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	generalization	1	⊢
1	instantiation	2, 3, 6, 4, 5	⊢
	: , : , :
2	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalCO
3	instantiation	170, 6	⊢
	:
4	instantiation	102, 79, 7	⊢
	: , :
5	instantiation	8, 9, 10	⊢
	: , :
6	instantiation	16, 138, 152, 100	⊢
	: , :
7	instantiation	170, 11	⊢
	:
8	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
9	instantiation	13, 12, 15	⊢
	: , : , :
10	instantiation	13, 14, 15	⊢
	: , : , :
11	instantiation	16, 118, 96, 43	⊢
	: , :
12	instantiation	17, 96, 137, 21, 18, 23, 19*	⊢
	: , : , :
13	theorem		⊢
	proveit.logic.equality.sub_right_side_into
14	instantiation	20, 96, 21, 157, 22, 23, 31*	⊢
	: , : , :
15	instantiation	24, 25, 106, 78, 43, 26*	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.division.div_real_closure
17	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
18	instantiation	27, 28, 29	⊢
	: , : , :
19	instantiation	30, 140, 78, 43, 31*	⊢
	: , :
20	theorem		⊢
	proveit.numbers.division.strong_div_from_numer_bound__pos_denom
21	instantiation	102, 46, 49	⊢
	: , :
22	instantiation	32, 33, 34	⊢
	: , : , :
23	instantiation	35, 125	⊢
	:
24	theorem		⊢
	proveit.numbers.division.distribute_frac_through_subtract
25	instantiation	199, 160, 46	⊢
	: , : , :
26	instantiation	127, 36, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
28	instantiation	48, 67, 137, 49, 38, 39*	⊢
	: , : , :
29	instantiation	40, 49, 67, 46, 41	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
31	instantiation	42, 140, 78, 43, 44*	⊢
	: , :
32	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
33	instantiation	45, 49, 46, 138, 47	⊢
	: , : , :
34	instantiation	48, 138, 49, 50, 51, 52*	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
36	instantiation	53, 54, 55, 58, 56*	⊢
	: , : , :
37	instantiation	57, 58	⊢
	:
38	instantiation	69, 161, 118, 157, 59, 71, 60*, 72*	⊢
	: , : , :
39	instantiation	61, 122	⊢
	:
40	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
41	instantiation	62, 67, 138, 68	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.division.div_as_mult
43	instantiation	111, 125	⊢
	:
44	instantiation	127, 63, 64	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
46	instantiation	65, 67, 138, 68	⊢
	: , : , :
47	instantiation	66, 67, 138, 68	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
49	instantiation	170, 118	⊢
	:
50	instantiation	102, 157, 161	⊢
	: , :
51	instantiation	69, 161, 154, 118, 70, 71, 72*, 73*	⊢
	: , : , :
52	instantiation	127, 74, 75	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.division.frac_cancel_left
54	instantiation	199, 130, 76	⊢
	: , : , :
55	instantiation	199, 130, 77	⊢
	: , : , :
56	instantiation	126, 78	⊢
	:
57	theorem		⊢
	proveit.numbers.division.frac_one_denom
58	instantiation	199, 160, 79	⊢
	: , : , :
59	instantiation	80, 179, 194, 167	⊢
	: , : , :
60	instantiation	90, 123, 140, 81*	⊢
	: , :
61	theorem		⊢
	proveit.numbers.addition.elim_zero_left
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
63	instantiation	119, 82	⊢
	: , : , :
64	instantiation	83, 133, 84, 159, 100, 85*	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
68	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
69	theorem		⊢
	proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound
70	instantiation	86, 179, 194, 167	⊢
	: , : , :
71	instantiation	87, 88	⊢
	: , :
72	instantiation	90, 123, 106, 89*	⊢
	: , :
73	instantiation	90, 123, 136, 91*	⊢
	: , :
74	instantiation	141, 196, 185, 142, 92, 143, 123, 140, 148	⊢
	: , : , : , : , : , :
75	instantiation	146, 123, 140, 93	⊢
	: , : , :
76	instantiation	199, 150, 94	⊢
	: , : , :
77	instantiation	199, 150, 95	⊢
	: , : , :
78	instantiation	199, 160, 96	⊢
	: , : , :
79	instantiation	97, 98	⊢
	:
80	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
81	instantiation	135, 140	⊢
	:
82	instantiation	99, 133, 171, 161, 100, 101*	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
84	instantiation	102, 171, 161	⊢
	: , :
85	instantiation	127, 103, 104	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
87	theorem		⊢
	proveit.numbers.ordering.relax_less
88	instantiation	105, 192	⊢
	:
89	instantiation	135, 106	⊢
	:
90	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
91	instantiation	127, 107, 108	⊢
	: , : , :
92	instantiation	158	⊢
	: , :
93	instantiation	162	⊢
	:
94	instantiation	199, 163, 109	⊢
	: , : , :
95	instantiation	199, 163, 110	⊢
	: , : , :
96	instantiation	180, 181, 125	⊢
	: , : , :
97	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
98	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
99	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
100	instantiation	111, 175	⊢
	:
101	instantiation	112, 147, 123, 113*	⊢
	: , :
102	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
103	instantiation	119, 114	⊢
	: , : , :
104	instantiation	115, 116, 198, 117*	⊢
	: , :
105	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
106	instantiation	199, 160, 118	⊢
	: , : , :
107	instantiation	119, 120	⊢
	: , : , :
108	instantiation	121, 122, 123, 124*	⊢
	: , :
109	instantiation	199, 174, 125	⊢
	: , : , :
110	instantiation	199, 174, 198	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
112	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
113	instantiation	126, 147	⊢
	:
114	instantiation	127, 128, 129	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
116	instantiation	199, 130, 131	⊢
	: , : , :
117	instantiation	132, 133	⊢
	:
118	instantiation	199, 168, 134	⊢
	: , : , :
119	axiom		⊢
	proveit.logic.equality.substitution
120	instantiation	135, 136	⊢
	:
121	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
122	instantiation	199, 160, 137	⊢
	: , : , :
123	instantiation	199, 160, 138	⊢
	: , : , :
124	instantiation	139, 140	⊢
	:
125	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
126	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
127	axiom		⊢
	proveit.logic.equality.equals_transitivity
128	instantiation	141, 142, 185, 196, 143, 144, 147, 148, 145	⊢
	: , : , : , : , : , :
129	instantiation	146, 147, 148, 149	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
131	instantiation	199, 150, 151	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
133	instantiation	199, 160, 152	⊢
	: , : , :
134	instantiation	199, 178, 153	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
136	instantiation	199, 160, 154	⊢
	: , : , :
137	instantiation	199, 168, 155	⊢
	: , : , :
138	instantiation	199, 168, 156	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.negation.double_negation
140	instantiation	199, 160, 157	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.addition.disassociation
142	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
143	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
144	instantiation	158	⊢
	: , :
145	instantiation	199, 160, 159	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
147	instantiation	199, 160, 171	⊢
	: , : , :
148	instantiation	199, 160, 161	⊢
	: , : , :
149	instantiation	162	⊢
	:
150	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
151	instantiation	199, 163, 164	⊢
	: , : , :
152	instantiation	199, 168, 165	⊢
	: , : , :
153	instantiation	199, 166, 167	⊢
	: , : , :
154	instantiation	199, 168, 169	⊢
	: , : , :
155	instantiation	199, 178, 187	⊢
	: , : , :
156	instantiation	199, 178, 188	⊢
	: , : , :
157	instantiation	180, 181, 201	⊢
	: , : , :
158	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
159	instantiation	170, 171	⊢
	:
160	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
161	instantiation	199, 172, 173	⊢
	: , : , :
162	axiom		⊢
	proveit.logic.equality.equals_reflexivity
163	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
164	instantiation	199, 174, 175	⊢
	: , : , :
165	instantiation	199, 178, 176	⊢
	: , : , :
166	instantiation	177, 179, 194	⊢
	: , :
167	assumption		⊢
168	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
169	instantiation	199, 178, 179	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.negation.real_closure
171	instantiation	180, 181, 182	⊢
	: , : , :
172	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
173	instantiation	199, 183, 184	⊢
	: , : , :
174	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
175	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
176	instantiation	199, 195, 185	⊢
	: , : , :
177	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
178	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
179	instantiation	186, 187, 188	⊢
	: , :
180	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
181	instantiation	189, 190	⊢
	: , :
182	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
183	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
184	instantiation	199, 191, 192	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
186	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
187	instantiation	193, 194	⊢
	:
188	instantiation	199, 195, 196	⊢
	: , : , :
189	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
190	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
191	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
192	instantiation	197, 198	⊢
	:
193	theorem		⊢
	proveit.numbers.negation.int_closure
194	instantiation	199, 200, 201	⊢
	: , : , :
195	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
196	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
197	theorem		⊢
	proveit.numbers.negation.int_neg_closure
198	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
199	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
200	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
201	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements