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	modus ponens	1, 2	⊢
1	theorem		⊢
	proveit.physics.quantum.QPE._alpha_ideal_case
2	instantiation	3, 4, 5, 16, 6	⊢
	: , : , :
3	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
4	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
5	instantiation	7, 126, 42	⊢
	: , :
6	instantiation	8, 9, 10	⊢
	: , :
7	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
8	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
9	instantiation	11, 121, 34, 89, 12, 13, 14*	⊢
	: , : , :
10	instantiation	15, 16, 126, 42, 17, 18	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
12	instantiation	19, 34, 98, 35	⊢
	: , : , :
13	instantiation	20, 26	⊢
	: , :
14	instantiation	21, 114	⊢
	:
15	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
16	instantiation	22, 124, 23	⊢
	: , : , :
17	instantiation	24, 121, 89, 98, 25, 26, 97*	⊢
	: , : , :
18	instantiation	27, 28, 29	⊢
	: , :
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
20	theorem		⊢
	proveit.numbers.ordering.relax_less
21	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
22	theorem		⊢
	proveit.logic.equality.sub_left_side_into
23	instantiation	30, 121, 89, 100, 31, 32*	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
25	instantiation	33, 34, 98, 35	⊢
	: , : , :
26	instantiation	36, 132	⊢
	:
27	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
28	instantiation	130, 109, 37	⊢
	: , : , :
29	instantiation	90	⊢
	:
30	theorem		⊢
	proveit.numbers.multiplication.left_mult_eq_real
31	instantiation	38, 39	⊢
	: , :
32	instantiation	66, 40, 41	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
35	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
36	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
37	instantiation	130, 125, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.equality.equals_reversal
39	instantiation	43, 110, 54, 44, 55, 45*, 46*	⊢
	: , : , :
40	instantiation	66, 47, 48	⊢
	: , : , :
41	instantiation	49, 50, 51, 52	⊢
	: , : , : , :
42	instantiation	53, 115	⊢
	:
43	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
44	instantiation	66, 54, 55	⊢
	: , : , :
45	instantiation	56, 88	⊢
	:
46	instantiation	94, 57, 58	⊢
	: , : , :
47	instantiation	59, 83, 84, 60, 61	⊢
	: , : , : , : , :
48	instantiation	94, 62, 63	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
50	instantiation	104, 64	⊢
	: , : , :
51	instantiation	104, 65	⊢
	: , : , :
52	instantiation	113, 84	⊢
	:
53	theorem		⊢
	proveit.numbers.negation.int_closure
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
55	instantiation	66, 67, 68	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.elim_zero_left
57	instantiation	69, 70, 71, 123, 72, 73, 76, 74, 88	⊢
	: , : , : , : , : , :
58	instantiation	75, 88, 76, 77	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
60	instantiation	130, 79, 78	⊢
	: , : , :
61	instantiation	130, 79, 80	⊢
	: , : , :
62	instantiation	104, 81	⊢
	: , : , :
63	instantiation	104, 82	⊢
	: , : , :
64	instantiation	106, 83	⊢
	:
65	instantiation	106, 84	⊢
	:
66	theorem		⊢
	proveit.logic.equality.sub_right_side_into
67	instantiation	85, 124	⊢
	:
68	assumption		⊢
69	theorem		⊢
	proveit.numbers.addition.disassociation
70	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
72	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
73	instantiation	86	⊢
	: , :
74	instantiation	87, 88	⊢
	:
75	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
76	instantiation	130, 120, 89	⊢
	: , : , :
77	instantiation	90	⊢
	:
78	instantiation	130, 92, 91	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
80	instantiation	130, 92, 93	⊢
	: , : , :
81	instantiation	94, 95, 96	⊢
	: , : , :
82	instantiation	104, 97	⊢
	: , : , :
83	instantiation	130, 120, 98	⊢
	: , : , :
84	instantiation	130, 120, 99	⊢
	: , : , :
85	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
86	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
87	theorem		⊢
	proveit.numbers.negation.complex_closure
88	instantiation	130, 120, 100	⊢
	: , : , :
89	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
90	axiom		⊢
	proveit.logic.equality.equals_reflexivity
91	instantiation	130, 102, 101	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
93	instantiation	130, 102, 103	⊢
	: , : , :
94	axiom		⊢
	proveit.logic.equality.equals_transitivity
95	instantiation	104, 105	⊢
	: , : , :
96	instantiation	106, 114	⊢
	:
97	instantiation	107, 114	⊢
	:
98	instantiation	130, 109, 108	⊢
	: , : , :
99	instantiation	130, 109, 117	⊢
	: , : , :
100	instantiation	130, 109, 110	⊢
	: , : , :
101	instantiation	130, 111, 132	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
103	instantiation	130, 111, 112	⊢
	: , : , :
104	axiom		⊢
	proveit.logic.equality.substitution
105	instantiation	113, 114	⊢
	:
106	theorem		⊢
	proveit.numbers.division.frac_one_denom
107	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
108	instantiation	130, 125, 115	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
110	instantiation	116, 117, 118, 119	⊢
	: , :
111	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
112	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
113	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
114	instantiation	130, 120, 121	⊢
	: , : , :
115	instantiation	130, 122, 123	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.division.div_rational_closure
117	instantiation	130, 125, 124	⊢
	: , : , :
118	instantiation	130, 125, 126	⊢
	: , : , :
119	instantiation	127, 132	⊢
	:
120	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
121	instantiation	128, 129, 132	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
123	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
124	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
125	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
126	instantiation	130, 131, 132	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
128	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
129	instantiation	133, 134	⊢
	: , :
130	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
131	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
132	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
133	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
134	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements