├── .gitignore ├── LICENSE ├── README.md ├── leanpkg.toml ├── src ├── Banach spaces.lean ├── Euclid_old │ ├── Euclids_Props.lean │ ├── axioms.lean │ ├── tarski_1.lean │ ├── tarski_2.lean │ ├── tarski_3.lean │ ├── tarski_4.lean │ ├── tarski_5.lean │ ├── tarski_6.lean │ ├── tarski_7.lean │ └── unordered_pairs.lean ├── Geometry │ ├── Geometry-in-Lean.docx │ ├── Geometry-in-Lean.odt │ ├── README.md │ ├── axioms.lean │ ├── tarski_1.lean │ ├── tarski_2.lean │ ├── tarski_3.lean │ ├── tarski_4.lean │ ├── tarski_5.lean │ ├── tarski_6.lean │ ├── tarski_7.lean │ ├── tarski_8.lean │ └── unordered_pairs.lean ├── Groups_example_sheet │ └── Sheet1.lean ├── KMB_talks │ └── keji.lean ├── M1F │ └── problem_bank │ │ ├── 1001 │ │ ├── Q1001.lean │ │ ├── Q1001.tex │ │ ├── S1001.lean │ │ └── S1001.tex │ │ ├── 1002 │ │ ├── Q1002.lean │ │ ├── Q1002.tex │ │ ├── S1002.lean │ │ └── S1002.tex │ │ ├── 1003 │ │ ├── Q1003.lean │ │ ├── Q1003.tex │ │ ├── S1003.lean │ │ └── S1003.tex │ │ ├── 1004 │ │ ├── Q1004.lean │ │ ├── Q1004.tex │ │ ├── S1004.lean │ │ └── S1004.tex │ │ ├── 1005 │ │ ├── Q1005.lean │ │ ├── Q1005.tex │ │ ├── S1005.lean │ │ └── S1005.tex │ │ ├── 1006 │ │ ├── Q1006.lean │ │ ├── Q1006.tex │ │ ├── S1006.lean │ │ └── S1006.tex │ │ ├── 1007 │ │ ├── Q1007.lean │ │ ├── Q1007.tex │ │ ├── S1007.lean │ │ └── S1007.tex │ │ ├── 1008 │ │ ├── Q1008.lean │ │ ├── Q1008.tex │ │ ├── S1008.lean │ │ └── S1008.tex │ │ ├── 1009 │ │ ├── Q1009.lean │ │ ├── Q1009.tex │ │ ├── S1009.lean │ │ └── S1009.tex │ │ ├── 0101 │ │ ├── Q0101.lean │ │ ├── Q0101.tex │ │ ├── S0101.lean │ │ └── S0101.tex │ │ ├── 0102 │ │ ├── Q0102.lean │ │ ├── Q0102.tex │ │ ├── S0102.lean │ │ └── S0102.tex │ │ ├── 0103 │ │ ├── Q0103.lean │ │ ├── Q0103.tex │ │ ├── S0103.lean │ │ └── S0103.tex │ │ ├── 0104 │ │ ├── Q0104.lean │ │ ├── Q0104.tex │ │ ├── S0104.lean │ │ └── S0104.tex │ │ ├── 0105 │ │ ├── Q0105.lean │ │ ├── Q0105.tex │ │ ├── S0105.lean │ │ └── S0105.tex │ │ ├── 0106 │ │ ├── Q0106.lean │ │ ├── Q0106.tex │ │ ├── S0106.lean │ │ └── S0106.tex │ │ ├── 0107 │ │ ├── 0107Q.lean │ │ ├── M1F_sheet01_solution07.lean │ │ ├── Q0107.tex │ │ └── S0107.tex │ │ ├── 0201 │ │ ├── Q0201.lean │ │ ├── Q0201.tex │ │ ├── S0201.lean │ │ └── S0201.tex │ │ ├── 0202 │ │ ├── Q0202.lean │ │ ├── Q0202.tex │ │ ├── S0202.lean │ │ └── S0202.tex │ │ ├── 0203 │ │ ├── Q0203.lean │ │ ├── Q0203.tex │ │ ├── S0203.lean │ │ └── S0203.tex │ │ ├── 0204 │ │ ├── Q0204.lean │ │ ├── Q0204.tex │ │ ├── S0204.lean │ │ └── S0204.tex │ │ ├── 0205 │ │ ├── Q0205.lean │ │ ├── Q0205.tex │ │ ├── S0205.lean │ │ └── S0205.tex │ │ ├── 0206 │ │ ├── Q0206.lean │ │ ├── Q0206.tex │ │ ├── S0206.lean │ │ └── S0206.tex │ │ ├── 0207 │ │ ├── Q0207.lean │ │ ├── Q0207.tex │ │ ├── S0207.lean │ │ └── S0207.tex │ │ ├── 0301 │ │ ├── Q0301.lean │ │ ├── Q0301.tex │ │ ├── S0301.lean │ │ └── S0301.tex │ │ ├── 0302 │ │ ├── Q0302.lean │ │ ├── Q0302.tex │ │ ├── S0302.lean │ │ └── S0302.tex │ │ ├── 0303 │ │ ├── Q0303.lean │ │ ├── Q0303.tex │ │ ├── S0303.lean │ │ └── S0303.tex │ │ ├── 0304 │ │ ├── Q0304.lean │ │ ├── Q0304.tex │ │ ├── S0304.lean │ │ └── S0304.tex │ │ ├── 0305 │ │ ├── Q0305.lean │ │ ├── Q0305.tex │ │ ├── S0305.lean │ │ └── S0305.tex │ │ ├── 0306 │ │ ├── Q0306.lean │ │ ├── Q0306.tex │ │ ├── S0306.lean │ │ └── S0306.tex │ │ ├── 0307 │ │ ├── Q0307.lean │ │ ├── Q0307.tex │ │ ├── S0307.lean │ │ └── S0307.tex │ │ ├── 0401 │ │ ├── Q0401.lean │ │ ├── Q0401.tex │ │ ├── S0401.lean │ │ └── S0401.tex │ │ ├── 0402 │ │ ├── Q0402.lean │ │ ├── Q0402.tex │ │ ├── S0402.lean │ │ └── S0402.tex │ │ ├── 0403 │ │ ├── Q0403.lean │ │ ├── Q0403.tex │ │ ├── S0403.lean │ │ └── S0403.tex │ │ ├── 0404 │ │ ├── Q0404.lean │ │ ├── Q0404.tex │ │ ├── S0404.lean │ │ └── S0404.tex │ │ ├── 0405 │ │ ├── Q0405.lean │ │ ├── Q0405.tex │ │ ├── S0405.lean │ │ └── S0405.tex │ │ ├── 0501 │ │ ├── Q0501.lean │ │ ├── Q0501.tex │ │ ├── S0501.lean │ │ └── S0501.tex │ │ ├── 0502 │ │ ├── Q0502.lean │ │ ├── Q0502.tex │ │ ├── S0502.lean │ │ └── S0502.tex │ │ ├── 0503 │ │ ├── Q0503.lean │ │ ├── Q0503.tex │ │ ├── S0503.lean │ │ └── S0503.tex │ │ ├── 0504 │ │ ├── Q0504.lean │ │ ├── Q0504.tex │ │ ├── S0504.lean │ │ └── S0504.tex │ │ ├── 0505 │ │ ├── Q0505.lean │ │ ├── Q0505.tex │ │ ├── S0505.lean │ │ └── S0505.tex │ │ ├── 0506 │ │ ├── Q0506.lean │ │ ├── Q0506.tex │ │ ├── S0506.lean │ │ └── S0506.tex │ │ ├── 0601 │ │ ├── Q0601.lean │ │ ├── Q0601.tex │ │ ├── S0601.lean │ │ └── S0601.tex │ │ ├── 0602 │ │ ├── Q0602.lean │ │ ├── Q0602.tex │ │ ├── S0602.lean │ │ └── S0602.tex │ │ ├── 0603 │ │ ├── Q0603.lean │ │ ├── Q0603.tex │ │ ├── S0603.lean │ │ └── S0603.tex │ │ ├── 0604 │ │ ├── Q0604.lean │ │ ├── Q0604.tex │ │ ├── S0604.lean │ │ └── S0604.tex │ │ ├── 0605 │ │ ├── Q0605.lean │ │ ├── Q0605.tex │ │ ├── S0605.lean │ │ └── S0605.tex │ │ ├── 0606 │ │ ├── Q0606.lean │ │ ├── Q0606.tex │ │ ├── S0606.lean │ │ └── S0606.tex │ │ ├── 0701 │ │ ├── Q0701.lean │ │ ├── Q0701.tex │ │ ├── S0701.lean │ │ └── S0701.tex │ │ ├── 0702 │ │ ├── Q0702.lean │ │ ├── Q0702.tex │ │ ├── S0702.lean │ │ └── S0702.tex │ │ ├── 0703 │ │ ├── Q0703.lean │ │ ├── Q0703.tex │ │ ├── S0703.lean │ │ └── S0703.tex │ │ ├── 0704 │ │ ├── Q0704.lean │ │ ├── Q0704.tex │ │ ├── S0704.lean │ │ └── S0704.tex │ │ ├── 0705 │ │ ├── Q0705.lean │ │ ├── Q0705.tex │ │ ├── S0705.lean │ │ └── S0705.tex │ │ ├── 0706 │ │ ├── Q0706.lean │ │ ├── Q0706.tex │ │ ├── S0706.lean │ │ └── S0706.tex │ │ ├── 0707 │ │ ├── Q0707.lean │ │ ├── Q0707.tex │ │ ├── S0707.lean │ │ └── S0707.tex │ │ ├── 0801 │ │ ├── Q0801.lean │ │ ├── Q0801.tex │ │ ├── S0801.lean │ │ └── S0801.tex │ │ ├── 0802 │ │ ├── Q0802.lean │ │ ├── Q0802.tex │ │ ├── S0802.lean │ │ └── S0802.tex │ │ ├── 0803 │ │ ├── Q0803.lean │ │ ├── Q0803.tex │ │ ├── S0803.lean │ │ └── S0803.tex │ │ ├── 0804 │ │ ├── Q0804.lean │ │ ├── Q0804.pdf │ │ ├── Q0804.tex │ │ ├── S0804.lean │ │ └── S0804.tex │ │ ├── 0805 │ │ ├── Q0805.lean │ │ ├── Q0805.tex │ │ ├── S0805.lean │ │ └── S0805.tex │ │ ├── 0901 │ │ ├── Q0901.lean │ │ ├── Q0901.tex │ │ ├── S0901.lean │ │ └── S0901.tex │ │ ├── 0902 │ │ ├── Q0902.lean │ │ ├── Q0902.tex │ │ ├── S0902.lean │ │ └── S0902.tex │ │ ├── 0903 │ │ ├── Q0903.lean │ │ ├── Q0903.tex │ │ ├── S0903.lean │ │ └── S0903.tex │ │ ├── 0904 │ │ ├── Q0904.lean │ │ ├── Q0904.tex │ │ ├── S0904.lean │ │ └── S0904.tex │ │ ├── 0905 │ │ ├── Q0905.lean │ │ ├── Q0905.tex │ │ ├── S0905.lean │ │ └── S0905.tex │ │ ├── 0906 │ │ ├── Q0906.lean │ │ ├── Q0906.tex │ │ ├── S0906.lean │ │ └── S0906.tex │ │ ├── 0907 │ │ ├── Q0907.lean │ │ ├── Q0907.tex │ │ ├── S0907.lean │ │ └── S0907.tex │ │ ├── PB0001 │ │ ├── Q0001.lean │ │ ├── S0001.lean │ │ └── S0001.lean~ │ │ ├── PB0002 │ │ ├── Q0002.lean │ │ ├── Q0002.lean~ │ │ └── S0002.lean │ │ ├── PB0003 │ │ ├── Q0003.lean │ │ ├── S0003.lean │ │ └── S0003.lean~ │ │ ├── PB0004 │ │ ├── Q0004.lean │ │ ├── S0004.lean │ │ └── S0004.lean~ │ │ ├── PB0005 │ │ ├── Q0005.lean │ │ ├── S0005.lean │ │ └── S0005.lean~ │ │ ├── PB0006 │ │ ├── Q0006.lean │ │ ├── S0006.lean │ │ └── S0006.lean~ │ │ ├── PB0007 │ │ ├── Q0007.lean │ │ ├── Q0007.lean~ │ │ └── S0007.lean │ │ └── PB0008 │ │ ├── Q0008.lean │ │ ├── S0008.lean │ │ └── S0008.lean~ ├── M1P2 │ ├── sheet_1.lean │ ├── sheet_10.lean │ ├── sheet_2.lean │ ├── sheet_3.lean │ ├── sheet_4.lean │ ├── sheet_5.lean │ ├── sheet_6.lean │ ├── sheet_7.lean │ ├── sheet_8.lean │ └── sheet_9.lean ├── M2PM2 │ └── isomorphism.lean ├── M3P14 │ ├── Arithmetic_functions │ │ ├── arithmetic_functions.lean │ │ ├── mobius.lean │ │ ├── phi.lean │ │ └── sum_over_divisors.lean │ ├── Problem_sheets │ │ ├── sheet1.lean │ │ ├── sheet2.lean │ │ ├── sheet3.lean │ │ └── sheet4.lean │ ├── Resources │ │ ├── M3P14.pdf │ │ ├── ps1.pdf │ │ ├── ps2.pdf │ │ ├── ps3.pdf │ │ └── ps4.pdf │ ├── jacobi_sym.lean │ ├── kronecker_sym.lean │ ├── lemmas_for_prime_int.lean │ ├── lqr.lean │ ├── order.lean │ ├── order_zmodn_kmb.lean │ ├── pminusone.lean │ ├── pow_example.lean │ ├── prime_int.lean │ ├── stupid3stuff.lean │ ├── sum_over_divisors.lean │ └── x_sq_plus_n_y_sq.lean ├── Topology │ ├── Heine-Borel (incomplete) │ ├── Material │ │ ├── Path_Homotopy_09_08.lean │ │ ├── Sutherland_Chapter_10.lean │ │ ├── Sutherland_Chapter_12.lean │ │ ├── Sutherland_Chapter_8.lean │ │ ├── Sutherland_Chapter_9.lean │ │ ├── banach_contraction.lean │ │ ├── connected_spaces.lean │ │ ├── fundamental_group.lean │ │ ├── homotopy.lean │ │ ├── homotopy_results.lean │ │ ├── local_connectedness.lean │ │ ├── pasting_lemma.lean │ │ ├── path.lean │ │ ├── path_connectedness.lean │ │ ├── real_results.lean │ │ ├── suth_prop_7_2.lean │ │ ├── topological_sequences.lean │ │ └── topology_thoughts.lean │ └── Problem_Sheets │ │ ├── BASIC_ps_2_ex_4b(incomplete).lean │ │ ├── FINSETS_ps_2_ex_4b(incomplete).lean │ │ └── ps_2_ex4a.lean ├── category_theory │ └── Problems │ │ ├── 1_1.lean │ │ ├── 1_2.lean │ │ └── 1_3.lean ├── chris_hughes_various │ ├── blue_eyed_islanders.lean │ ├── disjoint_finset.lean │ ├── exponential │ │ ├── exponential.lean │ │ └── limits.lean │ ├── fermat_sum_two_squares.lean │ ├── int_gcd.lean │ ├── lagrange_four_square.lean │ └── zmod.lean ├── classical_logic │ ├── predicate_lemmas.lean │ └── proposional_lemmas.lean ├── finite_dimensional_vector_spaces │ ├── basic.lean │ ├── eigen.lean │ ├── linear_map.lean │ ├── ring_n_is_module.lean │ └── tmp.lean ├── inner_product_spaces │ ├── basic.lean │ ├── norm_space.lean │ ├── ring_involution.lean │ ├── sesquilinear_forms │ ├── sesquilinear_forms.lean │ ├── subfield.lean │ └── subrings_subfields.lean ├── markov │ └── markov_intro.lean ├── vector_space.lean └── xenalib │ ├── Blair_Operation_on_Matrix.lean │ ├── Ellen_Arlt_matrix_rings.lean │ ├── Group_actions.lean │ ├── Keji_domains.lean │ ├── Keji_finite_dim_vector_spaces.lean │ ├── Keji_further_matrix_things.lean │ ├── Keji_mechanics.lean │ ├── Keji_permutation_group.lean │ ├── Keji_permutations_for_matrices.lean │ ├── M1F │ └── help_for_0107.lean │ ├── M1P1.lean │ ├── Sean_Leather_matrix_ring_cleanup.lean │ ├── keji_lemma.lean │ └── nat_stuff.lean └── tmp.lean /.gitignore: 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