Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	instantiation	1, 2, 3, 4*, 5*, 6*	⊢
	: , :
1	theorem		⊢
	proveit.trigonometry.complex_unit_circle_chord_length
2	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
3	reference	69	⊢
4	instantiation	26, 7, 8	⊢
	: , : , :
5	instantiation	9, 10	⊢
	: , :
6	instantiation	26, 11, 12	⊢
	: , : , :
7	instantiation	37, 13	⊢
	: , : , :
8	instantiation	14, 15	⊢
	:
9	theorem		⊢
	proveit.logic.equality.equals_reversal
10	instantiation	37, 16	⊢
	: , : , :
11	instantiation	37, 17	⊢
	: , : , :
12	instantiation	26, 18, 19	⊢
	: , : , :
13	instantiation	20, 33	⊢
	:
14	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
15	instantiation	107, 99, 21	⊢
	: , : , :
16	instantiation	26, 22, 23	⊢
	: , : , :
17	instantiation	26, 24, 25	⊢
	: , : , :
18	instantiation	26, 27, 28	⊢
	: , : , :
19	instantiation	29, 42	⊢
	:
20	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
21	instantiation	107, 103, 30	⊢
	: , : , :
22	instantiation	31, 88, 109, 89, 90, 91, 92, 93, 33, 94	⊢
	: , : , : , : , : , : , :
23	instantiation	51, 89, 32, 88, 48, 90, 33, 92, 93, 94	⊢
	: , : , : , : , : , :
24	instantiation	37, 34	⊢
	: , : , :
25	instantiation	35, 60, 36*	⊢
	:
26	axiom		⊢
	proveit.logic.equality.equals_transitivity
27	instantiation	37, 38	⊢
	: , : , :
28	instantiation	39, 40, 41, 42, 43*	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.division.frac_one_denom
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
31	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
34	instantiation	44, 45	⊢
	:
35	theorem		⊢
	proveit.numbers.absolute_value.abs_even
36	instantiation	46, 47, 48, 92, 93, 94, 49*, 50*	⊢
	: , :
37	axiom		⊢
	proveit.logic.equality.substitution
38	instantiation	51, 89, 109, 88, 52, 90, 92, 93, 57	⊢
	: , : , : , : , : , :
39	theorem		⊢
	proveit.numbers.division.frac_cancel_left
40	instantiation	107, 54, 53	⊢
	: , : , :
41	instantiation	107, 54, 55	⊢
	: , : , :
42	instantiation	56, 93, 57	⊢
	: , :
43	instantiation	58, 92	⊢
	:
44	theorem		⊢
	proveit.numbers.addition.elim_zero_left
45	instantiation	59, 60	⊢
	:
46	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
48	instantiation	61	⊢
	: , : , :
49	instantiation	63, 62	⊢
	:
50	instantiation	63, 64	⊢
	:
51	theorem		⊢
	proveit.numbers.multiplication.association
52	instantiation	96	⊢
	: , :
53	instantiation	107, 66, 65	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
55	instantiation	107, 66, 67	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
57	instantiation	107, 99, 68	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
59	theorem		⊢
	proveit.numbers.negation.complex_closure
60	instantiation	107, 99, 69	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
62	instantiation	70, 109	⊢
	:
63	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
64	instantiation	71, 72	⊢
	: , :
65	instantiation	107, 74, 73	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
67	instantiation	107, 74, 75	⊢
	: , : , :
68	instantiation	107, 76, 77	⊢
	: , : , :
69	instantiation	78, 79, 80	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
71	theorem		⊢
	proveit.numbers.ordering.relax_less
72	instantiation	81, 104	⊢
	:
73	instantiation	107, 83, 82	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
75	instantiation	107, 83, 84	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
77	instantiation	85, 94	⊢
	:
78	theorem		⊢
	proveit.logic.equality.sub_right_side_into
79	instantiation	95, 86, 100	⊢
	: , :
80	instantiation	87, 88, 109, 89, 90, 91, 92, 93, 94	⊢
	: , : , : , : , : , :
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
82	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
83	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
84	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
85	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
86	instantiation	95, 97, 98	⊢
	: , :
87	theorem		⊢
	proveit.numbers.multiplication.disassociation
88	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
89	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
90	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
91	instantiation	96	⊢
	: , :
92	instantiation	107, 99, 97	⊢
	: , : , :
93	instantiation	107, 99, 98	⊢
	: , : , :
94	instantiation	107, 99, 100	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
96	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
97	instantiation	107, 101, 102	⊢
	: , : , :
98	instantiation	107, 103, 104	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
100	assumption		⊢
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
102	instantiation	107, 105, 106	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
104	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
105	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
106	instantiation	107, 108, 109	⊢
	: , : , :
107	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
108	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
109	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements