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	instantiation	69, 86, 71	⊢
	: , : , :
4	instantiation	87, 7, 8	⊢
	: , : , :
5	instantiation	9, 10	⊢
	: , :
6	instantiation	87, 11, 12	⊢
	: , : , :
7	instantiation	35, 13	⊢
	: , : , :
8	instantiation	14, 15	⊢
	:
9	theorem		⊢
	proveit.logic.equality.equals_reversal
10	instantiation	35, 16	⊢
	: , : , :
11	instantiation	35, 17	⊢
	: , : , :
12	instantiation	87, 18, 19	⊢
	: , : , :
13	instantiation	20, 31	⊢
	:
14	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
15	instantiation	143, 137, 21	⊢
	: , : , :
16	instantiation	87, 22, 23	⊢
	: , : , :
17	instantiation	87, 24, 25	⊢
	: , : , :
18	instantiation	87, 26, 27	⊢
	: , : , :
19	instantiation	28, 40	⊢
	:
20	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
21	instantiation	143, 133, 29	⊢
	: , : , :
22	instantiation	78, 103, 145, 104, 105, 106, 107, 108, 31, 129, 109	⊢
	: , : , : , : , : , : , :
23	instantiation	62, 100, 30, 103, 46, 104, 31, 107, 108, 129, 109	⊢
	: , : , : , : , : , :
24	instantiation	35, 32	⊢
	: , : , :
25	instantiation	33, 57, 34*	⊢
	:
26	instantiation	35, 36	⊢
	: , : , :
27	instantiation	37, 38, 39, 40, 41*	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.division.frac_one_denom
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
32	instantiation	42, 43	⊢
	:
33	theorem		⊢
	proveit.numbers.absolute_value.abs_even
34	instantiation	44, 45, 46, 107, 108, 129, 109, 47*	⊢
	: , :
35	axiom		⊢
	proveit.logic.equality.substitution
36	instantiation	87, 48, 49	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.division.frac_cancel_left
38	instantiation	143, 51, 50	⊢
	: , : , :
39	instantiation	143, 51, 52	⊢
	: , : , :
40	instantiation	69, 53, 54	⊢
	: , : , :
41	instantiation	55, 107	⊢
	:
42	theorem		⊢
	proveit.numbers.addition.elim_zero_left
43	instantiation	56, 57	⊢
	:
44	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
46	instantiation	58	⊢
	: , : , : , :
47	instantiation	87, 59, 60	⊢
	: , : , :
48	instantiation	78, 103, 100, 145, 104, 61, 109, 107, 108, 81	⊢
	: , : , : , : , : , : , :
49	instantiation	62, 100, 79, 103, 63, 104, 107, 109, 108, 81	⊢
	: , : , : , : , : , :
50	instantiation	143, 65, 64	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
52	instantiation	143, 65, 66	⊢
	: , : , :
53	instantiation	143, 137, 67	⊢
	: , : , :
54	instantiation	102, 103, 145, 100, 104, 68, 109, 108, 81	⊢
	: , : , : , : , : , :
55	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
56	theorem		⊢
	proveit.numbers.negation.complex_closure
57	instantiation	69, 70, 71	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
59	instantiation	72, 79, 73, 74, 75, 76, 77	⊢
	: , : , : , :
60	instantiation	78, 103, 79, 104, 80, 107, 108, 81, 109	⊢
	: , : , : , : , : , : , :
61	instantiation	116	⊢
	: , :
62	theorem		⊢
	proveit.numbers.multiplication.association
63	instantiation	94	⊢
	: , : , :
64	instantiation	143, 83, 82	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
66	instantiation	143, 83, 84	⊢
	: , : , :
67	instantiation	122, 85, 95	⊢
	: , :
68	instantiation	116	⊢
	: , :
69	theorem		⊢
	proveit.logic.equality.sub_right_side_into
70	instantiation	143, 137, 86	⊢
	: , : , :
71	instantiation	87, 88, 89	⊢
	: , : , :
72	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
73	instantiation	94	⊢
	: , : , :
74	instantiation	94	⊢
	: , : , :
75	instantiation	92, 90	⊢
	:
76	instantiation	92, 91	⊢
	:
77	instantiation	92, 93	⊢
	:
78	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
79	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
80	instantiation	94	⊢
	: , : , :
81	instantiation	143, 137, 95	⊢
	: , : , :
82	instantiation	143, 97, 96	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
84	instantiation	143, 97, 98	⊢
	: , : , :
85	instantiation	122, 117, 124	⊢
	: , :
86	instantiation	122, 115, 99	⊢
	: , :
87	axiom		⊢
	proveit.logic.equality.equals_transitivity
88	instantiation	102, 100, 145, 103, 106, 104, 101, 129, 109	⊢
	: , : , : , : , : , :
89	instantiation	102, 103, 145, 104, 105, 106, 107, 108, 129, 109	⊢
	: , : , : , : , : , :
90	instantiation	110, 145	⊢
	:
91	instantiation	112, 111	⊢
	: , :
92	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
93	instantiation	112, 113	⊢
	: , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
95	instantiation	143, 133, 114	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
97	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
98	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
99	instantiation	122, 138, 117	⊢
	: , :
100	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
101	instantiation	143, 137, 115	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.multiplication.disassociation
103	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
104	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
105	instantiation	116	⊢
	: , :
106	instantiation	116	⊢
	: , :
107	instantiation	143, 137, 123	⊢
	: , : , :
108	instantiation	143, 137, 124	⊢
	: , : , :
109	instantiation	143, 137, 117	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
111	instantiation	118, 134	⊢
	:
112	theorem		⊢
	proveit.numbers.ordering.relax_less
113	instantiation	119, 127	⊢
	:
114	instantiation	120, 121	⊢
	:
115	instantiation	122, 123, 124	⊢
	: , :
116	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
117	instantiation	125, 126, 127	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
119	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
120	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
121	instantiation	128, 129, 130	⊢
	:
122	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
123	instantiation	143, 131, 132	⊢
	: , : , :
124	instantiation	143, 133, 134	⊢
	: , : , :
125	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
126	instantiation	135, 136	⊢
	: , :
127	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
128	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
129	instantiation	143, 137, 138	⊢
	: , : , :
130	assumption		⊢
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
132	instantiation	143, 139, 140	⊢
	: , : , :
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.logic.sets.inclusion.relax_proper_subset
136	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
137	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
138	instantiation	141, 142	⊢
	:
139	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
140	instantiation	143, 144, 145	⊢
	: , : , :
141	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
142	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
143	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
144	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
145	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements