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	instantiation	7, 90, 128	⊢
	: , :
3	reference	128	⊢
4	instantiation	8, 90, 9*	⊢
	:
5	instantiation	85, 10, 11	⊢
	: , : , :
6	instantiation	85, 12, 13	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
8	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.unit_length_complex_polar_negation
9	instantiation	14, 15	⊢
	: , :
10	instantiation	98, 16	⊢
	: , : , :
11	instantiation	17, 70	⊢
	:
12	instantiation	98, 18	⊢
	: , : , :
13	instantiation	85, 19, 20	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.equality.equals_reversal
15	instantiation	98, 21	⊢
	: , : , :
16	instantiation	104, 22, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.negation.double_negation
18	instantiation	85, 24, 25	⊢
	: , : , :
19	instantiation	85, 26, 27	⊢
	: , : , :
20	instantiation	28, 46	⊢
	:
21	instantiation	85, 29, 30	⊢
	: , : , :
22	instantiation	31, 88, 32, 33*, 34*	⊢
	: , :
23	instantiation	35, 36	⊢
	:
24	instantiation	98, 37	⊢
	: , : , :
25	instantiation	38, 39, 50, 120, 121, 122, 40*, 41*	⊢
	: , :
26	instantiation	98, 42	⊢
	: , : , :
27	instantiation	43, 44, 45, 46, 47*	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.division.frac_one_denom
29	instantiation	48, 117, 139, 124, 118, 119, 120, 121, 112, 122	⊢
	: , : , : , : , : , : , :
30	instantiation	61, 124, 49, 117, 50, 118, 112, 120, 121, 122	⊢
	: , : , : , : , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.complex_polar_negation
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
33	instantiation	51, 121	⊢
	:
34	instantiation	85, 52, 53	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
36	instantiation	54, 101, 55	⊢
	: , :
37	instantiation	85, 56, 57	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
40	instantiation	59, 58	⊢
	:
41	instantiation	59, 60	⊢
	:
42	instantiation	61, 124, 139, 117, 62, 118, 120, 121, 66	⊢
	: , : , : , : , : , :
43	theorem		⊢
	proveit.numbers.division.frac_cancel_left
44	instantiation	137, 64, 63	⊢
	: , : , :
45	instantiation	137, 64, 65	⊢
	: , : , :
46	instantiation	71, 121, 66	⊢
	: , :
47	instantiation	69, 120	⊢
	:
48	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
50	instantiation	67	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.addition.elim_zero_left
52	instantiation	98, 68	⊢
	: , : , :
53	instantiation	69, 70	⊢
	:
54	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
55	instantiation	71, 112, 121	⊢
	: , :
56	instantiation	72, 117, 139, 124, 118, 73, 76, 121, 74	⊢
	: , : , : , : , : , :
57	instantiation	75, 121, 76, 77	⊢
	: , : , :
58	instantiation	78, 139	⊢
	:
59	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
60	instantiation	79, 80	⊢
	: , :
61	theorem		⊢
	proveit.numbers.multiplication.association
62	instantiation	126	⊢
	: , :
63	instantiation	137, 82, 81	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
65	instantiation	137, 82, 83	⊢
	: , : , :
66	instantiation	137, 129, 84	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
68	instantiation	85, 86, 87	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
70	instantiation	137, 129, 88	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
72	theorem		⊢
	proveit.numbers.addition.disassociation
73	instantiation	126	⊢
	: , :
74	instantiation	137, 129, 89	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
76	instantiation	137, 129, 90	⊢
	: , : , :
77	instantiation	91	⊢
	:
78	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
79	theorem		⊢
	proveit.numbers.ordering.relax_less
80	instantiation	92, 134	⊢
	:
81	instantiation	137, 94, 93	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
83	instantiation	137, 94, 95	⊢
	: , : , :
84	instantiation	137, 96, 97	⊢
	: , : , :
85	axiom		⊢
	proveit.logic.equality.equals_transitivity
86	instantiation	98, 99	⊢
	: , : , :
87	instantiation	100, 101	⊢
	:
88	instantiation	137, 131, 102	⊢
	: , : , :
89	instantiation	103, 128	⊢
	:
90	instantiation	104, 105, 106	⊢
	: , : , :
91	axiom		⊢
	proveit.logic.equality.equals_reflexivity
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
93	instantiation	137, 108, 107	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
95	instantiation	137, 108, 109	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
97	instantiation	110, 122	⊢
	:
98	axiom		⊢
	proveit.logic.equality.substitution
99	instantiation	111, 112	⊢
	:
100	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
101	instantiation	137, 129, 113	⊢
	: , : , :
102	instantiation	137, 135, 114	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.negation.real_closure
104	theorem		⊢
	proveit.logic.equality.sub_right_side_into
105	instantiation	125, 115, 130	⊢
	: , :
106	instantiation	116, 117, 139, 124, 118, 119, 120, 121, 122	⊢
	: , : , : , : , : , :
107	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
108	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
109	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
110	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
111	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
112	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
113	instantiation	137, 133, 123	⊢
	: , : , :
114	instantiation	137, 138, 124	⊢
	: , : , :
115	instantiation	125, 127, 128	⊢
	: , :
116	theorem		⊢
	proveit.numbers.multiplication.disassociation
117	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
118	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
119	instantiation	126	⊢
	: , :
120	instantiation	137, 129, 127	⊢
	: , : , :
121	instantiation	137, 129, 128	⊢
	: , : , :
122	instantiation	137, 129, 130	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
124	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
125	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
126	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
127	instantiation	137, 131, 132	⊢
	: , : , :
128	instantiation	137, 133, 134	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
130	assumption		⊢
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
132	instantiation	137, 135, 136	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
134	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
135	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
136	instantiation	137, 138, 139	⊢
	: , : , :
137	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
138	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
139	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements