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