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.numbers.ordering.transitivity_less_less_eq
2	instantiation	4, 5, 9, 6	⊢
	: , : , :
3	instantiation	102, 7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
5	instantiation	19, 9	⊢
	:
6	instantiation	10, 11, 80, 79, 12, 13*, 14*, 24*	⊢
	: , : , : , :
7	instantiation	102, 15, 36	⊢
	: , : , :
8	instantiation	177, 16, 17	⊢
	: , : , :
9	instantiation	205, 191, 18	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rescale_interval_co_membership
11	instantiation	19, 80	⊢
	:
12	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
13	instantiation	105, 20, 21, 22	⊢
	: , : , : , :
14	instantiation	23, 54, 55, 24*	⊢
	: , :
15	instantiation	91, 25	⊢
	: , :
16	instantiation	188, 26	⊢
	: , : , :
17	instantiation	27, 200, 194, 28*	⊢
	: , : , : , :
18	instantiation	113, 192, 29, 30	⊢
	: , :
19	theorem		⊢
	proveit.numbers.negation.real_closure
20	instantiation	31, 207, 201, 48, 32, 49, 54, 198, 51	⊢
	: , : , : , : , : , :
21	instantiation	177, 33, 34	⊢
	: , : , :
22	instantiation	187, 51	⊢
	:
23	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
24	instantiation	177, 35, 36	⊢
	: , : , :
25	instantiation	37, 38, 39, 40, 41, 42	⊢
	: , : , :
26	instantiation	56, 165, 72, 108*, 43*	⊢
	: , : , : , :
27	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
28	instantiation	177, 44, 45	⊢
	: , : , :
29	instantiation	205, 199, 46	⊢
	: , : , :
30	instantiation	145, 75	⊢
	:
31	theorem		⊢
	proveit.numbers.multiplication.disassociation
32	instantiation	153	⊢
	: , :
33	instantiation	47, 48, 201, 207, 49, 50, 54, 198, 51	⊢
	: , : , : , : , : , :
34	instantiation	188, 52	⊢
	: , : , :
35	instantiation	53, 54, 55	⊢
	: , :
36	instantiation	56, 165, 72, 139, 108*, 57*	⊢
	: , : , : , :
37	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
38	instantiation	205, 191, 58	⊢
	: , : , :
39	instantiation	59, 62	⊢
	: , :
40	instantiation	205, 191, 60	⊢
	: , : , :
41	instantiation	61, 62, 63, 64, 65	⊢
	: , : , :
42	instantiation	125, 83	⊢
	:
43	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
44	instantiation	127, 201, 66, 67, 68, 69	⊢
	: , : , : , :
45	instantiation	70, 71, 72, 165, 73*, 74*	⊢
	: , : , :
46	instantiation	205, 166, 75	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.multiplication.association
48	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
49	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
50	instantiation	153	⊢
	: , :
51	instantiation	205, 203, 76	⊢
	: , : , :
52	instantiation	102, 77, 78	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.multiplication.commutation
54	instantiation	205, 203, 79	⊢
	: , : , :
55	instantiation	205, 203, 80	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.division.prod_of_fracs
57	instantiation	81, 149, 195, 159, 124*	⊢
	: , : , :
58	instantiation	82, 84, 85	⊢
	: , :
59	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
60	instantiation	205, 112, 83	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
62	instantiation	205, 191, 84	⊢
	: , : , :
63	instantiation	205, 191, 85	⊢
	: , : , :
64	instantiation	86, 87, 88, 89, 90	⊢
	: , : , :
65	instantiation	91, 92	⊢
	: , :
66	instantiation	153	⊢
	: , :
67	instantiation	153	⊢
	: , :
68	instantiation	177, 93, 94	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_4
70	theorem		⊢
	proveit.numbers.division.frac_cancel_left
71	instantiation	205, 161, 95	⊢
	: , : , :
72	instantiation	205, 161, 96	⊢
	: , : , :
73	instantiation	197, 97	⊢
	:
74	theorem		⊢
	proveit.numbers.numerals.decimals.mult_8_2
75	instantiation	98, 201, 99	⊢
	: , :
76	instantiation	100, 101	⊢
	:
77	instantiation	102, 103, 104	⊢
	: , : , :
78	instantiation	105, 106, 107, 108	⊢
	: , : , : , :
79	instantiation	109, 180, 204, 115	⊢
	: , :
80	instantiation	109, 180, 167, 110	⊢
	: , :
81	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
82	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
83	instantiation	150, 151, 111	⊢
	: , :
84	instantiation	205, 112, 126	⊢
	: , : , :
85	instantiation	113, 192, 114, 115	⊢
	: , :
86	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
87	instantiation	205, 116, 117	⊢
	: , : , :
88	instantiation	205, 118, 152	⊢
	: , : , :
89	instantiation	205, 118, 119	⊢
	: , : , :
90	instantiation	120, 167, 180, 121, 122, 123, 124*	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.ordering.relax_less
92	instantiation	125, 126	⊢
	:
93	instantiation	127, 201, 128, 129, 130, 131	⊢
	: , : , : , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_4
95	instantiation	205, 174, 132	⊢
	: , : , :
96	instantiation	205, 174, 133	⊢
	: , : , :
97	instantiation	205, 203, 134	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
99	instantiation	135, 207, 136	⊢
	: , :
100	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
101	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
102	theorem		⊢
	proveit.logic.equality.sub_right_side_into
103	instantiation	137, 165, 138, 139	⊢
	: , : , : , : , :
104	instantiation	177, 140, 141	⊢
	: , : , :
105	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
106	instantiation	188, 142	⊢
	: , : , :
107	instantiation	188, 142	⊢
	: , : , :
108	instantiation	197, 165	⊢
	:
109	theorem		⊢
	proveit.numbers.division.div_real_closure
110	instantiation	145, 171	⊢
	:
111	instantiation	205, 168, 143	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
113	theorem		⊢
	proveit.numbers.division.div_rational_closure
114	instantiation	205, 199, 144	⊢
	: , : , :
115	instantiation	145, 210	⊢
	:
116	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
117	instantiation	205, 146, 207	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
119	instantiation	205, 168, 210	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
121	instantiation	208, 209, 159	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
123	instantiation	147, 159	⊢
	:
124	instantiation	148, 149	⊢
	:
125	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
126	instantiation	150, 151, 152	⊢
	: , :
127	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
128	instantiation	153	⊢
	: , :
129	instantiation	153	⊢
	: , :
130	instantiation	187, 154	⊢
	:
131	instantiation	197, 154	⊢
	:
132	instantiation	205, 185, 155	⊢
	: , : , :
133	instantiation	205, 185, 156	⊢
	: , : , :
134	instantiation	205, 191, 157	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
136	instantiation	205, 158, 159	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
138	instantiation	205, 161, 160	⊢
	: , : , :
139	instantiation	205, 161, 162	⊢
	: , : , :
140	instantiation	188, 163	⊢
	: , : , :
141	instantiation	188, 164	⊢
	: , : , :
142	instantiation	190, 165	⊢
	:
143	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
144	instantiation	205, 166, 210	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
146	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
147	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
148	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
149	instantiation	205, 203, 167	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
151	instantiation	205, 168, 195	⊢
	: , : , :
152	instantiation	205, 168, 171	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
154	instantiation	205, 203, 169	⊢
	: , : , :
155	instantiation	205, 196, 170	⊢
	: , : , :
156	instantiation	205, 196, 171	⊢
	: , : , :
157	instantiation	205, 199, 172	⊢
	: , : , :
158	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
159	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
160	instantiation	205, 174, 173	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
162	instantiation	205, 174, 175	⊢
	: , : , :
163	instantiation	188, 176	⊢
	: , : , :
164	instantiation	177, 178, 179	⊢
	: , : , :
165	instantiation	205, 203, 180	⊢
	: , : , :
166	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
167	instantiation	205, 191, 181	⊢
	: , : , :
168	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
169	instantiation	205, 191, 182	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
171	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
172	instantiation	205, 206, 183	⊢
	: , : , :
173	instantiation	205, 185, 184	⊢
	: , : , :
174	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
175	instantiation	205, 185, 186	⊢
	: , : , :
176	instantiation	187, 198	⊢
	:
177	axiom		⊢
	proveit.logic.equality.equals_transitivity
178	instantiation	188, 189	⊢
	: , : , :
179	instantiation	190, 198	⊢
	:
180	instantiation	205, 191, 192	⊢
	: , : , :
181	instantiation	205, 199, 193	⊢
	: , : , :
182	instantiation	205, 199, 194	⊢
	: , : , :
183	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
184	instantiation	205, 196, 195	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
186	instantiation	205, 196, 210	⊢
	: , : , :
187	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
188	axiom		⊢
	proveit.logic.equality.substitution
189	instantiation	197, 198	⊢
	:
190	theorem		⊢
	proveit.numbers.division.frac_one_denom
191	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
192	instantiation	205, 199, 200	⊢
	: , : , :
193	instantiation	205, 206, 201	⊢
	: , : , :
194	instantiation	205, 206, 202	⊢
	: , : , :
195	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
196	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
197	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
198	instantiation	205, 203, 204	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
200	instantiation	205, 206, 207	⊢
	: , : , :
201	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
202	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
203	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
204	instantiation	208, 209, 210	⊢
	: , : , :
205	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
206	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
207	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
208	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
209	instantiation	211, 212	⊢
	: , :
210	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
211	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
212	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements