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	144	⊢
2	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
3	instantiation	4, 5	⊢
	:
4	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
5	instantiation	36, 97, 6	⊢
	: , : , :
6	instantiation	36, 7, 8	⊢
	: , : , :
7	instantiation	80, 9, 37	⊢
	: , : , :
8	instantiation	10, 146, 11	⊢
	: , :
9	modus ponens	12, 13	⊢
10	theorem		⊢
	proveit.numbers.modular.int_mod_elimination
11	instantiation	15, 16, 17, 138, 14	⊢
	: , : , :
12	theorem		⊢
	proveit.physics.quantum.QPE._alpha_ideal_case
13	instantiation	15, 16, 17, 30, 18	⊢
	: , : , :
14	instantiation	22, 19, 20	⊢
	: , :
15	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
16	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
17	instantiation	21, 140, 56	⊢
	: , :
18	instantiation	22, 23, 24	⊢
	: , :
19	instantiation	80, 23, 37	⊢
	: , : , :
20	instantiation	80, 24, 37	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
22	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
23	instantiation	25, 135, 48, 103, 26, 27, 28*	⊢
	: , : , :
24	instantiation	29, 30, 140, 56, 31, 32	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
26	instantiation	33, 48, 112, 49	⊢
	: , : , :
27	instantiation	34, 40	⊢
	: , :
28	instantiation	35, 128	⊢
	:
29	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
30	instantiation	36, 138, 37	⊢
	: , : , :
31	instantiation	38, 135, 103, 112, 39, 40, 111*	⊢
	: , : , :
32	instantiation	41, 42, 43	⊢
	: , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
34	theorem		⊢
	proveit.numbers.ordering.relax_less
35	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
36	theorem		⊢
	proveit.logic.equality.sub_left_side_into
37	instantiation	44, 135, 103, 114, 45, 46*	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
39	instantiation	47, 48, 112, 49	⊢
	: , : , :
40	instantiation	50, 146	⊢
	:
41	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
42	instantiation	144, 123, 51	⊢
	: , : , :
43	instantiation	104	⊢
	:
44	theorem		⊢
	proveit.numbers.multiplication.left_mult_eq_real
45	instantiation	52, 53	⊢
	: , :
46	instantiation	80, 54, 55	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
49	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
50	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
51	instantiation	144, 139, 56	⊢
	: , : , :
52	theorem		⊢
	proveit.logic.equality.equals_reversal
53	instantiation	57, 124, 68, 58, 69, 59*, 60*	⊢
	: , : , :
54	instantiation	80, 61, 62	⊢
	: , : , :
55	instantiation	63, 64, 65, 66	⊢
	: , : , : , :
56	instantiation	67, 129	⊢
	:
57	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
58	instantiation	80, 68, 69	⊢
	: , : , :
59	instantiation	70, 102	⊢
	:
60	instantiation	108, 71, 72	⊢
	: , : , :
61	instantiation	73, 97, 98, 74, 75	⊢
	: , : , : , : , :
62	instantiation	108, 76, 77	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
64	instantiation	118, 78	⊢
	: , : , :
65	instantiation	118, 79	⊢
	: , : , :
66	instantiation	127, 98	⊢
	:
67	theorem		⊢
	proveit.numbers.negation.int_closure
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
69	instantiation	80, 81, 82	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.addition.elim_zero_left
71	instantiation	83, 84, 85, 137, 86, 87, 90, 88, 102	⊢
	: , : , : , : , : , :
72	instantiation	89, 102, 90, 91	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
74	instantiation	144, 93, 92	⊢
	: , : , :
75	instantiation	144, 93, 94	⊢
	: , : , :
76	instantiation	118, 95	⊢
	: , : , :
77	instantiation	118, 96	⊢
	: , : , :
78	instantiation	120, 97	⊢
	:
79	instantiation	120, 98	⊢
	:
80	theorem		⊢
	proveit.logic.equality.sub_right_side_into
81	instantiation	99, 138	⊢
	:
82	assumption		⊢
83	theorem		⊢
	proveit.numbers.addition.disassociation
84	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
85	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
86	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
87	instantiation	100	⊢
	: , :
88	instantiation	101, 102	⊢
	:
89	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
90	instantiation	144, 134, 103	⊢
	: , : , :
91	instantiation	104	⊢
	:
92	instantiation	144, 106, 105	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
94	instantiation	144, 106, 107	⊢
	: , : , :
95	instantiation	108, 109, 110	⊢
	: , : , :
96	instantiation	118, 111	⊢
	: , : , :
97	instantiation	144, 134, 112	⊢
	: , : , :
98	instantiation	144, 134, 113	⊢
	: , : , :
99	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
100	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
101	theorem		⊢
	proveit.numbers.negation.complex_closure
102	instantiation	144, 134, 114	⊢
	: , : , :
103	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
104	axiom		⊢
	proveit.logic.equality.equals_reflexivity
105	instantiation	144, 116, 115	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
107	instantiation	144, 116, 117	⊢
	: , : , :
108	axiom		⊢
	proveit.logic.equality.equals_transitivity
109	instantiation	118, 119	⊢
	: , : , :
110	instantiation	120, 128	⊢
	:
111	instantiation	121, 128	⊢
	:
112	instantiation	144, 123, 122	⊢
	: , : , :
113	instantiation	144, 123, 131	⊢
	: , : , :
114	instantiation	144, 123, 124	⊢
	: , : , :
115	instantiation	144, 125, 146	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
117	instantiation	144, 125, 126	⊢
	: , : , :
118	axiom		⊢
	proveit.logic.equality.substitution
119	instantiation	127, 128	⊢
	:
120	theorem		⊢
	proveit.numbers.division.frac_one_denom
121	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
122	instantiation	144, 139, 129	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
124	instantiation	130, 131, 132, 133	⊢
	: , :
125	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
126	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
127	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
128	instantiation	144, 134, 135	⊢
	: , : , :
129	instantiation	144, 136, 137	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.division.div_rational_closure
131	instantiation	144, 139, 138	⊢
	: , : , :
132	instantiation	144, 139, 140	⊢
	: , : , :
133	instantiation	141, 146	⊢
	:
134	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
135	instantiation	142, 143, 146	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
137	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
138	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
139	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
140	instantiation	144, 145, 146	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
142	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
143	instantiation	147, 148	⊢
	: , :
144	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
145	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
146	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
147	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
148	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements