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, 6*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.exponentiation.exp_eq_real
2	reference	17	⊢
3	instantiation	159, 7, 8	⊢
	: , : , :
4	reference	127	⊢
5	instantiation	9, 14, 112, 18, 10*	⊢
	: , :
6	instantiation	11, 12	⊢
	:
7	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
8	instantiation	13, 14	⊢
	:
9	theorem		⊢
	proveit.numbers.absolute_value.abs_eq
10	instantiation	15, 16	⊢
	:
11	theorem		⊢
	proveit.numbers.exponentiation.exponentiated_one
12	instantiation	159, 149, 17	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
14	instantiation	51, 112, 18	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
16	instantiation	19, 152	⊢
	:
17	instantiation	159, 138, 20	⊢
	: , : , :
18	instantiation	51, 21, 22	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
20	instantiation	159, 154, 23	⊢
	: , : , :
21	instantiation	95, 24, 52	⊢
	: , : , :
22	instantiation	25, 161, 26	⊢
	: , :
23	instantiation	159, 151, 100	⊢
	: , : , :
24	modus ponens	27, 28	⊢
25	theorem		⊢
	proveit.numbers.modular.int_mod_elimination
26	instantiation	30, 31, 32, 153, 29	⊢
	: , : , :
27	theorem		⊢
	proveit.physics.quantum.QPE._alpha_ideal_case
28	instantiation	30, 31, 32, 45, 33	⊢
	: , : , :
29	instantiation	37, 34, 35	⊢
	: , :
30	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
31	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
32	instantiation	36, 155, 71	⊢
	: , :
33	instantiation	37, 38, 39	⊢
	: , :
34	instantiation	95, 38, 52	⊢
	: , : , :
35	instantiation	95, 39, 52	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
37	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
38	instantiation	40, 150, 63, 118, 41, 42, 43*	⊢
	: , : , :
39	instantiation	44, 45, 155, 71, 46, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
41	instantiation	48, 63, 127, 64	⊢
	: , : , :
42	instantiation	49, 55	⊢
	: , :
43	instantiation	50, 143	⊢
	:
44	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
45	instantiation	51, 153, 52	⊢
	: , : , :
46	instantiation	53, 150, 118, 127, 54, 55, 126*	⊢
	: , : , :
47	instantiation	56, 57, 58	⊢
	: , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
49	theorem		⊢
	proveit.numbers.ordering.relax_less
50	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
51	theorem		⊢
	proveit.logic.equality.sub_left_side_into
52	instantiation	59, 150, 118, 129, 60, 61*	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
54	instantiation	62, 63, 127, 64	⊢
	: , : , :
55	instantiation	65, 161	⊢
	:
56	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
57	instantiation	159, 138, 66	⊢
	: , : , :
58	instantiation	119	⊢
	:
59	theorem		⊢
	proveit.numbers.multiplication.left_mult_eq_real
60	instantiation	67, 68	⊢
	: , :
61	instantiation	95, 69, 70	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
64	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
65	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
66	instantiation	159, 154, 71	⊢
	: , : , :
67	theorem		⊢
	proveit.logic.equality.equals_reversal
68	instantiation	72, 139, 83, 73, 84, 74*, 75*	⊢
	: , : , :
69	instantiation	95, 76, 77	⊢
	: , : , :
70	instantiation	78, 79, 80, 81	⊢
	: , : , : , :
71	instantiation	82, 144	⊢
	:
72	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
73	instantiation	95, 83, 84	⊢
	: , : , :
74	instantiation	85, 117	⊢
	:
75	instantiation	123, 86, 87	⊢
	: , : , :
76	instantiation	88, 112, 113, 89, 90	⊢
	: , : , : , : , :
77	instantiation	123, 91, 92	⊢
	: , : , :
78	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
79	instantiation	133, 93	⊢
	: , : , :
80	instantiation	133, 94	⊢
	: , : , :
81	instantiation	142, 113	⊢
	:
82	theorem		⊢
	proveit.numbers.negation.int_closure
83	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
84	instantiation	95, 96, 97	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.addition.elim_zero_left
86	instantiation	98, 99, 100, 152, 101, 102, 105, 103, 117	⊢
	: , : , : , : , : , :
87	instantiation	104, 117, 105, 106	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
89	instantiation	159, 108, 107	⊢
	: , : , :
90	instantiation	159, 108, 109	⊢
	: , : , :
91	instantiation	133, 110	⊢
	: , : , :
92	instantiation	133, 111	⊢
	: , : , :
93	instantiation	135, 112	⊢
	:
94	instantiation	135, 113	⊢
	:
95	theorem		⊢
	proveit.logic.equality.sub_right_side_into
96	instantiation	114, 153	⊢
	:
97	assumption		⊢
98	theorem		⊢
	proveit.numbers.addition.disassociation
99	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
100	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
101	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
102	instantiation	115	⊢
	: , :
103	instantiation	116, 117	⊢
	:
104	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
105	instantiation	159, 149, 118	⊢
	: , : , :
106	instantiation	119	⊢
	:
107	instantiation	159, 121, 120	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
109	instantiation	159, 121, 122	⊢
	: , : , :
110	instantiation	123, 124, 125	⊢
	: , : , :
111	instantiation	133, 126	⊢
	: , : , :
112	instantiation	159, 149, 127	⊢
	: , : , :
113	instantiation	159, 149, 128	⊢
	: , : , :
114	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
115	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
116	theorem		⊢
	proveit.numbers.negation.complex_closure
117	instantiation	159, 149, 129	⊢
	: , : , :
118	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
119	axiom		⊢
	proveit.logic.equality.equals_reflexivity
120	instantiation	159, 131, 130	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
122	instantiation	159, 131, 132	⊢
	: , : , :
123	axiom		⊢
	proveit.logic.equality.equals_transitivity
124	instantiation	133, 134	⊢
	: , : , :
125	instantiation	135, 143	⊢
	:
126	instantiation	136, 143	⊢
	:
127	instantiation	159, 138, 137	⊢
	: , : , :
128	instantiation	159, 138, 146	⊢
	: , : , :
129	instantiation	159, 138, 139	⊢
	: , : , :
130	instantiation	159, 140, 161	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
132	instantiation	159, 140, 141	⊢
	: , : , :
133	axiom		⊢
	proveit.logic.equality.substitution
134	instantiation	142, 143	⊢
	:
135	theorem		⊢
	proveit.numbers.division.frac_one_denom
136	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
137	instantiation	159, 154, 144	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
139	instantiation	145, 146, 147, 148	⊢
	: , :
140	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
141	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
142	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
143	instantiation	159, 149, 150	⊢
	: , : , :
144	instantiation	159, 151, 152	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.division.div_rational_closure
146	instantiation	159, 154, 153	⊢
	: , : , :
147	instantiation	159, 154, 155	⊢
	: , : , :
148	instantiation	156, 161	⊢
	:
149	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
150	instantiation	157, 158, 161	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
152	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
153	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
154	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
155	instantiation	159, 160, 161	⊢
	: , : , :
156	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
157	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
158	instantiation	162, 163	⊢
	: , :
159	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
160	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
161	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
162	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
163	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements