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