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	reference	31	⊢
2	instantiation	75, 4, 32	⊢
	: , : , :
3	instantiation	5, 141, 6	⊢
	: , :
4	modus ponens	7, 8	⊢
5	theorem		⊢
	proveit.numbers.modular.int_mod_elimination
6	instantiation	10, 11, 12, 133, 9	⊢
	: , : , :
7	theorem		⊢
	proveit.physics.quantum.QPE._alpha_ideal_case
8	instantiation	10, 11, 12, 25, 13	⊢
	: , : , :
9	instantiation	17, 14, 15	⊢
	: , :
10	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
11	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
12	instantiation	16, 135, 51	⊢
	: , :
13	instantiation	17, 18, 19	⊢
	: , :
14	instantiation	75, 18, 32	⊢
	: , : , :
15	instantiation	75, 19, 32	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
17	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
18	instantiation	20, 130, 43, 98, 21, 22, 23*	⊢
	: , : , :
19	instantiation	24, 25, 135, 51, 26, 27	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
21	instantiation	28, 43, 107, 44	⊢
	: , : , :
22	instantiation	29, 35	⊢
	: , :
23	instantiation	30, 123	⊢
	:
24	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
25	instantiation	31, 133, 32	⊢
	: , : , :
26	instantiation	33, 130, 98, 107, 34, 35, 106*	⊢
	: , : , :
27	instantiation	36, 37, 38	⊢
	: , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
29	theorem		⊢
	proveit.numbers.ordering.relax_less
30	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
31	theorem		⊢
	proveit.logic.equality.sub_left_side_into
32	instantiation	39, 130, 98, 109, 40, 41*	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
34	instantiation	42, 43, 107, 44	⊢
	: , : , :
35	instantiation	45, 141	⊢
	:
36	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
37	instantiation	139, 118, 46	⊢
	: , : , :
38	instantiation	99	⊢
	:
39	theorem		⊢
	proveit.numbers.multiplication.left_mult_eq_real
40	instantiation	47, 48	⊢
	: , :
41	instantiation	75, 49, 50	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
44	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
45	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
46	instantiation	139, 134, 51	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.equality.equals_reversal
48	instantiation	52, 119, 63, 53, 64, 54*, 55*	⊢
	: , : , :
49	instantiation	75, 56, 57	⊢
	: , : , :
50	instantiation	58, 59, 60, 61	⊢
	: , : , : , :
51	instantiation	62, 124	⊢
	:
52	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
53	instantiation	75, 63, 64	⊢
	: , : , :
54	instantiation	65, 97	⊢
	:
55	instantiation	103, 66, 67	⊢
	: , : , :
56	instantiation	68, 92, 93, 69, 70	⊢
	: , : , : , : , :
57	instantiation	103, 71, 72	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
59	instantiation	113, 73	⊢
	: , : , :
60	instantiation	113, 74	⊢
	: , : , :
61	instantiation	122, 93	⊢
	:
62	theorem		⊢
	proveit.numbers.negation.int_closure
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
64	instantiation	75, 76, 77	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.addition.elim_zero_left
66	instantiation	78, 79, 80, 132, 81, 82, 85, 83, 97	⊢
	: , : , : , : , : , :
67	instantiation	84, 97, 85, 86	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
69	instantiation	139, 88, 87	⊢
	: , : , :
70	instantiation	139, 88, 89	⊢
	: , : , :
71	instantiation	113, 90	⊢
	: , : , :
72	instantiation	113, 91	⊢
	: , : , :
73	instantiation	115, 92	⊢
	:
74	instantiation	115, 93	⊢
	:
75	theorem		⊢
	proveit.logic.equality.sub_right_side_into
76	instantiation	94, 133	⊢
	:
77	assumption		⊢
78	theorem		⊢
	proveit.numbers.addition.disassociation
79	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
81	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
82	instantiation	95	⊢
	: , :
83	instantiation	96, 97	⊢
	:
84	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
85	instantiation	139, 129, 98	⊢
	: , : , :
86	instantiation	99	⊢
	:
87	instantiation	139, 101, 100	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
89	instantiation	139, 101, 102	⊢
	: , : , :
90	instantiation	103, 104, 105	⊢
	: , : , :
91	instantiation	113, 106	⊢
	: , : , :
92	instantiation	139, 129, 107	⊢
	: , : , :
93	instantiation	139, 129, 108	⊢
	: , : , :
94	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
95	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
96	theorem		⊢
	proveit.numbers.negation.complex_closure
97	instantiation	139, 129, 109	⊢
	: , : , :
98	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
99	axiom		⊢
	proveit.logic.equality.equals_reflexivity
100	instantiation	139, 111, 110	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
102	instantiation	139, 111, 112	⊢
	: , : , :
103	axiom		⊢
	proveit.logic.equality.equals_transitivity
104	instantiation	113, 114	⊢
	: , : , :
105	instantiation	115, 123	⊢
	:
106	instantiation	116, 123	⊢
	:
107	instantiation	139, 118, 117	⊢
	: , : , :
108	instantiation	139, 118, 126	⊢
	: , : , :
109	instantiation	139, 118, 119	⊢
	: , : , :
110	instantiation	139, 120, 141	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
112	instantiation	139, 120, 121	⊢
	: , : , :
113	axiom		⊢
	proveit.logic.equality.substitution
114	instantiation	122, 123	⊢
	:
115	theorem		⊢
	proveit.numbers.division.frac_one_denom
116	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
117	instantiation	139, 134, 124	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
119	instantiation	125, 126, 127, 128	⊢
	: , :
120	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
121	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
122	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
123	instantiation	139, 129, 130	⊢
	: , : , :
124	instantiation	139, 131, 132	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.division.div_rational_closure
126	instantiation	139, 134, 133	⊢
	: , : , :
127	instantiation	139, 134, 135	⊢
	: , : , :
128	instantiation	136, 141	⊢
	:
129	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
130	instantiation	137, 138, 141	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
132	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
133	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
134	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
135	instantiation	139, 140, 141	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
137	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
138	instantiation	142, 143	⊢
	: , :
139	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
140	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
141	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
142	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
143	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements