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.addition.weak_bound_via_left_term_bound
2	instantiation	117, 38	⊢
	:
3	instantiation	7, 38, 8	⊢
	: , :
4	instantiation	41, 42, 9	⊢
	: , : , :
5	axiom		⊢
	proveit.physics.quantum.QPE._t_req
6	instantiation	10, 11, 12, 13	⊢
	: , : , : , :
7	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
8	instantiation	140, 130, 14	⊢
	: , : , :
9	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
10	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
11	instantiation	65, 15, 16	⊢
	: , : , :
12	instantiation	35	⊢
	:
13	instantiation	17, 23	⊢
	: , :
14	instantiation	140, 137, 18	⊢
	: , : , :
15	instantiation	63, 19	⊢
	: , : , :
16	instantiation	65, 20, 21	⊢
	: , : , :
17	theorem		⊢
	proveit.logic.equality.equals_reversal
18	instantiation	51, 22	⊢
	:
19	instantiation	63, 23	⊢
	: , : , :
20	instantiation	24, 77, 139, 142, 78, 25, 33, 28, 26	⊢
	: , : , : , : , : , :
21	instantiation	27, 33, 28, 29	⊢
	: , : , :
22	instantiation	58, 115, 30, 60	⊢
	: , :
23	instantiation	63, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.disassociation
25	instantiation	91	⊢
	: , :
26	instantiation	32, 33	⊢
	:
27	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
28	instantiation	140, 111, 34	⊢
	: , : , :
29	instantiation	35	⊢
	:
30	instantiation	68, 115, 36	⊢
	: , :
31	instantiation	63, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.negation.complex_closure
33	instantiation	140, 111, 38	⊢
	: , : , :
34	instantiation	140, 130, 39	⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.equals_reflexivity
36	instantiation	113, 114, 62, 47	⊢
	: , :
37	instantiation	63, 40	⊢
	: , : , :
38	instantiation	41, 42, 43	⊢
	: , : , :
39	instantiation	140, 137, 44	⊢
	: , : , :
40	instantiation	45, 75, 46, 47, 48*	⊢
	: , :
41	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
42	instantiation	49, 50	⊢
	: , :
43	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
44	instantiation	51, 52	⊢
	:
45	theorem		⊢
	proveit.numbers.division.div_as_mult
46	instantiation	140, 111, 53	⊢
	: , : , :
47	instantiation	54, 55	⊢
	:
48	instantiation	65, 56, 57	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
51	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
52	instantiation	58, 115, 59, 60	⊢
	: , :
53	instantiation	140, 103, 62	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
55	instantiation	140, 61, 62	⊢
	: , : , :
56	instantiation	63, 64	⊢
	: , : , :
57	instantiation	65, 66, 67	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
59	instantiation	68, 115, 69	⊢
	: , :
60	instantiation	86, 70	⊢
	: , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
62	instantiation	82, 115, 97	⊢
	: , :
63	axiom		⊢
	proveit.logic.equality.substitution
64	instantiation	71, 102, 94, 105, 116, 72, 73*	⊢
	: , : , :
65	axiom		⊢
	proveit.logic.equality.equals_transitivity
66	instantiation	74, 142, 139, 77, 79, 78, 75, 80, 81	⊢
	: , : , : , : , : , :
67	instantiation	76, 77, 139, 78, 79, 80, 81	⊢
	: , : , : , :
68	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
69	instantiation	82, 104, 83	⊢
	: , :
70	instantiation	84, 142, 139, 85	⊢
	: , :
71	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
72	instantiation	86, 87	⊢
	: , :
73	instantiation	88, 89, 134, 90*	⊢
	: , :
74	theorem		⊢
	proveit.numbers.multiplication.disassociation
75	instantiation	140, 111, 121	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
77	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
78	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
79	instantiation	91	⊢
	: , :
80	instantiation	140, 111, 92	⊢
	: , : , :
81	instantiation	93, 94, 95	⊢
	: , :
82	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
83	instantiation	96, 97, 105	⊢
	: , :
84	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
85	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
86	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
87	instantiation	98, 120, 107, 108	⊢
	: , :
88	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
89	instantiation	140, 99, 100	⊢
	: , : , :
90	instantiation	101, 102	⊢
	:
91	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
92	instantiation	140, 103, 104	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
94	instantiation	140, 111, 107	⊢
	: , : , :
95	instantiation	140, 111, 105	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
97	instantiation	106, 107, 108	⊢
	:
98	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
99	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
100	instantiation	140, 109, 110	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
102	instantiation	140, 111, 112	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
104	instantiation	113, 114, 115, 116	⊢
	: , :
105	instantiation	117, 121	⊢
	:
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
107	instantiation	118, 120, 121, 122	⊢
	: , : , :
108	instantiation	119, 120, 121, 122	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
110	instantiation	140, 123, 124	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
112	instantiation	140, 130, 125	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
114	instantiation	140, 127, 126	⊢
	: , : , :
115	instantiation	140, 127, 128	⊢
	: , : , :
116	instantiation	129, 136	⊢
	:
117	theorem		⊢
	proveit.numbers.negation.real_closure
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
120	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
121	instantiation	140, 130, 131	⊢
	: , : , :
122	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
123	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
124	instantiation	140, 132, 136	⊢
	: , : , :
125	instantiation	140, 137, 133	⊢
	: , : , :
126	instantiation	140, 135, 134	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
128	instantiation	140, 135, 136	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
130	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
131	instantiation	140, 137, 138	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
133	instantiation	140, 141, 139	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
135	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
136	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
137	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
138	instantiation	140, 141, 142	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
140	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
141	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
142	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements