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, 4, 5	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOC
2	reference	50	⊢
3	reference	18	⊢
4	reference	104	⊢
5	instantiation	6, 7, 8	⊢
	: , :
6	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
7	instantiation	9, 50, 54, 10, 11, 12*, 13*	⊢
	: , : , :
8	instantiation	14, 15	⊢
	: , :
9	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
10	instantiation	16, 104, 18	⊢
	: , :
11	instantiation	17, 54, 104, 18, 19, 20	⊢
	: , : , :
12	instantiation	112, 21, 22	⊢
	: , : , :
13	instantiation	137, 23, 24	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.ordering.relax_less
15	instantiation	25, 26, 27	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
17	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
18	instantiation	158, 148, 28	⊢
	: , : , :
19	instantiation	29, 54, 41, 42	⊢
	: , : , :
20	instantiation	30, 49	⊢
	:
21	instantiation	31, 36	⊢
	:
22	instantiation	32, 36, 33	⊢
	: , :
23	instantiation	34, 95, 119, 160, 96, 35, 99, 38, 36	⊢
	: , : , : , : , : , :
24	instantiation	37, 38, 99, 39	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
26	instantiation	40, 54, 41, 42	⊢
	: , : , :
27	instantiation	43, 44, 45, 46, 47	⊢
	: , : , :
28	instantiation	158, 48, 49	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
31	theorem		⊢
	proveit.numbers.addition.elim_zero_right
32	theorem		⊢
	proveit.numbers.addition.commutation
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
34	theorem		⊢
	proveit.numbers.addition.disassociation
35	instantiation	102	⊢
	: , :
36	instantiation	158, 156, 50	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
38	instantiation	158, 156, 72	⊢
	: , : , :
39	instantiation	51	⊢
	:
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
41	instantiation	158, 148, 52	⊢
	: , : , :
42	instantiation	53, 54, 140, 103, 55, 56*, 57*, 58*	⊢
	: , : , : , :
43	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
44	instantiation	158, 59, 60	⊢
	: , : , :
45	instantiation	158, 61, 70	⊢
	: , : , :
46	instantiation	158, 61, 62	⊢
	: , : , :
47	instantiation	63, 91, 140, 64, 65, 66, 67*	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
49	instantiation	68, 69, 70	⊢
	: , :
50	instantiation	71, 72	⊢
	:
51	axiom		⊢
	proveit.logic.equality.equals_reflexivity
52	instantiation	73, 149, 74, 109	⊢
	: , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rescale_interval_co_membership
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
55	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
56	instantiation	115, 75, 76, 77	⊢
	: , : , : , :
57	instantiation	78, 98	⊢
	:
58	instantiation	152, 98	⊢
	:
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
60	instantiation	158, 79, 160	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
62	instantiation	158, 84, 163	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
64	instantiation	161, 162, 81	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
66	instantiation	80, 81	⊢
	:
67	instantiation	82, 83	⊢
	:
68	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
69	instantiation	158, 84, 150	⊢
	: , : , :
70	instantiation	158, 84, 92	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.negation.real_closure
72	instantiation	108, 140, 91, 85	⊢
	: , :
73	theorem		⊢
	proveit.numbers.division.div_rational_closure
74	instantiation	158, 154, 86	⊢
	: , : , :
75	instantiation	87, 160, 119, 95, 88, 96, 98, 153, 99	⊢
	: , : , : , : , : , :
76	instantiation	137, 89, 90	⊢
	: , : , :
77	instantiation	144, 99	⊢
	:
78	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
80	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
81	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
82	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
83	instantiation	158, 156, 91	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
85	instantiation	120, 92	⊢
	:
86	instantiation	158, 93, 163	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.multiplication.disassociation
88	instantiation	102	⊢
	: , :
89	instantiation	94, 95, 119, 160, 96, 97, 98, 153, 99	⊢
	: , : , : , : , : , :
90	instantiation	145, 100	⊢
	: , : , :
91	instantiation	158, 148, 101	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
93	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
94	theorem		⊢
	proveit.numbers.multiplication.association
95	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
96	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
97	instantiation	102	⊢
	: , :
98	instantiation	158, 156, 103	⊢
	: , : , :
99	instantiation	158, 156, 104	⊢
	: , : , :
100	instantiation	112, 105, 106	⊢
	: , : , :
101	instantiation	158, 154, 107	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
103	instantiation	108, 140, 157, 109	⊢
	: , :
104	instantiation	110, 111	⊢
	:
105	instantiation	112, 113, 114	⊢
	: , : , :
106	instantiation	115, 116, 117, 118	⊢
	: , : , : , :
107	instantiation	158, 159, 119	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.division.div_real_closure
109	instantiation	120, 163	⊢
	:
110	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
111	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
112	theorem		⊢
	proveit.logic.equality.sub_right_side_into
113	instantiation	121, 132, 122, 123	⊢
	: , : , : , : , :
114	instantiation	137, 124, 125	⊢
	: , : , :
115	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
116	instantiation	145, 126	⊢
	: , : , :
117	instantiation	145, 126	⊢
	: , : , :
118	instantiation	152, 132	⊢
	:
119	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
120	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
121	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
122	instantiation	158, 128, 127	⊢
	: , : , :
123	instantiation	158, 128, 129	⊢
	: , : , :
124	instantiation	145, 130	⊢
	: , : , :
125	instantiation	145, 131	⊢
	: , : , :
126	instantiation	147, 132	⊢
	:
127	instantiation	158, 134, 133	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
129	instantiation	158, 134, 135	⊢
	: , : , :
130	instantiation	145, 136	⊢
	: , : , :
131	instantiation	137, 138, 139	⊢
	: , : , :
132	instantiation	158, 156, 140	⊢
	: , : , :
133	instantiation	158, 142, 141	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
135	instantiation	158, 142, 143	⊢
	: , : , :
136	instantiation	144, 153	⊢
	:
137	axiom		⊢
	proveit.logic.equality.equals_transitivity
138	instantiation	145, 146	⊢
	: , : , :
139	instantiation	147, 153	⊢
	:
140	instantiation	158, 148, 149	⊢
	: , : , :
141	instantiation	158, 151, 150	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
143	instantiation	158, 151, 163	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
145	axiom		⊢
	proveit.logic.equality.substitution
146	instantiation	152, 153	⊢
	:
147	theorem		⊢
	proveit.numbers.division.frac_one_denom
148	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
149	instantiation	158, 154, 155	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
151	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
152	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
153	instantiation	158, 156, 157	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
155	instantiation	158, 159, 160	⊢
	: , : , :
156	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
157	instantiation	161, 162, 163	⊢
	: , : , :
158	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
159	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
160	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
161	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
162	instantiation	164, 165	⊢
	: , :
163	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
164	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
165	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements