{"rule":"POSSESSIVE_APOSTROPHE","sentence":"^\\QFurthermore, in mathematical textbooks equality between morphisms is usually taken for granted, i.e. there is some global notion of equality that is clear to everyone.\\E$"}
{"rule":"SENTENCE_WHITESPACE","sentence":"^\\QKleisli').\\E$"}
{"rule":"SENTENCE_WHITESPACE","sentence":"^\\QConstruction.\\E$"}
{"rule":"NO_SPACE_CLOSING_QUOTE","sentence":"^\\Q[inline]Change quotation marks ”\\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q”: Given a Kleisli triple \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, we get a monad \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q where \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q is the object mapping of the Kleisli triple together with the functor action \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q is the morphism family of the Kleisli triple where naturality is easy to show and \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q is a natural transformation defined as \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"IF_IS","sentence":"^\\QLet \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q and \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q be a setoid morphism, we define \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q point wise: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q where \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q is defined corecursively by: \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QThe following conditions hold: There exists a unit morphism \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any DX, satisfying \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q For any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q there exists a unique morphism \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q satisfying: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q There exists a unique morphism \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q satisfying: &&&& &&&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q We will make use of the fact that every \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q is a final coalgebra: [\\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q] This follows by definition of \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QWe call a morphism \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q guarded if there exists an \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q such that the following diagram commutes: &&& &&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QIt suffices to show \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, because then follows: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q We prove this by coinduction using: [inline]Change name of morphism &&& &&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\Q[inline]Make this more explicit The first step in both equations can be proven by monicity of \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q and then using \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q and the dual diagram for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q which is a direct consequence of \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q: &&&& &&&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q the last step holds generally for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QFirst we need to show naturality of \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, i.e. we need to show that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q The needed coalgebra is shown in this diagram: &&&& &&&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q Next we check the strength laws: [\\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q] To show that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q we do coinduction using the following coalgebra: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q [\\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q] We don't need coinduction to show \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, but we need a small helper lemma: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q which is a direct consequence of \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QFirst we need to show naturality of \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, i.e. we need to show that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q The coalgebra for coinduction is: &&&& &&&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q We write \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q to abbreviate the rather long coalgebra, i.e. in this diagram \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\Q&&&&&&& &&&&&&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q then follows from this diagram.\\E$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QSince \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q is a final coalgebra we get the following proof principle: Given two morphisms \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, to show that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q it suffices to show that there exists a coalgebra structure \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q such that the following diagrams commute: &&&&&& &&&&&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q Uniqueness of the coalgebra morphism \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q then gives us that indeed \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QFirst we need to show naturality of \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, i.e. we need to show that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q The coalgebra for coinduction is: &&&& &&&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q We write \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q to abbreviate the used coalgebra, i.e. in this diagram \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QNext we check the strength laws: [\\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q] To show that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q we do coinduction using the following coalgebra: &&& &&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q [\\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q] We don't need coinduction to show \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, but we need a small helper lemma: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q which is a direct consequence of \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QIt suffices to show \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, because then follows: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q We prove this by coinduction using: &&& &&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\Q[inline]Move this remark to the beginning of proof The first step in both equations can be proven by monicity of \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q and then using \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q and the dual diagram for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q which is a direct consequence of \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q: &&&& &&&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QTo show that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q it suffices to show that there exists a coalgebra structure \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q such that the following diagrams commute: &&&&&& &&&&&& \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q Uniqueness of the coalgebra morphism \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q then results in \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QA (unguarded) Elgot Algebra \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q consists of: An object X for every \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q the iteration \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, satisfying: law:fixpoint Fixpoint: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q Uniformity: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q Folding: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q test: \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QA (unguarded) Elgot Algebra \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q consists of: An object X for every \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q the iteration \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, satisfying: law:fixpoint Fixpoint: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:uniformity Uniformity: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:folding Folding: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q test: \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QA (unguarded) Elgot Algebra \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q consists of: An object X for every \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q the iteration \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, satisfying: law:fixpoint Fixpoint: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:uniformity Uniformity: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:folding Folding: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\Qlaw:diamond Diamond\\E$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QA (unguarded) Elgot Algebra \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q consists of: An object X for every \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q the iteration \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, satisfying: law:fixpoint Fixpoint: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:uniformity Uniformity: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:folding Folding: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\Qlaw:stutter Stutter: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:diamond Diamond: \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\Qlaw:stutter Stutter: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:diamond Diamond: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:compositionality Compositionality: \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QA (unguarded) Elgot Algebra \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q consists of: An object A for every \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q the iteration \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, satisfying: law:fixpoint Fixpoint: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:uniformity Uniformity: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:folding Folding: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\Qlaw:stutter Stutter: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:diamond Diamond: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:compositionality Compositionality: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\Qlaw:compositionality Compositionality: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:stutter Stutter: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:diamond Diamond: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q: Note that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q since \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\Qlaw:compositionality Compositionality: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:stutter Stutter: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:diamond Diamond: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q: Note that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q since \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"UPPERCASE_SENTENCE_START","sentence":"^\\Qlaw:compositionality Compositionality: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:stutter Stutter: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:diamond Diamond: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q: Note that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q since \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\Qlaw:compositionality Compositionality: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:stutter Stutter: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:diamond Diamond: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q: First, note that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q can equivalently be reformulated as \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q since \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q Using \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, we are left to show that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"UPPERCASE_SENTENCE_START","sentence":"^\\Qlaw:compositionality Compositionality: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:stutter Stutter: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:diamond Diamond: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q: First, note that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q can equivalently be reformulated as \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q since \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q Using \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, we are left to show that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"IF_IS","sentence":"^\\QLet \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q and \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q be a setoid morphism, we define \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q point wise: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"IF_IS","sentence":"^\\Q\\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QA (unguarded) Elgot Algebra \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q consists of: An object A for every \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q an iteration \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, satisfying: law:fixpoint Fixpoint: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:uniformity Uniformity: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q law:folding Folding: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\Qlaw:compositionality Compositionality: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, law:stutter Stutter: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, law:diamond Diamond: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QA (unguarded) Elgot Algebra \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q consists of: An object \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, and for every \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q an iteration \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, satisfying: law:fixpoint Fixpoint: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, law:uniformity Uniformity: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q implies \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, law:folding Folding: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"ENGLISH_WORD_REPEAT_RULE","sentence":"^\\QA (unguarded) Elgot Algebra \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q consists of: An object \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, and for every \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q an iteration \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, satisfying the following axioms: law:fixpoint Fixpoint: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, law:uniformity Uniformity: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q implies \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, law:folding Folding: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"MORFOLOGIK_RULE_EN_US","sentence":"^\\QGiven a functor \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, a (H-)guarded Elgot algebra consists of: An object \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, a H-algebra structure \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, and for every \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q an iteration \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, satisfying the following axioms: law:guardedfixpoint Fixpoint: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, law:guardeduniformity Uniformity: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q implies \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, law:guardedcompositionality Compositionality: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"UPPERCASE_SENTENCE_START","sentence":"^\\Qlaw:compositionality Compositionality: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, law:stutter Stutter: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, law:diamond Diamond: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"MORFOLOGIK_RULE_EN_US","sentence":"^\\QAn Elgot monad consists of A monad \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, for every \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q an iteration \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q satisfying: Fixpoint: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, Uniformity: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q implies \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, Naturality: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, Codiagonal: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"IF_IS","sentence":"^\\QLet \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q be a setoid and \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q be a setoid function, we define \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q point wise: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"IF_IS","sentence":"^\\QGiven a function \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, the lifted function \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q is defined as \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"IF_IS","sentence":"^\\QConsider, \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q and \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q where \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q is a setoid function that maps every \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q to \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
{"rule":"IF_IS","sentence":"^\\QNow, consider the following function \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q which tries running two computations and returns the one that finished first: \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q and \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q and \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"IF_IS","sentence":"^\\QLastly, consider the function \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, which adds a number of \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q constructors in front of a value and is given by \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"IF_IS","sentence":"^\\QConsider another setoid function \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, defined by \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"IF_IS","sentence":"^\\QNext, let us consider functions for counting steps of computations, first regard \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, which returns the number of steps a terminating computation has to take and is defined by \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q and \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"IF_IS","sentence":"^\\QConsider \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q defined by \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"IF_IS","sentence":"^\\QFurthermore, consider the setoid function \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q defined by \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q if \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q Now, by coinduction we can easily follow that \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q for any \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q \\E(?:Dummy|Ina|Jimmy-)[0-9]+$"}
{"rule":"WHITESPACE_RULE","sentence":"^\\QFriedrich-Alexander-Universität Erlangen-Nürnberg [] Chair for Computer Science 8 Theoretical Computer Science  Bachelor Thesis in Computer Science [0.5]  Advisor: Sergey Goncharov Erlangen,\\E$"}