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	reference	26	⊢
2	reference	144	⊢
3	instantiation	179, 142, 69	⊢
	: , : , :
4	instantiation	179, 169, 7	⊢
	: , : , :
5	instantiation	8, 151, 61, 9, 124, 10, 11*	⊢
	: , : , :
6	instantiation	104, 12, 13	⊢
	: , : , :
7	instantiation	179, 14, 15	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
9	instantiation	40, 29, 27	⊢
	: , :
10	instantiation	16, 17, 18	⊢
	: , : , :
11	instantiation	19, 154, 69, 99	⊢
	: , :
12	instantiation	63, 116, 178, 181, 117, 20, 141, 35, 134	⊢
	: , : , : , : , : , :
13	instantiation	104, 21, 22	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
15	instantiation	23, 149, 24	⊢
	: , :
16	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
17	instantiation	25, 61	⊢
	:
18	instantiation	26, 27, 28, 29, 30, 31*	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.exponentiation.exponent_log_with_same_base
20	instantiation	130	⊢
	: , :
21	instantiation	32, 181, 116, 117, 141, 35, 134	⊢
	: , : , : , : , : , : , :
22	instantiation	33, 116, 178, 181, 117, 34, 141, 134, 35, 36*	⊢
	: , : , : , : , : , :
23	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
24	instantiation	37, 38, 39	⊢
	: , :
25	theorem		⊢
	proveit.numbers.rounding.ceil_x_ge_x
26	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
27	instantiation	156, 77	⊢
	:
28	instantiation	40, 77, 41	⊢
	: , :
29	instantiation	80, 81, 49	⊢
	: , : , :
30	axiom		⊢
	proveit.physics.quantum.QPE._t_req
31	instantiation	42, 43, 44, 45	⊢
	: , : , : , :
32	theorem		⊢
	proveit.numbers.addition.leftward_commutation
33	theorem		⊢
	proveit.numbers.addition.association
34	instantiation	130	⊢
	: , :
35	instantiation	179, 150, 46	⊢
	: , : , :
36	instantiation	47, 114, 141, 48	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
38	instantiation	179, 56, 49	⊢
	: , : , :
39	instantiation	50, 51	⊢
	:
40	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
41	instantiation	179, 169, 52	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
43	instantiation	104, 53, 54	⊢
	: , : , :
44	instantiation	74	⊢
	:
45	instantiation	55, 62	⊢
	: , :
46	instantiation	179, 142, 75	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
48	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
49	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
50	theorem		⊢
	proveit.numbers.negation.int_closure
51	instantiation	179, 56, 82	⊢
	: , : , :
52	instantiation	179, 176, 57	⊢
	: , : , :
53	instantiation	102, 58	⊢
	: , : , :
54	instantiation	104, 59, 60	⊢
	: , : , :
55	theorem		⊢
	proveit.logic.equality.equals_reversal
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
57	instantiation	90, 61	⊢
	:
58	instantiation	102, 62	⊢
	: , : , :
59	instantiation	63, 116, 178, 181, 117, 64, 72, 67, 65	⊢
	: , : , : , : , : , :
60	instantiation	66, 72, 67, 68	⊢
	: , : , :
61	instantiation	97, 154, 69, 99	⊢
	: , :
62	instantiation	102, 70	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.addition.disassociation
64	instantiation	130	⊢
	: , :
65	instantiation	71, 72	⊢
	:
66	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
67	instantiation	179, 150, 73	⊢
	: , : , :
68	instantiation	74	⊢
	:
69	instantiation	107, 154, 75	⊢
	: , :
70	instantiation	102, 76	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.negation.complex_closure
72	instantiation	179, 150, 77	⊢
	: , : , :
73	instantiation	179, 169, 78	⊢
	: , : , :
74	axiom		⊢
	proveit.logic.equality.equals_reflexivity
75	instantiation	152, 153, 101, 86	⊢
	: , :
76	instantiation	102, 79	⊢
	: , : , :
77	instantiation	80, 81, 82	⊢
	: , : , :
78	instantiation	179, 176, 83	⊢
	: , : , :
79	instantiation	84, 114, 85, 86, 87*	⊢
	: , :
80	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
81	instantiation	88, 89	⊢
	: , :
82	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
83	instantiation	90, 91	⊢
	:
84	theorem		⊢
	proveit.numbers.division.div_as_mult
85	instantiation	179, 150, 92	⊢
	: , : , :
86	instantiation	93, 94	⊢
	:
87	instantiation	104, 95, 96	⊢
	: , : , :
88	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
89	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
90	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
91	instantiation	97, 154, 98, 99	⊢
	: , :
92	instantiation	179, 142, 101	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
94	instantiation	179, 100, 101	⊢
	: , : , :
95	instantiation	102, 103	⊢
	: , : , :
96	instantiation	104, 105, 106	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
98	instantiation	107, 154, 108	⊢
	: , :
99	instantiation	125, 109	⊢
	: , :
100	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
101	instantiation	121, 154, 136	⊢
	: , :
102	axiom		⊢
	proveit.logic.equality.substitution
103	instantiation	110, 141, 133, 144, 155, 111, 112*	⊢
	: , : , :
104	axiom		⊢
	proveit.logic.equality.equals_transitivity
105	instantiation	113, 181, 178, 116, 118, 117, 114, 119, 120	⊢
	: , : , : , : , : , :
106	instantiation	115, 116, 178, 117, 118, 119, 120	⊢
	: , : , : , :
107	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
108	instantiation	121, 143, 122	⊢
	: , :
109	instantiation	123, 181, 178, 124	⊢
	: , :
110	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
111	instantiation	125, 126	⊢
	: , :
112	instantiation	127, 128, 173, 129*	⊢
	: , :
113	theorem		⊢
	proveit.numbers.multiplication.disassociation
114	instantiation	179, 150, 160	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
116	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
117	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
118	instantiation	130	⊢
	: , :
119	instantiation	179, 150, 131	⊢
	: , : , :
120	instantiation	132, 133, 134	⊢
	: , :
121	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
122	instantiation	135, 136, 144	⊢
	: , :
123	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
124	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
125	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
126	instantiation	137, 159, 146, 147	⊢
	: , :
127	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
128	instantiation	179, 138, 139	⊢
	: , : , :
129	instantiation	140, 141	⊢
	:
130	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
131	instantiation	179, 142, 143	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
133	instantiation	179, 150, 146	⊢
	: , : , :
134	instantiation	179, 150, 144	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
136	instantiation	145, 146, 147	⊢
	:
137	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
138	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
139	instantiation	179, 148, 149	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
141	instantiation	179, 150, 151	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
143	instantiation	152, 153, 154, 155	⊢
	: , :
144	instantiation	156, 160	⊢
	:
145	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
146	instantiation	157, 159, 160, 161	⊢
	: , : , :
147	instantiation	158, 159, 160, 161	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
149	instantiation	179, 162, 163	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
151	instantiation	179, 169, 164	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
153	instantiation	179, 166, 165	⊢
	: , : , :
154	instantiation	179, 166, 167	⊢
	: , : , :
155	instantiation	168, 175	⊢
	:
156	theorem		⊢
	proveit.numbers.negation.real_closure
157	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
158	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
159	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
160	instantiation	179, 169, 170	⊢
	: , : , :
161	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
162	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
163	instantiation	179, 171, 175	⊢
	: , : , :
164	instantiation	179, 176, 172	⊢
	: , : , :
165	instantiation	179, 174, 173	⊢
	: , : , :
166	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
167	instantiation	179, 174, 175	⊢
	: , : , :
168	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
169	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
170	instantiation	179, 176, 177	⊢
	: , : , :
171	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
172	instantiation	179, 180, 178	⊢
	: , : , :
173	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
174	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
175	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
176	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
177	instantiation	179, 180, 181	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
179	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
180	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
181	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements