1 } ) ( Marker "upperdim" ) ( Axiom [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "x" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "y" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "z" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "u" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "v" ) ] ) ] ( Connected Implication ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "x" ) , TermVar ( NamedVar "u" ) , TermVar ( NamedVar "x" ) , TermVar ( NamedVar "v" ) ] ) ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "y" ) , TermVar ( NamedVar "u" ) , TermVar ( NamedVar "y" ) , TermVar ( NamedVar "v" ) ] ) ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "z" ) , TermVar ( NamedVar "u" ) , TermVar ( NamedVar "z" ) , TermVar ( NamedVar "v" ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateRelation ( Command "neq" ) ) ) [ TermVar ( NamedVar "u" ) , TermVar ( NamedVar "v" ) ] ) ) ) ) ( TermSymbol ( SymbolPredicate ( PredicateAdj [ Just ( Word "collinear" ) , Just ( Word "with" ) , Nothing , Just ( Word "and" ) , Nothing ] ) ) [ TermVar ( NamedVar "x" ) , TermVar ( NamedVar "y" ) , TermVar ( NamedVar "z" ) ] ) ) ) , BlockLemma ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 82 , sourceColumn = Pos 1 } ) ( Marker "cong_refl" ) ( Lemma [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "a" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "b" ) ] ) ] ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) ] ) ) , BlockLemma ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 88 , sourceColumn = Pos 1 } ) ( Marker "cong_sym" ) ( Lemma [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "a" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "b" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "c" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "d" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "c" ) , TermVar ( NamedVar "d" ) ] ) ] ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "c" ) , TermVar ( NamedVar "d" ) , TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) ] ) ) , BlockLemma ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 95 , sourceColumn = Pos 1 } ) ( Marker "cong_transitive" ) ( Lemma [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "a" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "b" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "c" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "d" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "e" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "f" ) ] ) ] ( Connected Implication ( Connected Conjunction ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "c" ) , TermVar ( NamedVar "d" ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "c" ) , TermVar ( NamedVar "d" ) , TermVar ( NamedVar "e" ) , TermVar ( NamedVar "f" ) ] ) ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "e" ) , TermVar ( NamedVar "f" ) ] ) ) ) , BlockLemma ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 102 , sourceColumn = Pos 1 } ) ( Marker "cong_shuffle_left" ) ( Lemma [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "a" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "b" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "c" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "d" ) ] ) ] ( Connected Implication ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "c" ) , TermVar ( NamedVar "d" ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "b" ) , TermVar ( NamedVar "a" ) , TermVar ( NamedVar "c" ) , TermVar ( NamedVar "d" ) ] ) ) ) , BlockLemma ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 109 , sourceColumn = Pos 1 } ) ( Marker "cong_shuffle_right" ) ( Lemma [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "a" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "b" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "c" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "d" ) ] ) ] ( Connected Implication ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "c" ) , TermVar ( NamedVar "d" ) ] ) ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "b" ) , TermVar ( NamedVar "a" ) , TermVar ( NamedVar "d" ) , TermVar ( NamedVar "c" ) ] ) ) ) , BlockLemma ( SourcePos { sourceName = "test/examples/geometry.tex" , sourceLine = Pos 116 , sourceColumn = Pos 1 } ) ( Marker "cong_zero" ) ( Lemma [ Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "a" ) ] ) , Asm ( TermSymbol ( SymbolPredicate ( PredicateNoun ( SgPl { sg = [ Just ( Word "point" ) ] , pl = [ Just ( Word "points" ) ] } ) ) ) [ TermVar ( NamedVar "b" ) ] ) ] ( TermSymbol ( SymbolPredicate ( PredicateSymbol "Cong" ) ) [ TermVar ( NamedVar "a" ) , TermVar ( NamedVar "a" ) , TermVar ( NamedVar "b" ) , TermVar ( NamedVar "b" ) ] ) ) ]