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