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	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
2	instantiation	4, 26	⊢
	:
3	instantiation	5, 6, 7, 8, 9, 10*	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.rounding.ceil_x_ge_x
5	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
6	instantiation	121, 42	⊢
	:
7	instantiation	11, 42, 12	⊢
	: , :
8	instantiation	45, 46, 13	⊢
	: , : , :
9	axiom		⊢
	proveit.physics.quantum.QPE._t_req
10	instantiation	14, 15, 16, 17	⊢
	: , : , : , :
11	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
12	instantiation	144, 134, 18	⊢
	: , : , :
13	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
14	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
15	instantiation	69, 19, 20	⊢
	: , : , :
16	instantiation	39	⊢
	:
17	instantiation	21, 27	⊢
	: , :
18	instantiation	144, 141, 22	⊢
	: , : , :
19	instantiation	67, 23	⊢
	: , : , :
20	instantiation	69, 24, 25	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.equality.equals_reversal
22	instantiation	55, 26	⊢
	:
23	instantiation	67, 27	⊢
	: , : , :
24	instantiation	28, 81, 143, 146, 82, 29, 37, 32, 30	⊢
	: , : , : , : , : , :
25	instantiation	31, 37, 32, 33	⊢
	: , : , :
26	instantiation	62, 119, 34, 64	⊢
	: , :
27	instantiation	67, 35	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.disassociation
29	instantiation	95	⊢
	: , :
30	instantiation	36, 37	⊢
	:
31	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
32	instantiation	144, 115, 38	⊢
	: , : , :
33	instantiation	39	⊢
	:
34	instantiation	72, 119, 40	⊢
	: , :
35	instantiation	67, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.negation.complex_closure
37	instantiation	144, 115, 42	⊢
	: , : , :
38	instantiation	144, 134, 43	⊢
	: , : , :
39	axiom		⊢
	proveit.logic.equality.equals_reflexivity
40	instantiation	117, 118, 66, 51	⊢
	: , :
41	instantiation	67, 44	⊢
	: , : , :
42	instantiation	45, 46, 47	⊢
	: , : , :
43	instantiation	144, 141, 48	⊢
	: , : , :
44	instantiation	49, 79, 50, 51, 52*	⊢
	: , :
45	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
46	instantiation	53, 54	⊢
	: , :
47	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
48	instantiation	55, 56	⊢
	:
49	theorem		⊢
	proveit.numbers.division.div_as_mult
50	instantiation	144, 115, 57	⊢
	: , : , :
51	instantiation	58, 59	⊢
	:
52	instantiation	69, 60, 61	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
55	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
56	instantiation	62, 119, 63, 64	⊢
	: , :
57	instantiation	144, 107, 66	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
59	instantiation	144, 65, 66	⊢
	: , : , :
60	instantiation	67, 68	⊢
	: , : , :
61	instantiation	69, 70, 71	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
63	instantiation	72, 119, 73	⊢
	: , :
64	instantiation	90, 74	⊢
	: , :
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
66	instantiation	86, 119, 101	⊢
	: , :
67	axiom		⊢
	proveit.logic.equality.substitution
68	instantiation	75, 106, 98, 109, 120, 76, 77*	⊢
	: , : , :
69	axiom		⊢
	proveit.logic.equality.equals_transitivity
70	instantiation	78, 146, 143, 81, 83, 82, 79, 84, 85	⊢
	: , : , : , : , : , :
71	instantiation	80, 81, 143, 82, 83, 84, 85	⊢
	: , : , : , :
72	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
73	instantiation	86, 108, 87	⊢
	: , :
74	instantiation	88, 146, 143, 89	⊢
	: , :
75	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
76	instantiation	90, 91	⊢
	: , :
77	instantiation	92, 93, 138, 94*	⊢
	: , :
78	theorem		⊢
	proveit.numbers.multiplication.disassociation
79	instantiation	144, 115, 125	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
81	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
82	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
83	instantiation	95	⊢
	: , :
84	instantiation	144, 115, 96	⊢
	: , : , :
85	instantiation	97, 98, 99	⊢
	: , :
86	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
87	instantiation	100, 101, 109	⊢
	: , :
88	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
89	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
90	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
91	instantiation	102, 124, 111, 112	⊢
	: , :
92	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
93	instantiation	144, 103, 104	⊢
	: , : , :
94	instantiation	105, 106	⊢
	:
95	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
96	instantiation	144, 107, 108	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
98	instantiation	144, 115, 111	⊢
	: , : , :
99	instantiation	144, 115, 109	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
101	instantiation	110, 111, 112	⊢
	:
102	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
103	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
104	instantiation	144, 113, 114	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
106	instantiation	144, 115, 116	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
108	instantiation	117, 118, 119, 120	⊢
	: , :
109	instantiation	121, 125	⊢
	:
110	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
111	instantiation	122, 124, 125, 126	⊢
	: , : , :
112	instantiation	123, 124, 125, 126	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
114	instantiation	144, 127, 128	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
116	instantiation	144, 134, 129	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
118	instantiation	144, 131, 130	⊢
	: , : , :
119	instantiation	144, 131, 132	⊢
	: , : , :
120	instantiation	133, 140	⊢
	:
121	theorem		⊢
	proveit.numbers.negation.real_closure
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
125	instantiation	144, 134, 135	⊢
	: , : , :
126	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
127	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
128	instantiation	144, 136, 140	⊢
	: , : , :
129	instantiation	144, 141, 137	⊢
	: , : , :
130	instantiation	144, 139, 138	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
132	instantiation	144, 139, 140	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
134	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
135	instantiation	144, 141, 142	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
137	instantiation	144, 145, 143	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
139	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
140	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
141	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
142	instantiation	144, 145, 146	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
144	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
145	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
146	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements