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.addition.weak_bound_via_left_term_bound
2	modus ponens	6, 7	⊢
3	modus ponens	8, 9	⊢
4	modus ponens	10, 11	⊢
5	modus ponens	12, 13	⊢
6	instantiation	16	⊢
	: , : , :
7	generalization	14	⊢
8	instantiation	16	⊢
	: , : , :
9	generalization	15	⊢
10	instantiation	16	⊢
	: , : , :
11	generalization	17	⊢
12	instantiation	18	⊢
	: , : , :
13	generalization	19	⊢
14	instantiation	44, 20, 152	,  ⊢
	: , :
15	instantiation	44, 21, 152	,  ⊢
	: , :
16	theorem		⊢
	proveit.numbers.summation.summation_real_closure
17	instantiation	22, 23, 24, 25	,  ⊢
	: , :
18	theorem		⊢
	proveit.numbers.summation.weak_summation_from_summands_bound
19	instantiation	26, 27, 94	,  ⊢
	:
20	instantiation	150, 29, 28	,  ⊢
	: , : , :
21	instantiation	150, 29, 30	,  ⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.division.div_real_closure
23	instantiation	150, 88, 31	⊢
	: , : , :
24	instantiation	96, 32, 33	,  ⊢
	: , :
25	instantiation	34, 152, 35, 36, 37	,  ⊢
	: , :
26	theorem		⊢
	proveit.physics.quantum.QPE._alpha_sqrd_upper_bound
27	instantiation	38, 118, 144, 103, 39	,  ⊢
	: , : , :
28	instantiation	41, 40	,  ⊢
	:
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
30	instantiation	41, 42	,  ⊢
	:
31	instantiation	150, 95, 139	⊢
	: , : , :
32	instantiation	150, 88, 43	⊢
	: , : , :
33	instantiation	44, 72, 152	,  ⊢
	: , :
34	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
35	instantiation	45	⊢
	: , :
36	instantiation	150, 46, 47	⊢
	: , : , :
37	instantiation	48, 49, 50	,  ⊢
	: , :
38	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
39	instantiation	51, 52, 53	,  ⊢
	: , :
40	instantiation	55, 54	,  ⊢
	:
41	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
42	instantiation	55, 56	,  ⊢
	:
43	instantiation	150, 95, 57	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
47	instantiation	150, 58, 59	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
49	instantiation	60, 61, 62	,  ⊢
	:
50	instantiation	150, 71, 63	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
52	instantiation	138, 118, 119, 120	,  ⊢
	: , : , :
53	instantiation	64, 65	,  ⊢
	: , :
54	instantiation	67, 110, 66	,  ⊢
	: , :
55	theorem		⊢
	proveit.physics.quantum.QPE._alpha_are_complex
56	instantiation	67, 110, 103	,  ⊢
	: , :
57	instantiation	150, 151, 68	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
59	instantiation	150, 69, 70	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
61	instantiation	150, 71, 72	,  ⊢
	: , : , :
62	instantiation	73, 74	,  ⊢
	: , :
63	instantiation	150, 88, 75	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.ordering.relax_less
65	instantiation	76, 105, 77	,  ⊢
	: , : , :
66	instantiation	150, 78, 79	,  ⊢
	: , : , :
67	theorem		⊢
	proveit.physics.quantum.QPE._mod_add_closure
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
69	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
70	instantiation	150, 80, 81	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
72	instantiation	82, 83, 84	,  ⊢
	: , :
73	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
74	instantiation	85, 86	,  ⊢
	: , :
75	instantiation	150, 95, 149	⊢
	: , : , :
76	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
77	instantiation	87, 147	⊢
	:
78	instantiation	137, 124, 144	⊢
	: , :
79	assumption		⊢
80	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
81	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
82	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
83	instantiation	150, 88, 89	,  ⊢
	: , : , :
84	instantiation	90, 91	⊢
	:
85	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
86	instantiation	92, 93, 103, 94	,  ⊢
	: , :
87	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
89	instantiation	150, 95, 103	,  ⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.negation.real_closure
91	instantiation	96, 97, 98	⊢
	: , :
92	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
93	instantiation	99, 100, 142, 101	⊢
	: , : , : , : , :
94	instantiation	102, 103, 104, 105	,  ⊢
	: , :
95	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
96	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
97	instantiation	106, 107, 108	⊢
	: , : , :
98	instantiation	109, 110	⊢
	:
99	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
100	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
101	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
102	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
103	instantiation	150, 111, 120	,  ⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
105	instantiation	112, 113, 114	,  ⊢
	: , : , :
106	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
107	instantiation	115, 116	⊢
	: , :
108	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
109	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
110	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
111	instantiation	137, 118, 119	⊢
	: , :
112	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
113	instantiation	117, 118, 119, 120	,  ⊢
	: , : , :
114	instantiation	121, 122	⊢
	:
115	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
116	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
117	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
118	instantiation	143, 123, 139	⊢
	: , :
119	instantiation	148, 124	⊢
	:
120	assumption		⊢
121	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
122	instantiation	125, 126	⊢
	:
123	instantiation	148, 144	⊢
	:
124	instantiation	143, 131, 139	⊢
	: , :
125	theorem		⊢
	proveit.numbers.negation.int_neg_closure
126	instantiation	127, 128, 129	⊢
	: , :
127	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
128	instantiation	130, 131, 132	⊢
	:
129	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
130	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
131	instantiation	150, 133, 141	⊢
	: , : , :
132	instantiation	134, 135, 136	⊢
	: , : , :
133	instantiation	137, 139, 140	⊢
	: , :
134	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
135	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
136	instantiation	138, 139, 140, 141	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
138	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
139	instantiation	150, 151, 142	⊢
	: , : , :
140	instantiation	143, 144, 145	⊢
	: , :
141	assumption		⊢
142	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
143	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
144	instantiation	150, 146, 147	⊢
	: , : , :
145	instantiation	148, 149	⊢
	:
146	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
147	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
148	theorem		⊢
	proveit.numbers.negation.int_closure
149	instantiation	150, 151, 152	⊢
	: , : , :
150	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
151	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
152	theorem		⊢
	proveit.numbers.numerals.decimals.nat2