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_eq_less
2	instantiation	4, 5, 6, 7*	,  ⊢
	: , : , :
3	instantiation	8, 145, 191, 9, 146, 10, 174	⊢
	: , : , : , : , :
4	theorem		⊢
	proveit.logic.equality.sub_right_side_into
5	instantiation	11, 12, 13	,  ⊢
	: , : , :
6	instantiation	14, 176, 15, 16, 114, 51, 103, 17*	⊢
	: , : , :
7	instantiation	130, 18, 19	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.term_as_strong_upper_bound
9	instantiation	85, 20	⊢
	:
10	instantiation	21, 22	⊢
	:
11	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
12	instantiation	23, 27, 24, 90, 25	,  ⊢
	: , : , :
13	instantiation	26, 90, 27, 28, 29	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.division.distribute_frac_through_sum
15	instantiation	161	⊢
	: , :
16	instantiation	189, 167, 30	⊢
	: , : , :
17	instantiation	31, 50, 51, 103, 32*	⊢
	: , :
18	instantiation	116, 33	⊢
	: , : , :
19	instantiation	130, 34, 35	⊢
	: , : , :
20	instantiation	36, 191, 145, 146, 37	⊢
	: , : , : , : , :
21	theorem		⊢
	proveit.numbers.negation.real_neg_closure
22	instantiation	38, 39, 40, 103	⊢
	: , :
23	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
24	instantiation	41, 74, 90, 43	⊢
	: , : , :
25	instantiation	42, 74, 90, 43	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
27	instantiation	173, 46	⊢
	:
28	instantiation	173, 45	⊢
	:
29	instantiation	44, 45, 46, 47	⊢
	: , :
30	instantiation	189, 181, 48	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
32	instantiation	49, 50, 51, 103, 52*	⊢
	: , :
33	instantiation	53, 54, 78, 55*	⊢
	: , :
34	instantiation	144, 191, 188, 145, 56, 146, 76, 59	⊢
	: , : , : , : , : , :
35	instantiation	57, 145, 188, 191, 146, 58, 76, 59, 60*	⊢
	: , : , : , : , : , :
36	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
37	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
38	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
39	instantiation	189, 62, 61	⊢
	: , : , :
40	instantiation	189, 62, 63	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
43	instantiation	64, 65	⊢
	:
44	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
45	instantiation	101, 67, 102, 103	⊢
	: , :
46	instantiation	101, 68, 102, 103	⊢
	: , :
47	instantiation	66, 102, 67, 68, 69, 70	⊢
	: , : , :
48	instantiation	189, 186, 143	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.division.div_as_mult
50	instantiation	189, 167, 71	⊢
	: , : , :
51	instantiation	189, 167, 102	⊢
	: , : , :
52	instantiation	130, 72, 73	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
54	instantiation	189, 167, 74	⊢
	: , : , :
55	instantiation	75, 76	⊢
	:
56	instantiation	161	⊢
	: , :
57	theorem		⊢
	proveit.numbers.addition.association
58	instantiation	161	⊢
	: , :
59	instantiation	77, 78	⊢
	:
60	instantiation	79, 187, 183, 80*	⊢
	: , : , : , :
61	instantiation	189, 81, 120	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
63	instantiation	189, 81, 122	⊢
	: , : , :
64	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_in_interval
65	assumption		⊢
66	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
67	instantiation	189, 181, 82	⊢
	: , : , :
68	instantiation	189, 181, 83	⊢
	: , : , :
69	instantiation	84, 129, 160, 112	⊢
	: , : , :
70	instantiation	85, 122	⊢
	:
71	instantiation	178, 179, 171	⊢
	: , : , :
72	instantiation	116, 86	⊢
	: , : , :
73	instantiation	87, 157, 88, 162, 100, 89*	⊢
	: , : , :
74	instantiation	173, 90	⊢
	:
75	theorem		⊢
	proveit.numbers.negation.double_negation
76	instantiation	189, 167, 90	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.negation.complex_closure
78	instantiation	189, 167, 91	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
80	instantiation	130, 92, 93	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
82	instantiation	189, 186, 129	⊢
	: , : , :
83	instantiation	189, 186, 94	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
85	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
86	instantiation	95, 157, 172, 163, 100, 96*	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
88	instantiation	97, 172, 163	⊢
	: , :
89	instantiation	130, 98, 99	⊢
	: , : , :
90	instantiation	101, 174, 168, 100	⊢
	: , :
91	instantiation	101, 174, 102, 103	⊢
	: , :
92	instantiation	136, 188, 104, 105, 106, 107	⊢
	: , : , : , :
93	instantiation	108, 109, 110	⊢
	:
94	instantiation	189, 111, 112	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
96	instantiation	113, 150, 114, 115*	⊢
	: , :
97	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
98	instantiation	116, 117	⊢
	: , : , :
99	instantiation	118, 119, 120, 121*	⊢
	: , :
100	instantiation	126, 176	⊢
	:
101	theorem		⊢
	proveit.numbers.division.div_real_closure
102	instantiation	178, 179, 122	⊢
	: , : , :
103	instantiation	126, 122	⊢
	:
104	instantiation	161	⊢
	: , :
105	instantiation	161	⊢
	: , :
106	instantiation	130, 123, 124	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
108	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
109	instantiation	189, 167, 125	⊢
	: , : , :
110	instantiation	126, 127	⊢
	:
111	instantiation	128, 129, 160	⊢
	: , :
112	assumption		⊢
113	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
114	instantiation	189, 167, 174	⊢
	: , : , :
115	instantiation	156, 150	⊢
	:
116	axiom		⊢
	proveit.logic.equality.substitution
117	instantiation	130, 131, 132	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
119	instantiation	189, 133, 134	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
121	instantiation	135, 157	⊢
	:
122	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
123	instantiation	136, 188, 137, 138, 139, 140	⊢
	: , : , : , :
124	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
125	instantiation	189, 181, 141	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
127	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
128	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
129	instantiation	142, 143, 187	⊢
	: , :
130	axiom		⊢
	proveit.logic.equality.equals_transitivity
131	instantiation	144, 145, 188, 191, 146, 147, 150, 151, 148	⊢
	: , : , : , : , : , :
132	instantiation	149, 150, 151, 152	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
134	instantiation	189, 153, 154	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
136	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
137	instantiation	161	⊢
	: , :
138	instantiation	161	⊢
	: , :
139	instantiation	155, 157	⊢
	:
140	instantiation	156, 157	⊢
	:
141	instantiation	189, 186, 158	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
143	instantiation	159, 160	⊢
	:
144	theorem		⊢
	proveit.numbers.addition.disassociation
145	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
146	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
147	instantiation	161	⊢
	: , :
148	instantiation	189, 167, 162	⊢
	: , : , :
149	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
150	instantiation	189, 167, 172	⊢
	: , : , :
151	instantiation	189, 167, 163	⊢
	: , : , :
152	instantiation	164	⊢
	:
153	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
154	instantiation	189, 165, 166	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
156	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
157	instantiation	189, 167, 168	⊢
	: , : , :
158	instantiation	189, 190, 169	⊢
	: , : , :
159	theorem		⊢
	proveit.numbers.negation.int_closure
160	instantiation	189, 170, 171	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
162	instantiation	173, 172	⊢
	:
163	instantiation	173, 174	⊢
	:
164	axiom		⊢
	proveit.logic.equality.equals_reflexivity
165	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
166	instantiation	189, 175, 176	⊢
	: , : , :
167	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
168	instantiation	189, 181, 177	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
170	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
171	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
172	instantiation	178, 179, 180	⊢
	: , : , :
173	theorem		⊢
	proveit.numbers.negation.real_closure
174	instantiation	189, 181, 182	⊢
	: , : , :
175	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
176	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
177	instantiation	189, 186, 183	⊢
	: , : , :
178	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
179	instantiation	184, 185	⊢
	: , :
180	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
181	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
182	instantiation	189, 186, 187	⊢
	: , : , :
183	instantiation	189, 190, 188	⊢
	: , : , :
184	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
185	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
186	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
187	instantiation	189, 190, 191	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
189	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
190	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
191	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements