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FormalBook.lean

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import FormalBook.Ch01_Six_proofs_of_the_infinity_of_primes
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import FormalBook.«Ch02_Bertrand's_postulate»
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import FormalBook.«Ch03_Binomial_coefficients_are_(almost)_never_powers»
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import FormalBook.Ch04_Representing_numbers_as_sums_of_two_squares
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import FormalBook.Ch05_The_law_of_quadratic_reciprocity
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import FormalBook.Ch06_Every_finite_division_ring_is_a_field
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import FormalBook.«Ch07_The_spectral_theorem_and_Hadamard's_determinant_problem»
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import FormalBook.Ch08_Some_irrational_numbers
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import FormalBook.«Ch09_Four_times_pi²_over_6»
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import FormalBook.«Ch10_Hilbert's_third_problem_decomposing_polyhedra»
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import FormalBook.Ch11_Lines_in_the_plane_and_decompositions_of_graphs
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import FormalBook.Ch12_The_slope_problem
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import FormalBook.«Ch13_Three_applications_of_Euler's_formula»
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import FormalBook.«Ch14_Cauchy's_rigidity_theorem»
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import FormalBook.«Ch15_The_Borromean_rings_don't_exist»
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import FormalBook.Ch16_Touching_simplices
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import FormalBook.Ch17_Every_large_point_set_has_an_obtuse_angle
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import FormalBook.«Ch18_Borsuk's_conjecture»
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import FormalBook.«Ch19_Sets,_functions,_and_the_continuum_hypothesis»
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import FormalBook.Ch20_In_praise_of_inequalities
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import FormalBook.Ch21_The_fundamental_theorem_of_algebra
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import FormalBook.Ch22_One_square_and_an_odd_number_of_triangles
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import FormalBook.«Ch23_A_theorem_of_Pólya_on_polynomials»
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import FormalBook.«Ch24_Van_der_Waerden's_permanent_conjecture»
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import FormalBook.Ch25_On_a_lemma_of_Littlewook_and_Offord
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import FormalBook.Ch26_Cotangent_and_the_Herglotz_trick
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import FormalBook.«Ch27_Buffon's_needle_problem»
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import FormalBook.«Ch28_Pigeon-hole_and_double_counting»
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import FormalBook.Ch29_Tiling_rectangles
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import FormalBook.Ch30_Three_famous_theorems_on_finite_sets
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import FormalBook.Ch31_Shuffling_cards
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import FormalBook.«Ch33_Cayley's_formula_for_the_number_of_trees»
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import FormalBook.Ch32_Lattice_paths_and_determinants
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import FormalBook.Ch34_Identities_versus_bijections
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import FormalBook.Ch35_The_finite_Kakeya_problem
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import FormalBook.Ch36_Completing_Latin_squares
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import FormalBook.Ch37_Permanents_and_the_power_of_entropy
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import FormalBook.Ch38_The_Dinitz_problem
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import FormalBook.«Ch39_Five-coloring_plane_graphs»
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import FormalBook.Ch40_How_to_guard_a_museum
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import FormalBook.«Ch41_Turán's_graph_theorem»
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import FormalBook.Ch42_Communicating_without_errors
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import FormalBook.Ch43_The_chromatic_number_of_Kneser_graphs
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import FormalBook.Ch44_Of_friends_and_politicians
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import FormalBook.«Ch45_Probability_makes_counting_(sometimes)_easy»
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import FormalBook.Chapter_01
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import FormalBook.Chapter_02
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import FormalBook.Chapter_03
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import FormalBook.Chapter_04
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import FormalBook.Chapter_05
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import FormalBook.Chapter_06
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import FormalBook.Chapter_07
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import FormalBook.Chapter_08
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import FormalBook.Chapter_09
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import FormalBook.Chapter_10
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import FormalBook.Chapter_11
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import FormalBook.Chapter_12
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import FormalBook.Chapter_13
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import FormalBook.Chapter_14
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import FormalBook.Chapter_15
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import FormalBook.Chapter_16
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import FormalBook.Chapter_17
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import FormalBook.Chapter_18
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import FormalBook.Chapter_19
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import FormalBook.Chapter_20
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import FormalBook.Chapter_21
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import FormalBook.Chapter_22
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import FormalBook.Chapter_23
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import FormalBook.Chapter_24
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import FormalBook.Chapter_25
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import FormalBook.Chapter_26
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import FormalBook.Chapter_27
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import FormalBook.Chapter_28
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import FormalBook.Chapter_29
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import FormalBook.Chapter_30
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import FormalBook.Chapter_31
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import FormalBook.Chapter_33
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import FormalBook.Chapter_32
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import FormalBook.Chapter_34
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import FormalBook.Chapter_35
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import FormalBook.Chapter_36
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import FormalBook.Chapter_37
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import FormalBook.Chapter_38
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import FormalBook.Chapter_39
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import FormalBook.Chapter_40
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import FormalBook.Chapter_41
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import FormalBook.Chapter_42
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import FormalBook.Chapter_43
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import FormalBook.Chapter_44
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import FormalBook.Chapter_45

FormalBook/Ch01_Six_proofs_of_the_infinity_of_primes.lean FormalBook/Chapter_01.lean

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intro h1
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have h : (2 - 1 : ZMod q) = 0 := by exact Iff.mpr sub_eq_zero h1
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norm_num at h
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#check pred_le_pred
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lemma sub_one_le_sub_one {n m : ℕ} : n ≤ m → n - 1 ≤ m - 1 := by
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intro h
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exact pred_le_pred h
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exact fun h => pred_le_pred h
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theorem infinity_of_primes₃:
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README.md

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