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Try doing some basic maths questions in the Lean Theorem Prover. Functions, real numbers, equivalence relations and groups. Click on README.md and then on "Open in CoCalc with one click".
Project: Xena
Views: 18536License: APACHE
oleanfile 3.4.2, commit cbd2b6686ddb ��)� init algebra group basic � �export_decl option none none some some export_decl bool ff ff tt tt export_decl has_andthen andthen andthen export_decl has_pow pow pow export_decl has_append append append export_decl decidable is_true is_true is_false is_false to_bool to_bool export_decl has_pure pure pure export_decl has_bind bind bind export_decl has_monad_lift_t monad_lift !monad_lift export_decl monad_functor_t monad_map $monad_map export_decl monad_run run 'run export_decl list mmap *mmap mmap' *mmap' mfilter *mfilter mfoldl *mfoldl export_decl native nat_map 3rb_map mk export_decl name_map native rb_map mk export_decl expr_map native rb_map mk export_decl tactic interaction_monad failed fail export_decl tactic_result interaction_monad result export_decl tactic Ftransparency reducible Greducible semireducible Gsemireducible export_decl tactic mk_simp_attr Lmk_simp_attr export_decl monad_except throw Othrow catch Ocatch export_decl monad_except_adapter adapt_except Tadapt_except export_decl monad_state_adapter adapt_state Wadapt_state export_decl monad_reader read Zread export_decl monad_reader_adapter adapt_reader ]adapt_reader export_decl is_lawful_functor map_const_eq `map_const_eq id_map `id_map comp_map `comp_map export_decl is_lawful_applicative seq_left_eq gseq_left_eq seq_right_eq gseq_right_eq pure_seq_eq_map gpure_seq_eq_map map_pure gmap_pure seq_pure gseq_pure seq_assoc gseq_assoc export_decl is_lawful_monad bind_pure_comp_eq_map tbind_pure_comp_eq_map bind_map_eq_seq tbind_map_eq_seq pure_bind tpure_bind bind_assoc tbind_assoc export_decl traversable traverse }traverse PInfo is_group_anti_hom ind l u_1 u_2 α �Annot as_is Annot �β �Annot �Annot �_inst_1 group Annot �_inst_2 group Annot �f a C �e_1 map_mul a b eq has_mul mul semigroup to_has_mul monoid to_semigroup group to_monoid � � � � " n � � � . @ � � � � � � � � �mk � � � � � � � . � @ . " & ( * , @ " @ ; . @ � � � � � � � : � � � . x x x " & ( * , . " . "� nspace �prt �rec gind � � decl �map_mul � � � � � � � c ; . @ " 9 � � � � � � � "Proj � � � � � 9 �rec � � . @ 9 � 9 " "� PInfo �ATTR reducibility � � � proj � � decl �rec_on � � � � � � � � � � p � � � @ @ � � � � � � � p � � �rec � � � . @ " � PInfo �ATTR �� � � auxrec �prt �auxrec �rec_on decl �cases_on � � � � �� PInfo �ATTR �� � � auxrec �decl �drec � � � � � � � � �h � � � 9 � � � . @ " � A e � � � � � � � � � � A � � ; . 3 � � � x x � � � " & x ( x * x , x " _ ; x . 5 " "� PInfo �ATTR �� � � auxrec �prt �decl �drec_on � � � � � � � � � � � p � � � @ � . " g � � � � � � � � p � � " � � � _ � g � PInfo �ATTR �� � � auxrec �prt �decl �dcases_on � � � � * � 7� PInfo �ATTR �� � � auxrec �prt �doc �Predicate for group anti-homomorphism, or a homomorphism into the opposite group. ATTR class � � � class �decl is_group_anti_hom map_one � � � � � � f w � . has_one one �to_has_one � . � . , . @ � � � � � � �iff mp � 8 & . ( . * . � H � A � A � A � Kmul_self_iff_eq_one . @ � Aeq mpr � \ � 8 � > � @ � @ � Aid eq J � \ � peq rec . � Z_a . � t P d @ � 9 � ; U � � P " � eq refl J � \ � neq symm . � n � Z �map_mul . @ " � @ � @ � d � p � B � A � r � t � p � � � � m_a � t P @ X � ~ � ~ � P e � � � � p � @one_mul � > � @eq refl . � A� PInfo �decl �map_inv � � � � � � � � �a P @has_inv inv �to_has_inv . " � � e � � � � � � � � eq_inv_of_mul_eq_one � � e � d P d � � e � C � E a P @ X " � � � � � r � t � � � � � x � �_a � t 2 � � � � 5 � C � E / " � � � � � � � � � � � � � � � . @ " � � � d � � P � � � � r � t � � � # � � � �_a � t ! � � � 3 � � � � � � ~mul_inv_self . " � d � # P � � � � � r � t � # � @ � � � _a � t � 9 � ; � � � � � # � � �map_one . @ � � � �� PInfo �decl inv_is_group_anti_hom � � � "is_group_anti_hom " "x � � @ � � @ " � � � k � " " � vmul_inv_rev "� PInfo � EndFile