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	,  ⊢
	:
1	axiom		⊢
	proveit.logic.booleans.eq_true_intro
2	instantiation	100, 3, 4	,  ⊢
	: , : , :
3	instantiation	5, 133, 15, 6, 7, 8*, 9*	,  ⊢
	: , : , :
4	instantiation	10, 11, 12*	,  ⊢
	:
5	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
6	instantiation	13, 40, 112	,  ⊢
	: , :
7	instantiation	14, 15, 40, 112, 56, 92	,  ⊢
	: , : , :
8	instantiation	67, 16, 17	⊢
	: , : , :
9	instantiation	67, 18, 19	,  ⊢
	: , : , :
10	theorem		⊢
	proveit.physics.quantum.QPE._modabs_in_full_domain_simp
11	instantiation	20, 21, 116, 49, 22	,  ⊢
	: , : , :
12	instantiation	23, 24	,  ⊢
	:
13	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
14	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
15	instantiation	160, 144, 25	⊢
	: , : , :
16	instantiation	28, 29, 157, 162, 30, 26, 27, 99, 120	⊢
	: , : , : , : , : , :
17	instantiation	32, 99, 27, 34	⊢
	: , : , :
18	instantiation	28, 29, 157, 162, 30, 31, 33, 99, 120	,  ⊢
	: , : , : , : , : , :
19	instantiation	32, 99, 33, 34	,  ⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
21	instantiation	115, 84, 156	⊢
	: , :
22	instantiation	35, 36, 37	,  ⊢
	: , :
23	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
24	instantiation	41, 48	,  ⊢
	: , :
25	instantiation	160, 151, 65	⊢
	: , : , :
26	instantiation	39	⊢
	: , :
27	instantiation	160, 134, 38	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.disassociation
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
31	instantiation	39	⊢
	: , :
32	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
33	instantiation	160, 134, 40	,  ⊢
	: , : , :
34	instantiation	80	⊢
	:
35	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
36	instantiation	41, 42	,  ⊢
	: , :
37	instantiation	43, 65, 116, 64	,  ⊢
	: , : , :
38	instantiation	160, 144, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	instantiation	160, 144, 45	,  ⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.ordering.relax_less
42	instantiation	46, 47, 48	,  ⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
44	instantiation	160, 151, 82	⊢
	: , : , :
45	instantiation	160, 151, 49	,  ⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
47	instantiation	50, 66, 112, 51, 52, 53*, 54*	⊢
	: , : , :
48	instantiation	91, 55, 56	,  ⊢
	: , : , :
49	instantiation	160, 57, 64	,  ⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
51	instantiation	140, 141, 131	⊢
	: , : , :
52	instantiation	58, 131	⊢
	:
53	instantiation	118, 99, 59	⊢
	: , :
54	instantiation	67, 60, 61	⊢
	: , : , :
55	instantiation	62, 63	⊢
	:
56	instantiation	104, 65, 116, 64	,  ⊢
	: , : , :
57	instantiation	103, 65, 116	⊢
	: , :
58	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
59	instantiation	160, 134, 66	⊢
	: , : , :
60	instantiation	67, 68, 69	⊢
	: , : , :
61	instantiation	70, 71, 72	⊢
	: , :
62	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
63	instantiation	73, 74, 126	⊢
	: , :
64	assumption		⊢
65	instantiation	115, 82, 156	⊢
	: , :
66	instantiation	160, 144, 75	⊢
	: , : , :
67	axiom		⊢
	proveit.logic.equality.equals_transitivity
68	instantiation	110, 85	⊢
	: , : , :
69	instantiation	110, 76	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
71	instantiation	77, 78, 79	⊢
	: , :
72	instantiation	80	⊢
	:
73	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
74	instantiation	81, 82, 83	⊢
	:
75	instantiation	160, 151, 84	⊢
	: , : , :
76	instantiation	110, 85	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
78	instantiation	86, 99, 87, 88	⊢
	: , :
79	instantiation	160, 134, 89	⊢
	: , : , :
80	axiom		⊢
	proveit.logic.equality.equals_reflexivity
81	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
82	instantiation	160, 90, 106	⊢
	: , : , :
83	instantiation	91, 92, 93	⊢
	: , : , :
84	instantiation	155, 116	⊢
	:
85	instantiation	94, 95, 96, 97	⊢
	: , : , : , :
86	theorem		⊢
	proveit.numbers.division.div_complex_closure
87	instantiation	98, 122, 99	⊢
	: , :
88	instantiation	100, 123, 101	⊢
	: , : , :
89	instantiation	160, 144, 102	⊢
	: , : , :
90	instantiation	103, 156, 105	⊢
	: , :
91	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
92	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
93	instantiation	104, 156, 105, 106	⊢
	: , : , :
94	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
95	instantiation	110, 107	⊢
	: , : , :
96	instantiation	108, 109	⊢
	: , :
97	instantiation	110, 111	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
99	instantiation	160, 134, 112	⊢
	: , : , :
100	theorem		⊢
	proveit.logic.equality.sub_left_side_into
101	instantiation	113, 122	⊢
	:
102	instantiation	160, 151, 114	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
104	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
105	instantiation	115, 116, 117	⊢
	: , :
106	assumption		⊢
107	instantiation	118, 119, 120	⊢
	: , :
108	theorem		⊢
	proveit.logic.equality.equals_reversal
109	instantiation	121, 122, 133, 132, 123	⊢
	: , : , :
110	axiom		⊢
	proveit.logic.equality.substitution
111	instantiation	124, 125, 126	⊢
	: , :
112	instantiation	160, 144, 127	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
114	instantiation	128, 152, 129	⊢
	: , :
115	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
116	instantiation	160, 130, 131	⊢
	: , : , :
117	instantiation	155, 152	⊢
	:
118	theorem		⊢
	proveit.numbers.addition.commutation
119	instantiation	160, 134, 132	⊢
	: , : , :
120	instantiation	160, 134, 133	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
122	instantiation	160, 134, 135	⊢
	: , : , :
123	instantiation	136, 159	⊢
	:
124	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
125	instantiation	160, 137, 138	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
127	instantiation	160, 151, 156	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
129	instantiation	160, 139, 142	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
131	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
132	instantiation	140, 141, 142	⊢
	: , : , :
133	instantiation	160, 144, 143	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
135	instantiation	160, 144, 145	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
137	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
138	instantiation	160, 146, 147	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
140	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
141	instantiation	148, 149	⊢
	: , :
142	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
143	instantiation	160, 151, 150	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
145	instantiation	160, 151, 152	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
147	instantiation	160, 153, 154	⊢
	: , : , :
148	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
149	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
150	instantiation	155, 156	⊢
	:
151	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
152	instantiation	160, 161, 157	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
154	instantiation	160, 158, 159	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.negation.int_closure
156	instantiation	160, 161, 162	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
158	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
159	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
160	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
161	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
162	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements