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	⊢
	: , :
1	reference	93	⊢
2	instantiation	3, 4, 5	⊢
	: , : , :
3	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
4	instantiation	6, 7, 11, 8	⊢
	: , : , :
5	instantiation	104, 9, 10	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
7	instantiation	21, 11	⊢
	:
8	instantiation	12, 13, 82, 81, 14, 15*, 16*, 26*	⊢
	: , : , : , :
9	instantiation	104, 17, 38	⊢
	: , : , :
10	instantiation	179, 18, 19	⊢
	: , : , :
11	instantiation	207, 193, 20	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rescale_interval_co_membership
13	instantiation	21, 82	⊢
	:
14	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
15	instantiation	107, 22, 23, 24	⊢
	: , : , : , :
16	instantiation	25, 56, 57, 26*	⊢
	: , :
17	instantiation	93, 27	⊢
	: , :
18	instantiation	190, 28	⊢
	: , : , :
19	instantiation	29, 202, 196, 30*	⊢
	: , : , : , :
20	instantiation	115, 194, 31, 32	⊢
	: , :
21	theorem		⊢
	proveit.numbers.negation.real_closure
22	instantiation	33, 209, 203, 50, 34, 51, 56, 200, 53	⊢
	: , : , : , : , : , :
23	instantiation	179, 35, 36	⊢
	: , : , :
24	instantiation	189, 53	⊢
	:
25	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
26	instantiation	179, 37, 38	⊢
	: , : , :
27	instantiation	39, 40, 41, 42, 43, 44	⊢
	: , : , :
28	instantiation	58, 167, 74, 110*, 45*	⊢
	: , : , : , :
29	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
30	instantiation	179, 46, 47	⊢
	: , : , :
31	instantiation	207, 201, 48	⊢
	: , : , :
32	instantiation	147, 77	⊢
	:
33	theorem		⊢
	proveit.numbers.multiplication.disassociation
34	instantiation	155	⊢
	: , :
35	instantiation	49, 50, 203, 209, 51, 52, 56, 200, 53	⊢
	: , : , : , : , : , :
36	instantiation	190, 54	⊢
	: , : , :
37	instantiation	55, 56, 57	⊢
	: , :
38	instantiation	58, 167, 74, 141, 110*, 59*	⊢
	: , : , : , :
39	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
40	instantiation	207, 193, 60	⊢
	: , : , :
41	instantiation	61, 64	⊢
	: , :
42	instantiation	207, 193, 62	⊢
	: , : , :
43	instantiation	63, 64, 65, 66, 67	⊢
	: , : , :
44	instantiation	127, 85	⊢
	:
45	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
46	instantiation	129, 203, 68, 69, 70, 71	⊢
	: , : , : , :
47	instantiation	72, 73, 74, 167, 75*, 76*	⊢
	: , : , :
48	instantiation	207, 168, 77	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.multiplication.association
50	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
51	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
52	instantiation	155	⊢
	: , :
53	instantiation	207, 205, 78	⊢
	: , : , :
54	instantiation	104, 79, 80	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.multiplication.commutation
56	instantiation	207, 205, 81	⊢
	: , : , :
57	instantiation	207, 205, 82	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.division.prod_of_fracs
59	instantiation	83, 151, 197, 161, 126*	⊢
	: , : , :
60	instantiation	84, 86, 87	⊢
	: , :
61	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
62	instantiation	207, 114, 85	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
64	instantiation	207, 193, 86	⊢
	: , : , :
65	instantiation	207, 193, 87	⊢
	: , : , :
66	instantiation	88, 89, 90, 91, 92	⊢
	: , : , :
67	instantiation	93, 94	⊢
	: , :
68	instantiation	155	⊢
	: , :
69	instantiation	155	⊢
	: , :
70	instantiation	179, 95, 96	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_4
72	theorem		⊢
	proveit.numbers.division.frac_cancel_left
73	instantiation	207, 163, 97	⊢
	: , : , :
74	instantiation	207, 163, 98	⊢
	: , : , :
75	instantiation	199, 99	⊢
	:
76	theorem		⊢
	proveit.numbers.numerals.decimals.mult_8_2
77	instantiation	100, 203, 101	⊢
	: , :
78	instantiation	102, 103	⊢
	:
79	instantiation	104, 105, 106	⊢
	: , : , :
80	instantiation	107, 108, 109, 110	⊢
	: , : , : , :
81	instantiation	111, 182, 206, 117	⊢
	: , :
82	instantiation	111, 182, 169, 112	⊢
	: , :
83	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
84	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
85	instantiation	152, 153, 113	⊢
	: , :
86	instantiation	207, 114, 128	⊢
	: , : , :
87	instantiation	115, 194, 116, 117	⊢
	: , :
88	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
89	instantiation	207, 118, 119	⊢
	: , : , :
90	instantiation	207, 120, 154	⊢
	: , : , :
91	instantiation	207, 120, 121	⊢
	: , : , :
92	instantiation	122, 169, 182, 123, 124, 125, 126*	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.ordering.relax_less
94	instantiation	127, 128	⊢
	:
95	instantiation	129, 203, 130, 131, 132, 133	⊢
	: , : , : , :
96	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_4
97	instantiation	207, 176, 134	⊢
	: , : , :
98	instantiation	207, 176, 135	⊢
	: , : , :
99	instantiation	207, 205, 136	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
101	instantiation	137, 209, 138	⊢
	: , :
102	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
103	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
104	theorem		⊢
	proveit.logic.equality.sub_right_side_into
105	instantiation	139, 167, 140, 141	⊢
	: , : , : , : , :
106	instantiation	179, 142, 143	⊢
	: , : , :
107	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
108	instantiation	190, 144	⊢
	: , : , :
109	instantiation	190, 144	⊢
	: , : , :
110	instantiation	199, 167	⊢
	:
111	theorem		⊢
	proveit.numbers.division.div_real_closure
112	instantiation	147, 173	⊢
	:
113	instantiation	207, 170, 145	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
115	theorem		⊢
	proveit.numbers.division.div_rational_closure
116	instantiation	207, 201, 146	⊢
	: , : , :
117	instantiation	147, 212	⊢
	:
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
119	instantiation	207, 148, 209	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
121	instantiation	207, 170, 212	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
123	instantiation	210, 211, 161	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
125	instantiation	149, 161	⊢
	:
126	instantiation	150, 151	⊢
	:
127	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
128	instantiation	152, 153, 154	⊢
	: , :
129	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
130	instantiation	155	⊢
	: , :
131	instantiation	155	⊢
	: , :
132	instantiation	189, 156	⊢
	:
133	instantiation	199, 156	⊢
	:
134	instantiation	207, 187, 157	⊢
	: , : , :
135	instantiation	207, 187, 158	⊢
	: , : , :
136	instantiation	207, 193, 159	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
138	instantiation	207, 160, 161	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
140	instantiation	207, 163, 162	⊢
	: , : , :
141	instantiation	207, 163, 164	⊢
	: , : , :
142	instantiation	190, 165	⊢
	: , : , :
143	instantiation	190, 166	⊢
	: , : , :
144	instantiation	192, 167	⊢
	:
145	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
146	instantiation	207, 168, 212	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
148	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
149	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
150	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
151	instantiation	207, 205, 169	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
153	instantiation	207, 170, 197	⊢
	: , : , :
154	instantiation	207, 170, 173	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
156	instantiation	207, 205, 171	⊢
	: , : , :
157	instantiation	207, 198, 172	⊢
	: , : , :
158	instantiation	207, 198, 173	⊢
	: , : , :
159	instantiation	207, 201, 174	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
161	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
162	instantiation	207, 176, 175	⊢
	: , : , :
163	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
164	instantiation	207, 176, 177	⊢
	: , : , :
165	instantiation	190, 178	⊢
	: , : , :
166	instantiation	179, 180, 181	⊢
	: , : , :
167	instantiation	207, 205, 182	⊢
	: , : , :
168	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
169	instantiation	207, 193, 183	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
171	instantiation	207, 193, 184	⊢
	: , : , :
172	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
173	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
174	instantiation	207, 208, 185	⊢
	: , : , :
175	instantiation	207, 187, 186	⊢
	: , : , :
176	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
177	instantiation	207, 187, 188	⊢
	: , : , :
178	instantiation	189, 200	⊢
	:
179	axiom		⊢
	proveit.logic.equality.equals_transitivity
180	instantiation	190, 191	⊢
	: , : , :
181	instantiation	192, 200	⊢
	:
182	instantiation	207, 193, 194	⊢
	: , : , :
183	instantiation	207, 201, 195	⊢
	: , : , :
184	instantiation	207, 201, 196	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
186	instantiation	207, 198, 197	⊢
	: , : , :
187	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
188	instantiation	207, 198, 212	⊢
	: , : , :
189	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
190	axiom		⊢
	proveit.logic.equality.substitution
191	instantiation	199, 200	⊢
	:
192	theorem		⊢
	proveit.numbers.division.frac_one_denom
193	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
194	instantiation	207, 201, 202	⊢
	: , : , :
195	instantiation	207, 208, 203	⊢
	: , : , :
196	instantiation	207, 208, 204	⊢
	: , : , :
197	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
198	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
199	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
200	instantiation	207, 205, 206	⊢
	: , : , :
201	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
202	instantiation	207, 208, 209	⊢
	: , : , :
203	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
204	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
205	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
206	instantiation	210, 211, 212	⊢
	: , : , :
207	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
208	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
209	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
210	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
211	instantiation	213, 214	⊢
	: , :
212	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
213	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
214	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements