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. Commercial Alternative to JupyterHub.

| 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: 20365
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