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	reference	103	⊢
2	reference	181	⊢
3	instantiation	152	⊢
	: , :
4	instantiation	152	⊢
	: , :
5	instantiation	10, 11, 7, 13*, 8*, 9*	⊢
	: , :
6	instantiation	10, 11, 12, 13*, 14*, 15*	⊢
	: , :
7	instantiation	114, 121, 102	⊢
	: , : , :
8	instantiation	21, 16	⊢
	: , :
9	instantiation	122, 17, 18	⊢
	: , : , :
10	theorem		⊢
	proveit.trigonometry.complex_unit_circle_chord_length
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
12	instantiation	114, 131, 116	⊢
	: , : , :
13	instantiation	122, 19, 20	⊢
	: , : , :
14	instantiation	21, 22	⊢
	: , :
15	instantiation	122, 23, 24	⊢
	: , : , :
16	instantiation	61, 25	⊢
	: , : , :
17	instantiation	61, 26	⊢
	: , : , :
18	instantiation	122, 27, 28	⊢
	: , : , :
19	instantiation	61, 29	⊢
	: , : , :
20	instantiation	30, 31	⊢
	:
21	theorem		⊢
	proveit.logic.equality.equals_reversal
22	instantiation	61, 32	⊢
	: , : , :
23	instantiation	61, 33	⊢
	: , : , :
24	instantiation	122, 34, 35	⊢
	: , : , :
25	instantiation	122, 36, 37	⊢
	: , : , :
26	instantiation	122, 38, 39	⊢
	: , : , :
27	instantiation	122, 40, 41	⊢
	: , : , :
28	instantiation	50, 55	⊢
	:
29	instantiation	42, 57	⊢
	:
30	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
31	instantiation	179, 173, 43	⊢
	: , : , :
32	instantiation	122, 44, 45	⊢
	: , : , :
33	instantiation	122, 46, 47	⊢
	: , : , :
34	instantiation	122, 48, 49	⊢
	: , : , :
35	instantiation	50, 66	⊢
	:
36	instantiation	109, 139, 181, 140, 141, 142, 143, 144, 57, 165, 145	⊢
	: , : , : , : , : , : , :
37	instantiation	91, 136, 51, 139, 70, 140, 57, 143, 144, 165, 145	⊢
	: , : , : , : , : , :
38	instantiation	61, 52	⊢
	: , : , :
39	instantiation	59, 86, 53*	⊢
	:
40	instantiation	61, 54	⊢
	: , : , :
41	instantiation	63, 64, 65, 55, 67*	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
43	instantiation	179, 169, 56	⊢
	: , : , :
44	instantiation	109, 139, 181, 136, 140, 141, 143, 144, 57, 165	⊢
	: , : , : , : , : , : , :
45	instantiation	91, 136, 110, 139, 80, 140, 57, 143, 144, 165	⊢
	: , : , : , : , : , :
46	instantiation	61, 58	⊢
	: , : , :
47	instantiation	59, 96, 60*	⊢
	:
48	instantiation	61, 62	⊢
	: , : , :
49	instantiation	63, 64, 65, 66, 67*	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.division.frac_one_denom
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
52	instantiation	76, 68	⊢
	:
53	instantiation	78, 69, 70, 143, 144, 165, 145, 71*	⊢
	: , :
54	instantiation	122, 72, 73	⊢
	: , : , :
55	instantiation	114, 74, 75	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
58	instantiation	76, 77	⊢
	:
59	theorem		⊢
	proveit.numbers.absolute_value.abs_even
60	instantiation	78, 79, 80, 143, 144, 165, 106*, 107*	⊢
	: , :
61	axiom		⊢
	proveit.logic.equality.substitution
62	instantiation	91, 136, 181, 139, 90, 140, 143, 144, 112	⊢
	: , : , : , : , : , :
63	theorem		⊢
	proveit.numbers.division.frac_cancel_left
64	instantiation	179, 82, 81	⊢
	: , : , :
65	instantiation	179, 82, 83	⊢
	: , : , :
66	instantiation	179, 173, 84	⊢
	: , : , :
67	instantiation	85, 143	⊢
	:
68	instantiation	95, 86	⊢
	:
69	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
70	instantiation	87	⊢
	: , : , : , :
71	instantiation	122, 88, 89	⊢
	: , : , :
72	instantiation	109, 139, 136, 181, 140, 90, 145, 143, 144, 112	⊢
	: , : , : , : , : , : , :
73	instantiation	91, 136, 110, 139, 92, 140, 143, 145, 144, 112	⊢
	: , : , : , : , : , :
74	instantiation	179, 173, 93	⊢
	: , : , :
75	instantiation	138, 139, 181, 136, 140, 94, 145, 144, 112	⊢
	: , : , : , : , : , :
76	theorem		⊢
	proveit.numbers.addition.elim_zero_left
77	instantiation	95, 96	⊢
	:
78	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
79	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
80	instantiation	129	⊢
	: , : , :
81	instantiation	179, 98, 97	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
83	instantiation	179, 98, 99	⊢
	: , : , :
84	instantiation	179, 169, 100	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
86	instantiation	114, 101, 102	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
88	instantiation	103, 110, 104, 105, 106, 107, 108	⊢
	: , : , : , :
89	instantiation	109, 139, 110, 140, 111, 143, 144, 112, 145	⊢
	: , : , : , : , : , : , :
90	instantiation	152	⊢
	: , :
91	theorem		⊢
	proveit.numbers.multiplication.association
92	instantiation	129	⊢
	: , : , :
93	instantiation	158, 113, 130	⊢
	: , :
94	instantiation	152	⊢
	: , :
95	theorem		⊢
	proveit.numbers.negation.complex_closure
96	instantiation	114, 115, 116	⊢
	: , : , :
97	instantiation	179, 118, 117	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
99	instantiation	179, 118, 119	⊢
	: , : , :
100	instantiation	120, 170, 150	⊢
	: , :
101	instantiation	179, 173, 121	⊢
	: , : , :
102	instantiation	122, 123, 124	⊢
	: , : , :
103	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
104	instantiation	129	⊢
	: , : , :
105	instantiation	129	⊢
	: , : , :
106	instantiation	127, 125	⊢
	:
107	instantiation	127, 126	⊢
	:
108	instantiation	127, 128	⊢
	:
109	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
110	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
111	instantiation	129	⊢
	: , : , :
112	instantiation	179, 173, 130	⊢
	: , : , :
113	instantiation	158, 153, 160	⊢
	: , :
114	theorem		⊢
	proveit.logic.equality.sub_right_side_into
115	instantiation	179, 173, 131	⊢
	: , : , :
116	instantiation	138, 139, 181, 136, 140, 141, 143, 144, 165	⊢
	: , : , : , : , : , :
117	instantiation	179, 133, 132	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
119	instantiation	179, 133, 134	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
121	instantiation	158, 151, 135	⊢
	: , :
122	axiom		⊢
	proveit.logic.equality.equals_transitivity
123	instantiation	138, 136, 181, 139, 142, 140, 137, 165, 145	⊢
	: , : , : , : , : , :
124	instantiation	138, 139, 181, 140, 141, 142, 143, 144, 165, 145	⊢
	: , : , : , : , : , :
125	instantiation	146, 181	⊢
	:
126	instantiation	148, 147	⊢
	: , :
127	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
128	instantiation	148, 149	⊢
	: , :
129	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
130	instantiation	179, 169, 150	⊢
	: , : , :
131	instantiation	158, 151, 174	⊢
	: , :
132	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
133	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
134	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
135	instantiation	158, 174, 153	⊢
	: , :
136	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
137	instantiation	179, 173, 151	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.multiplication.disassociation
139	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
140	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
141	instantiation	152	⊢
	: , :
142	instantiation	152	⊢
	: , :
143	instantiation	179, 173, 159	⊢
	: , : , :
144	instantiation	179, 173, 160	⊢
	: , : , :
145	instantiation	179, 173, 153	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
147	instantiation	154, 170	⊢
	:
148	theorem		⊢
	proveit.numbers.ordering.relax_less
149	instantiation	155, 163	⊢
	:
150	instantiation	156, 157	⊢
	:
151	instantiation	158, 159, 160	⊢
	: , :
152	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
153	instantiation	161, 162, 163	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
155	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
156	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
157	instantiation	164, 165, 166	⊢
	:
158	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
159	instantiation	179, 167, 168	⊢
	: , : , :
160	instantiation	179, 169, 170	⊢
	: , : , :
161	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
162	instantiation	171, 172	⊢
	: , :
163	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
164	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
165	instantiation	179, 173, 174	⊢
	: , : , :
166	assumption		⊢
167	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
168	instantiation	179, 175, 176	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
170	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
171	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
172	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
173	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
174	instantiation	177, 178	⊢
	:
175	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
176	instantiation	179, 180, 181	⊢
	: , : , :
177	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
178	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
179	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
180	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
181	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements