CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutSign UpSign In

Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place.

| Download

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: 18536
License: APACHE
oleanfile3.4.2, commit cbd2b6686ddb��initdataequivbasicdatanatpairingdatapnatbasic�"�export_decloptionnonenonesomesomeexport_declboolffffttttexport_declhas_andthenandthenandthenexport_declhas_powpowpowexport_declhas_appendappendappendexport_decldecidableis_trueis_trueis_falseis_falseto_boolto_boolexport_declhas_purepurepureexport_declhas_bindbindbindexport_declhas_monad_lift_tmonad_lift!monad_liftexport_declmonad_functor_tmonad_map$monad_mapexport_declmonad_runrun'runexport_decllistmmap*mmapmmap'*mmap'mfilter*mfiltermfoldl*mfoldlexport_declnativenat_map3rb_mapmkexport_declname_mapnativerb_mapmkexport_declexpr_mapnativerb_mapmkexport_decltacticinteraction_monadfailedfailexport_decltactic_resultinteraction_monadresultexport_decltacticFtransparencyreducibleGreduciblesemireducibleGsemireducibleexport_decltacticmk_simp_attrLmk_simp_attrexport_declmonad_exceptthrowOthrowcatchOcatchexport_declmonad_except_adapteradapt_exceptTadapt_exceptexport_declmonad_state_adapteradapt_stateWadapt_stateexport_declmonad_readerreadZreadexport_declmonad_reader_adapteradapt_reader]adapt_readerexport_declis_lawful_functormap_const_eq`map_const_eqid_map`id_mapcomp_map`comp_mapexport_declis_lawful_applicativeseq_left_eqgseq_left_eqseq_right_eqgseq_right_eqpure_seq_eq_mapgpure_seq_eq_mapmap_puregmap_pureseq_puregseq_pureseq_assocgseq_assocexport_declis_lawful_monadbind_pure_comp_eq_maptbind_pure_comp_eq_mapbind_map_eq_seqtbind_map_eq_seqpure_bindtpure_bindbind_assoctbind_assocexport_decltraversabletraverse}traversedeclequivnat_prod_nat_equiv_nat_proof_1pprodnat�eqnatunpairpnatmkpair�fst�snd�prodcases_onp_fstp_sndnatunpair_mkpair
prodmk&�PInfo�decl�equivequivmk�natmkpair_unpair�PInfo�VMR�_lambda_1VMR�VMC��

natmkpairVMC���unpairdecl�equations_eqn_11�:eqrefl1<�PInfo�ATTR_refl_lemma���EqnL�SEqnL�ATTRsimp���decl�bool_prod_nat_equiv_nat_match_1_abool�D�B�DfstBsndid_rhsnatbit$�PInfo�decl�equations_eqn_1bBn�!B$P�B�?id_delta\�PInfo�ATTR����EqnL�decl�_match_2_aDD�bodd_div2_xDW�DB�Do�B��hik[[eqmprztrueidz~eqtrans�zand~~~��B$$V��h[[�aD�De_1h$aD�De_2�congrD�hh$congr_argD�D���hx[�DxY�boddP�div2P[�iP�a�e_1V$�D�$iwP�$natbodd_div2_eqP�B�Be_1���e_2��DY�Y��$�B�D��Y��$�bodd_bit$��div2_bit$[[?D[propext��prodmkinj_iffB$$a���e_1�$b���e_2���������$����������~��~eq_self_iff_trueB$�~��~�5��~and_self~trivial�PInfo�decl�equations_eqn_1bBneqz�[�M�B��z�z�V�PInfo�ATTR����EqnL�decl�bool_prod_nat_equiv_nat_proof_1_xDo�D�U�PInfo�decl�_proof_2nVki�|�i~���i~��i�~��e_1�a�e_2���V�V��$�����V��g�W�fN����WY�������D�De_1���$W�f���������bit_decompa�@�L�PInfo�decl�/D2Dki���PInfo�VMR�_lambda_1VMR�VMC��D�VMC��natbodd_div2decl�equations_eqn_1�����?�����PInfo�ATTR����EqnL�SEqnL�ATTR����decl�nat_sum_nat_equiv_nat/sum�trans��D�symmD���bool_prod_equiv_sum���PInfo�VMR�VMC��equivbool_prod_equiv_sum�symm�transdecl�equations_eqn_1�����?�����PInfo�ATTR����EqnL�SEqnL�ATTR����decl�int_equiv_nat/int�������int_equiv_nat_sum_nat��	�PInfo�VMR�VMC���int_equiv_nat_sum_nat�decl�equations_eqn_1�����?�����PInfo�ATTR����EqnL�SEqnL�decl�prod_equiv_of_equiv_natu_1u_2��e�	�		�$$$�������		��$�	��
�prod_congr$$Annotcalc
<Annot�
�symm	$Annot��PInfo� VMR�VMC� �����prod_congr��decl�equations_eqn_1����������������$������������PInfo� ATTR����EqnL�SEqnL�decl�pnat_equiv_nat_match_1_apnat�#natsucc_pnatn�#natpredsubtypevalnhas_ltlt�has_lthas_zerozeronathas_zero��#subtypecases_on�3��#�;valproperty�2v�$�%�7�mk�3$�Gnatcases_onnh�2�K$�$�1�!zero�less_than_or_equaldcases_on�!succ�0t_1�$�&�VH_1V�R$H_2heq�S��Y�$�$�%�7�E�R��d�R�*�[�V�no_confusion�+�^$�Y�V�&refl�V�$�%�7�c��x�R�Vh_bh_a�Z�*�[�U$�q�+�_�Y�U��&step�V�$�h�R��a�Rheqrefl�S�#�$�1�U|�$�%�7�E����~����~����$~��V���������$���
succ_pos$������#��#e_1�$$��#��#e_2����#��$��$��$��#��#����$�������#���%$��n�7e_1���#�$�%��$natpred_succ$�equations_eqn_1$����?��3�����������subtypemk_eq_mk�3�������(inj_eq$$���~�>$�L�PInfo�
%decl�
equations_eqn_1�#�$�2�S�K�
�G��#�$�2�[�K�]�K��PInfo�A%ATTR����AEqnL�Adecl�pnat_equiv_nat_proof_1_x�#�;�D�#��PInfo�C%decl�B_proof_2nV�7�%�F|�.~���.~��.�~���,���&�4�+�&��a�Ge_1���$�&�:��c���I��e_1��$����$�4�+�E�����������@�L�PInfo�E%decl�B/�#2�#�7�%�C�E�PInfo�B%VMR�BVMC�B%�pred_main�decl�Bequations_eqn_1�k�B�s?�k�u�PInfo�N%ATTR����NEqnL�NSEqnL�BEndFile