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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: 21656License: APACHE
oleanfile 3.4.2, commit cbd2b6686ddb ���# init data vector data bitvec � �,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 PInfo pos_num ind l C n } ~e_1 }one e_2 a ih }bit1 e_3 � ih }bit0 � } � � � � � � � � � � � }rec � � � � '� decl }rec_on ~ � � � � � � � � � � 5 � 8 � < # � PInfo � ATTR reducibility � � � auxrec �prt �decl }cases_on ~ � � 5 � � � � = � � 5 � N � Q C � � 9 � � W � PInfo � ATTR �� � � auxrec �prt �decl }no_confusion_type ~P v1 v2 � � � � ~ � k � � p � l � � a_eq eq 9 9 � � t } {� PInfo � ATTR �� � � prt �decl }no_confusion ~ � � � h12 x � ~ � � � � xeq rec a h1a v � 9 h11 v � � � � � � � v eq refl � � PInfo � ATTR �� � � no_conf �prt �decl �inj � v true � �true intro � PInfo � decl �inj_arrow l � �P � � � � � � � � �inj � PInfo � decl �inj_eq u � �propext � �iff intro � �h � � a � � � PInfo � decl �inj � � � v L � � � � � }no_confusion � � � � PInfo � decl �inj_arrow l � � � �P � � � � � � � � � � �inj � PInfo � decl �inj_eq � � � � x � a_1 � � x � � xh � � a_2 x � � e_1 xcongr_arg � PInfo � decl �inj � � � v O � � � � � � � � PInfo � decl �inj_arrow l � � � � � � � � � P � � �inj � PInfo � decl �inj_eq � � � � x � a_1 � � x � � xh � � , a_2 x � � e_1 x � � PInfo � decl }below ~ � ~ � }rec � � Ppunit � � � Ppprod � X � V � _ � PInfo � ATTR �� � � prt �decl }ibelow � � � e � e � � � � � � � �and � k X � � q � PInfo � ATTR �� � � prt �decl }brec_on ~ � F � f }below ~ X \ � � � {pprod fst \ � x � � � Y � w pprod mk � V punit star � � � � � � � � 6 � X � Y � w � V � � � � V � � � � � � � � � � � � � � � � � PInfo � ATTR �� � � auxrec �prt �decl }binduction_on � e � F � f }ibelow X \ � e � � � �and elim_left \ � � � � � k � � and intro � � � � � � � � � � � 6 � k � k � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � PInfo � ATTR �� � � auxrec �prt �decl }sizeof x nat � gx � �has_one one � �nat has_one � ih � �has_add add � �nat has_add � � � � � PInfo � ATTR �� � � prt �decl }has_sizeof_inst has_sizeof has_sizeof mk � � PInfo � ATTR instance � � � class � �� �prt �decl �sizeof_spec u � � � � � � � � � � PInfo � ATTR _refl_lemma � � � EqnL �prt �decl �sizeof_spec � � � L � �sizeof � � � � � PInfo � ATTR �� � � EqnL �prt �decl �sizeof_spec � � � O � � � � � PInfo � ATTR �� � � EqnL �prt �gind } � � � prt }rec nspace }doc }The type of positive binary numbers. 13 = 1101(base 2) = bit1 (bit0 (bit1 one)) ATTR derive � � } list cons pexpr Quote has_reflect list nil � !decl }has_reflect has_reflect id � *_v }brec_on � reflected _v _F � � 1 � � � � � 6 � / � � � 5 Quote a_0 � � � 5 Lreflected subst a Quote pprod fst � 1 � � � � � � � R � K � P � X � J � S � [ � P a_1 � � � 5 O � E Quote � a � PInfo � VMR �_rec_2 VMR �_rec_3 VMR �_rec_1 VMR �VMC � R n expr bool tt _fresh � � expr cases_on "*2:BJ � expr app � � � � � � � � � � � expr subst � � � � � � VMC � R � � w � _fresh � B � "*2:BJ � � � � � � � � � � � � � � � � � � � � VMC � � � � � � VMC � � � ATTR �� � }has_reflect class � � � �ATTR �� � } � " Quote decidable_eq � 'decl }decidable_eq decidable_eq � + � }a � - � b decidable x _v _F � 4 � � � 7 � " � # � � � � � � # � � w � 7 � $ � � � !is_true � � � $ � !is_false � La � � �false � $ � � � O � ' � � � � � � # � � Lw � 7 � ) � v � � v � a_1 � � � � � � � ) decidable by_cases � � � � L � J � � � Q � � � R � R � � � P � � � J � R � � � � � P a_1 � � � ) � v 9 L � � v � � � � � a_1 not � � � � � � � � � �a_2 � � �inj_arrow 9 � �h_1 v 9 absurd v � � � � ) � � � � Oa_1 � � � � � � � # � � Ow � 7 � 5 � v � � v � ! a_1 � " � � � � 5 � � � La_1 � * � � � 5 � � � � O � �a_1 � � � � 5 � v 9 O � � v � , � , � � , a_1 � � � � � >