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*	,  ⊢
	: , :
1	reference	103	⊢
2	reference	117	⊢
3	instantiation	52, 6, 7	⊢
	: , : , :
4	instantiation	8, 27, 23, 49, 9, 38	,  ⊢
	: , :
5	instantiation	60, 10, 11	,  ⊢
	: , : , :
6	instantiation	12, 13, 45	⊢
	: , :
7	instantiation	26, 143, 179, 189, 144, 14, 86, 105, 45	⊢
	: , : , : , : , : , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
9	instantiation	190, 87, 15	⊢
	: , : , :
10	instantiation	91, 16	,  ⊢
	: , : , :
11	instantiation	60, 17, 18	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
13	instantiation	190, 154, 19	⊢
	: , : , :
14	instantiation	84	⊢
	: , :
15	instantiation	190, 99, 20	⊢
	: , : , :
16	instantiation	21, 22, 23, 86, 105, 45, 118, 43, 106, 24, 25*, 107*	,  ⊢
	: , : , :
17	instantiation	26, 189, 27, 143, 28, 144, 117, 32, 33, 34	⊢
	: , : , : , : , : , :
18	instantiation	29, 143, 179, 144, 30, 31, 117, 32, 33, 34, 35*	⊢
	: , : , : , : , : , :
19	instantiation	135, 98, 115	⊢
	: , :
20	instantiation	190, 176, 36	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_products
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
23	instantiation	41	⊢
	: , : , :
24	instantiation	37, 38	,  ⊢
	:
25	instantiation	39, 49, 96, 40*	⊢
	: , :
26	theorem		⊢
	proveit.numbers.multiplication.disassociation
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
28	instantiation	41	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.multiplication.association
30	instantiation	84	⊢
	: , :
31	instantiation	84	⊢
	: , :
32	instantiation	42, 133, 86, 43	⊢
	: , :
33	instantiation	190, 154, 137	⊢
	: , : , :
34	instantiation	44, 45, 46	⊢
	: , :
35	instantiation	47, 117, 133, 48, 49, 50*, 51*	⊢
	: , : , : , :
36	instantiation	190, 183, 130	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
38	instantiation	52, 53, 54	,  ⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
40	instantiation	55, 86	⊢
	:
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
42	theorem		⊢
	proveit.numbers.division.div_complex_closure
43	instantiation	162, 97	⊢
	:
44	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
45	instantiation	190, 154, 56	⊢
	: , : , :
46	instantiation	190, 154, 118	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.division.prod_of_fracs
48	instantiation	190, 87, 57	⊢
	: , : , :
49	instantiation	190, 87, 58	⊢
	: , : , :
50	instantiation	59, 117	⊢
	:
51	instantiation	60, 61, 62	⊢
	: , : , :
52	theorem		⊢
	proveit.logic.equality.sub_right_side_into
53	instantiation	190, 87, 63	,  ⊢
	: , : , :
54	instantiation	91, 64	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
56	instantiation	190, 65, 66	⊢
	: , : , :
57	instantiation	190, 99, 67	⊢
	: , : , :
58	instantiation	190, 99, 68	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.division.frac_one_denom
60	axiom		⊢
	proveit.logic.equality.equals_transitivity
61	instantiation	69, 179, 70, 71, 75, 72	⊢
	: , : , : , :
62	instantiation	73, 74, 133, 75*, 76*	⊢
	: , : , :
63	instantiation	190, 77, 78	,  ⊢
	: , : , :
64	instantiation	91, 79	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
66	instantiation	80, 81	⊢
	:
67	instantiation	190, 176, 82	⊢
	: , : , :
68	instantiation	190, 176, 83	⊢
	: , : , :
69	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
70	instantiation	84	⊢
	: , :
71	instantiation	84	⊢
	: , :
72	instantiation	85, 86	⊢
	:
73	theorem		⊢
	proveit.numbers.division.frac_cancel_left
74	instantiation	190, 87, 88	⊢
	: , : , :
75	instantiation	146, 117	⊢
	:
76	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
78	instantiation	89, 90	,  ⊢
	:
79	instantiation	91, 92	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
81	instantiation	93, 94, 95	⊢
	: , :
82	instantiation	190, 183, 96	⊢
	: , : , :
83	instantiation	190, 183, 97	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
85	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
86	instantiation	190, 154, 98	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
88	instantiation	190, 99, 168	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
90	instantiation	100, 101, 102	,  ⊢
	:
91	axiom		⊢
	proveit.logic.equality.substitution
92	instantiation	103, 104, 105, 106, 107*	⊢
	: , :
93	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
94	instantiation	190, 154, 108	⊢
	: , : , :
95	instantiation	109, 110	⊢
	:
96	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
97	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
98	instantiation	190, 160, 111	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
100	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
101	instantiation	190, 154, 112	⊢
	: , : , :
102	instantiation	113, 114	,  ⊢
	: , :
103	theorem		⊢
	proveit.numbers.division.div_as_mult
104	instantiation	190, 154, 136	⊢
	: , : , :
105	instantiation	190, 154, 115	⊢
	: , : , :
106	instantiation	162, 130	⊢
	:
107	instantiation	116, 117, 155, 118, 153, 119*	⊢
	: , : , :
108	instantiation	120, 121	⊢
	:
109	theorem		⊢
	proveit.numbers.negation.complex_closure
110	instantiation	190, 154, 122	⊢
	: , : , :
111	instantiation	190, 170, 123	⊢
	: , : , :
112	instantiation	124, 125, 140, 126	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
114	instantiation	127, 128, 156, 129	,  ⊢
	: , :
115	instantiation	163, 164, 130	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
117	instantiation	190, 154, 152	⊢
	: , : , :
118	instantiation	190, 160, 131	⊢
	: , : , :
119	instantiation	132, 147, 133, 134*	⊢
	: , :
120	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
121	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
122	instantiation	135, 136, 137	⊢
	: , :
123	instantiation	190, 188, 138	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
125	instantiation	139, 140	⊢
	:
126	instantiation	141, 166	⊢
	:
127	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt
128	instantiation	142, 143, 189, 144	⊢
	: , : , : , : , :
129	assumption		⊢
130	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
131	instantiation	190, 170, 145	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
133	instantiation	190, 154, 151	⊢
	: , : , :
134	instantiation	146, 147	⊢
	:
135	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
136	instantiation	190, 160, 148	⊢
	: , : , :
137	instantiation	190, 160, 149	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
139	theorem		⊢
	proveit.numbers.negation.real_closure
140	instantiation	150, 151, 152, 153	⊢
	: , :
141	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
142	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
143	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
144	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
145	instantiation	186, 182	⊢
	:
146	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
147	instantiation	190, 154, 155	⊢
	: , : , :
148	instantiation	190, 170, 156	⊢
	: , : , :
149	instantiation	190, 157, 158	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.division.div_real_closure
151	instantiation	190, 160, 159	⊢
	: , : , :
152	instantiation	190, 160, 161	⊢
	: , : , :
153	instantiation	162, 184	⊢
	:
154	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
155	instantiation	163, 164, 185	⊢
	: , : , :
156	instantiation	190, 165, 166	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
158	instantiation	167, 168, 169	⊢
	: , :
159	instantiation	190, 170, 182	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
161	instantiation	190, 170, 171	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
163	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
164	instantiation	172, 173	⊢
	: , :
165	instantiation	174, 175, 187	⊢
	: , :
166	assumption		⊢
167	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
168	instantiation	190, 176, 177	⊢
	: , : , :
169	instantiation	186, 178	⊢
	:
170	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
171	instantiation	190, 188, 179	⊢
	: , : , :
172	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
173	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
174	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
175	instantiation	180, 181, 182	⊢
	: , :
176	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
177	instantiation	190, 183, 184	⊢
	: , : , :
178	instantiation	190, 191, 185	⊢
	: , : , :
179	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
180	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
181	instantiation	186, 187	⊢
	:
182	instantiation	190, 188, 189	⊢
	: , : , :
183	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
184	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
185	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
186	theorem		⊢
	proveit.numbers.negation.int_closure
187	instantiation	190, 191, 192	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
189	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
190	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
191	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
192	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements