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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: 21677License: APACHE
oleanfile 3.4.2, commit cbd2b6686ddb ���6� init data rat order � I�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 decl rat cast _main u_1 α �_inst_1 division_ring a rat � � � rat cases_on � a_num int a_denom nat a_pos has_lt lt nat has_lt has_zero zero nat has_zero a_cop nat coprime �nat_abs id_rhs has_div div !division_ring_has_div' !coe !coe_to_lift !coe_base !int cast_coe !add_group to_has_neg !add_comm_group to_add_group !ring to_add_comm_group !domain to_ring !division_ring to_domain ! 'no_zero_divisors to_has_zero ! �to_no_zero_divisors ! ?zero_ne_one_class to_has_one ! �to_zero_ne_one_class ! ?distrib to_has_add ! �to_distrib ! @ * ! - ! 0 !nat cast_coe ! J Q X � PInfo �#VMR �VMC �4# � � � �_c_1 �_c_2 � �_c_3 � �_c_4 � � _c_5 �cast _main � � � �cast _main algebra div decl �equations _eqn_1 � � � n d h c eq ' � � ' �mk' # ' % ' | + ' . ' 1 ' 3 ' 5 ' 7 ' 9 ' ; ' = ' | E ' G ' � L ' N ' � S ' U ' � _ ' a ' c ' e ' � � � � � � � � � eq refl 'id_delta ' �� PInfo �#ATTR _refl_lemma � � � EqnL �decl �cast � � � z � PInfo �#prt �VMR �VMC �# � � �doc �Construct the canonical injection from `ℚ` into an arbitrary division ring. If the field has positive characteristic `p`, we define `1 / p = 1 / 0 = 0` for consistency with our division by zero convention. decl �equations _eqn_1 � � � � � � � y � � ' | � � � � �equations _eqn_1 � PInfo �#ATTR �� � � EqnL �decl �_sunfold � w � PInfo �#decl �cast_coe � � � has_coe � � has_coe mk � � PInfo �&prt �VMR �VMC �& � � �decl �equations _eqn_1 � � � � � � � � � � � � �� PInfo �&ATTR �� � � EqnL �SEqnL �ATTR instance � class � � decl �cast_of_int � � � n x * - 0 � �of_int + . 1 3 5 7 9 ; = E G � L N � S U � � � � this � # % � , _ a c e � � " � 'has_one one nat has_one � , eq mpr � G � � 5 � � " � ,id � � G � Peq rec � 6 � 7 � 8 � 9add_monoid to_has_zero �to_add_monoid � � "add_semigroup to_has_add �to_add_semigroup � _ � C_a � U x # % + . 1 3 5 7 9 ; = E G � } L N � } S U � ~ _ a c e � � � � � � � C � � � o � � � � � � T � G � Mnat cast_one � _ � " � I � P � � , � , � R � U � P � � � Z � 1division_ring_has_div � , � L � division_ring to_zero_ne_one_class _a � U � o � � � K � � � � � o � � � � � P � ,div_one � , � � ,Annot show � PInfo �(ATTR simp � � � decl �cast_coe_int � � � n � � � � � � rat has_neg �has_zero �has_one �has_add � , � � � � I � � - � R � U � � - � � _a � U � o � � � � � � � � � o � � � � � � � �coe_int_eq_of_int � I � - � � � R � U � - � � � Z � _a � U � o � � � � � � � � � - � , �cast_of_int � �� PInfo �+ATTR �� � � ATTR squash_cast � � � unit star decl �cast_coe_nat � � � n � � � � � � � � � � � � � � � � ? � � � �cast_coe_int � H � J � L int has_coe � PInfo � .ATTR �� � � ATTR � � � � � Gdecl �cast_zero � � � x � � � � � � � E G = � � eq trans � s � int has_zero + . 1 3 5 7 9 ; � } � L N � } S U � � � � � � � ; � �int cast_zero � � � � � � �� PInfo � 0ATTR �� � � ATTR � � � � � Gdecl �cast_one � � � � m � s � @ � � � K � � � � � � � s � � @ � has_one � � � � � � � � � �int cast_one � ] � � � � � �� PInfo � 3ATTR �� � � ATTR � � � � � Gdecl �mul_cast_comm � � � a n � ne � � �denom � x � � x |has_mul mul | �to_has_mul | G | = | � | � | � | � | � � � � � � � � � � � � � � � � ' � � � � x ' � x ! � � ! � � ! I | � ! � ! � ! � ! ' � � | n_num n_denom n_pos n_cop � � � _ � a � c � e � E � G � = � L � N � � & S � U � ; � � & � � � � x � � ( � x � � � @ � � � @ G � @ = � @ � � % � I + � @ . � @ 1 � @ 3 � @ 5 � @ 7 � @ 9 � @ ; � @ � F E � @ � G L � @ N � @ � F S � @ U � @ � S |has_inv inv � @ �to_has_inv � @ � _ � @ a � @ c � @ e � @ � Y � ^ � c � I � | � % � � � � I � � � A � Bsemigroup to_has_mul � @monoid to_semigroup � @ �to_monoid � @ � S � � � % � h � { � � � R � U � � � � � Y � @ � � � � � h � {_a � @ � U x � � � � � � � � G � � = � � � @ � � � + � � . � � 1 � � 3 � � 5 � � 7 � � 9 � � ; � � � � E � � � � L � � N � � � � S � � U � � � � ' � j � � � l � � � @ _ � � a � � c � � e � � � � � � � � | � � � � � � � � � � � � � � �eq symm � @ � � � �mul_assoc � @ � � � % � h � { � I � � � A � � � Bmul_zero_class to_has_mul � @semiring to_mul_zero_class � @ring to_semiring � @ � S � K � L � M � W � 1to_has_zero � @ � � � *to_has_one � @ � � � c | � % � { � � � R � U � � � � � � � � % � _a � @ � U � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � int mul_cast_comm � @ � S � % | � I � � A � � � � � � { � � � R � U � � ? � � � � � ; � % � {_a � @ � U � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � L � � � � � � ' � � � � � � � � � � � = � � � � % � { � I � ? � > � � � � � { � % � R � U � ? � q � � � � � � � %_a � @ � U � � � � Y � ! � � � � � | � � � ? � p � � � h � { � % � I � q � A � ; � I � { � % � p � R � U � q � � � � � J � {_a � @ � U � | � � � � � � � � � � y � � � � � q � � � � � � � � � � A � � � � division_ring inv_comm_of_comm � @ � � z � % � � � � � g � � � � � % � 5 � �Annot � � � @ � �Annot � � PInfo � 6decl �cast_mk_of_ne_zero � � � a b b0 � � � � � � � � � �rat mk # | % | + | . | 1 | 3 | 5 | 7 | 9 | ; | � � E | � � L | N | � � S | U | � � � � � � B � C � D � �_x e � S � � � � � G � H � � � ' | x � � � � � � � � � � % # � % � � % + � . � 1 � 3 � 5 � 7 � 9 � � 2 � ( � - � 4 ! � 3 ' n d h c � H � � � � � % � � � # � A % � A � � + � A . � A 1 � A 3 � A 5 � A 7 � A 9 � A ; � A = � A � � E � A G � A � P L � A N � A � P S � A U � A � Q � @ � g � � � A � � A � � A � � A � � ~ | � R x � A � k � y � I � { � � � A � � � A � X � h � j � A � l � A � � � j � F � g | _ � A a � A c � A e � A � Y � ^ � c � { � � � � A � � � A � � � A �to_ring � A � � � � � � � � � R � U � � � � � � T � � � C � � � A � � � � � � � �_a � T � U x � � � � � � � � G � � = � � � A + � � . � � 1 � � 3 � � 5 � � 7 � � 9 � � ; � � � � E � � � � L � � N � � � � S � � U � � � � � � � j � � � l � � � A � � � @ # � � % � � � A � � ' _ � � a � � c � � e � � � � � � � � | � � � � � �propext � � � �eq_div_iff_mul_eq � A � � � � � � � � � R � � � A � � � x � A � Yd0 � { � � � Exists dcases_on c � S � �has_mul mul � 2 � 4 comm_semiring to_semiring � comm_semiring � g ' _x has_dvd dvd comm_semiring_has_dvd � � g | � @false � � 1 eq mp � . � g � � � � � � � @ � @ � . � g � � ~ ' | � @ � � 8_a � U � . � g � � � � � A � � � � � . � g � � � � � � � <