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	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	4, 5, 177, 6	,  ⊢
	: , :
3	instantiation	106, 7, 8, 9	⊢
	: , : , : , :
4	theorem		⊢
	proveit.physics.quantum.QPE._non_int_delta_b_diff
5	instantiation	10, 96, 200, 97	⊢
	: , : , : , : , :
6	assumption		⊢
7	instantiation	37, 11, 12, 13, 14*	⊢
	: , :
8	instantiation	161	⊢
	:
9	instantiation	15, 16	⊢
	: , :
10	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
11	instantiation	103, 17, 18	⊢
	: , : , :
12	instantiation	203, 181, 30	⊢
	: , : , :
13	instantiation	19, 202, 25, 124, 20	⊢
	: , :
14	instantiation	155, 21, 22	⊢
	: , : , :
15	theorem		⊢
	proveit.logic.equality.equals_reversal
16	instantiation	166, 23	⊢
	: , : , :
17	instantiation	203, 181, 24	⊢
	: , : , :
18	instantiation	94, 96, 202, 200, 97, 25, 175, 136, 76	⊢
	: , : , : , : , : , :
19	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
20	instantiation	203, 140, 115	⊢
	: , : , :
21	instantiation	166, 26	⊢
	: , : , :
22	instantiation	155, 27, 28	⊢
	: , : , :
23	instantiation	166, 29	⊢
	: , : , :
24	instantiation	145, 30, 89	⊢
	: , :
25	instantiation	119	⊢
	: , :
26	instantiation	31, 175, 136, 110, 84, 91, 32*	⊢
	: , : , :
27	instantiation	155, 33, 34	⊢
	: , : , :
28	instantiation	155, 35, 36	⊢
	: , : , :
29	instantiation	37, 99, 38, 39, 40*	⊢
	: , :
30	instantiation	145, 182, 151	⊢
	: , :
31	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
32	instantiation	41, 124, 173, 42*	⊢
	: , :
33	instantiation	155, 43, 44	⊢
	: , : , :
34	instantiation	155, 45, 46	⊢
	: , : , :
35	instantiation	95, 96, 67, 97, 69, 136, 76, 75	⊢
	: , : , : , :
36	instantiation	155, 47, 48	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.division.div_as_mult
38	instantiation	203, 181, 49	⊢
	: , : , :
39	instantiation	102, 63	⊢
	:
40	instantiation	50, 175, 101, 110, 84, 51*	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
42	instantiation	116, 175	⊢
	:
43	instantiation	94, 96, 67, 200, 97, 54, 175, 136, 76, 52	⊢
	: , : , : , : , : , :
44	instantiation	94, 67, 202, 96, 54, 53, 97, 175, 136, 76, 70, 75	⊢
	: , : , : , : , : , :
45	instantiation	72, 96, 67, 200, 97, 54, 175, 136, 76, 70, 75	⊢
	: , : , : , : , : , : , :
46	instantiation	155, 55, 56	⊢
	: , : , :
47	instantiation	155, 57, 58	⊢
	: , : , :
48	instantiation	59, 200, 96, 97, 149, 78, 60, 61*, 62*	⊢
	: , : , : , : , : , :
49	instantiation	120, 121, 63	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
51	instantiation	64, 81, 149, 65*	⊢
	: , :
52	instantiation	66, 70, 75	⊢
	: , :
53	instantiation	119	⊢
	: , :
54	instantiation	82	⊢
	: , : , :
55	instantiation	73, 96, 202, 67, 97, 68, 69, 70, 175, 136, 76, 75	⊢
	: , : , : , : , : , :
56	instantiation	166, 71	⊢
	: , : , :
57	instantiation	72, 200, 96, 97, 136, 76, 75	⊢
	: , : , : , : , : , : , :
58	instantiation	73, 96, 202, 200, 97, 74, 136, 75, 76, 77*	⊢
	: , : , : , : , : , :
59	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
60	instantiation	203, 181, 132	⊢
	: , : , :
61	instantiation	165, 78	⊢
	:
62	instantiation	155, 79, 80	⊢
	: , : , :
63	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
64	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
65	instantiation	174, 81	⊢
	:
66	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
68	instantiation	119	⊢
	: , :
69	instantiation	82	⊢
	: , : , :
70	instantiation	83, 149, 175, 84	⊢
	: , :
71	instantiation	103, 85, 86	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
73	theorem		⊢
	proveit.numbers.multiplication.association
74	instantiation	119	⊢
	: , :
75	instantiation	87, 136, 88	⊢
	: , :
76	instantiation	203, 181, 89	⊢
	: , : , :
77	instantiation	90, 136, 160, 110, 91, 92*, 93*	⊢
	: , : , :
78	instantiation	203, 181, 112	⊢
	: , : , :
79	instantiation	94, 200, 202, 96, 98, 97, 149, 99, 100	⊢
	: , : , : , : , : , :
80	instantiation	95, 96, 202, 97, 98, 99, 100	⊢
	: , : , : , :
81	instantiation	203, 181, 101	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
83	theorem		⊢
	proveit.numbers.division.div_complex_closure
84	instantiation	102, 194	⊢
	:
85	instantiation	103, 104, 105	⊢
	: , : , :
86	instantiation	106, 107, 108, 109	⊢
	: , : , : , :
87	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
88	instantiation	203, 181, 110	⊢
	: , : , :
89	instantiation	111, 112, 113	⊢
	: , :
90	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
91	instantiation	114, 115	⊢
	:
92	instantiation	116, 136	⊢
	:
93	instantiation	155, 117, 118	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.multiplication.disassociation
95	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
96	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
97	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
98	instantiation	119	⊢
	: , :
99	instantiation	203, 181, 146	⊢
	: , : , :
100	instantiation	203, 181, 147	⊢
	: , : , :
101	instantiation	120, 121, 195	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
103	theorem		⊢
	proveit.logic.equality.sub_right_side_into
104	instantiation	122, 149, 123, 124	⊢
	: , : , : , : , :
105	instantiation	155, 125, 126	⊢
	: , : , :
106	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
107	instantiation	166, 127	⊢
	: , : , :
108	instantiation	166, 127	⊢
	: , : , :
109	instantiation	174, 149	⊢
	:
110	instantiation	203, 188, 128	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
112	instantiation	129, 130	⊢
	:
113	instantiation	131, 132	⊢
	:
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
115	instantiation	203, 133, 163	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
117	instantiation	166, 134	⊢
	: , : , :
118	instantiation	135, 136	⊢
	:
119	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
120	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
121	instantiation	137, 138	⊢
	: , :
122	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
123	instantiation	203, 140, 139	⊢
	: , : , :
124	instantiation	203, 140, 141	⊢
	: , : , :
125	instantiation	166, 142	⊢
	: , : , :
126	instantiation	166, 143	⊢
	: , : , :
127	instantiation	168, 149	⊢
	:
128	instantiation	203, 196, 144	⊢
	: , : , :
129	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
130	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
131	theorem		⊢
	proveit.numbers.negation.real_closure
132	instantiation	145, 146, 147	⊢
	: , :
133	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
134	instantiation	148, 149, 150	⊢
	: , :
135	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
136	instantiation	203, 181, 151	⊢
	: , : , :
137	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
138	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
139	instantiation	203, 153, 152	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
141	instantiation	203, 153, 179	⊢
	: , : , :
142	instantiation	166, 154	⊢
	: , : , :
143	instantiation	155, 156, 157	⊢
	: , : , :
144	instantiation	198, 192	⊢
	:
145	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
146	instantiation	203, 188, 158	⊢
	: , : , :
147	instantiation	203, 188, 159	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
149	instantiation	203, 181, 160	⊢
	: , : , :
150	instantiation	161	⊢
	:
151	instantiation	203, 162, 163	⊢
	: , : , :
152	instantiation	203, 185, 164	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
154	instantiation	165, 175	⊢
	:
155	axiom		⊢
	proveit.logic.equality.equals_transitivity
156	instantiation	166, 167	⊢
	: , : , :
157	instantiation	168, 175	⊢
	:
158	instantiation	203, 196, 169	⊢
	: , : , :
159	instantiation	203, 170, 171	⊢
	: , : , :
160	instantiation	203, 188, 172	⊢
	: , : , :
161	axiom		⊢
	proveit.logic.equality.equals_reflexivity
162	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
163	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
164	instantiation	203, 193, 173	⊢
	: , : , :
165	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
166	axiom		⊢
	proveit.logic.equality.substitution
167	instantiation	174, 175	⊢
	:
168	theorem		⊢
	proveit.numbers.division.frac_one_denom
169	instantiation	203, 176, 177	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
171	instantiation	178, 179, 180	⊢
	: , :
172	instantiation	203, 196, 192	⊢
	: , : , :
173	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
174	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
175	instantiation	203, 181, 182	⊢
	: , : , :
176	instantiation	183, 184, 199	⊢
	: , :
177	assumption		⊢
178	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
179	instantiation	203, 185, 186	⊢
	: , : , :
180	instantiation	198, 187	⊢
	:
181	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
182	instantiation	203, 188, 189	⊢
	: , : , :
183	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
184	instantiation	190, 191, 192	⊢
	: , :
185	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
186	instantiation	203, 193, 194	⊢
	: , : , :
187	instantiation	203, 204, 195	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
189	instantiation	203, 196, 197	⊢
	: , : , :
190	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
191	instantiation	198, 199	⊢
	:
192	instantiation	203, 201, 200	⊢
	: , : , :
193	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
194	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
195	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
196	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
197	instantiation	203, 201, 202	⊢
	: , : , :
198	theorem		⊢
	proveit.numbers.negation.int_closure
199	instantiation	203, 204, 205	⊢
	: , : , :
200	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
201	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
202	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
203	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
204	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
205	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements