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.logic.booleans.conjunction.and_if_both
2	instantiation	4, 5	⊢
	:
3	instantiation	31, 149, 6, 7, 8, 9*	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg
5	instantiation	184, 10, 11	⊢
	: , : , :
6	instantiation	184, 147, 74	⊢
	: , : , :
7	instantiation	184, 174, 12	⊢
	: , : , :
8	instantiation	13, 156, 66, 14, 129, 15, 16*	⊢
	: , : , :
9	instantiation	109, 17, 18	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg
11	instantiation	112, 158, 80	⊢
	: , :
12	instantiation	184, 19, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
14	instantiation	45, 34, 32	⊢
	: , :
15	instantiation	21, 22, 23	⊢
	: , : , :
16	instantiation	24, 159, 74, 104	⊢
	: , :
17	instantiation	68, 121, 183, 186, 122, 25, 146, 40, 139	⊢
	: , : , : , : , : , :
18	instantiation	109, 26, 27	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
20	instantiation	28, 154, 29	⊢
	: , :
21	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
22	instantiation	30, 66	⊢
	:
23	instantiation	31, 32, 33, 34, 35, 36*	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.exponentiation.exponent_log_with_same_base
25	instantiation	135	⊢
	: , :
26	instantiation	37, 186, 121, 122, 146, 40, 139	⊢
	: , : , : , : , : , : , :
27	instantiation	38, 121, 183, 186, 122, 39, 146, 139, 40, 41*	⊢
	: , : , : , : , : , :
28	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
29	instantiation	42, 43, 44	⊢
	: , :
30	theorem		⊢
	proveit.numbers.rounding.ceil_x_ge_x
31	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
32	instantiation	161, 82	⊢
	:
33	instantiation	45, 82, 46	⊢
	: , :
34	instantiation	85, 86, 54	⊢
	: , : , :
35	axiom		⊢
	proveit.physics.quantum.QPE._t_req
36	instantiation	47, 48, 49, 50	⊢
	: , : , : , :
37	theorem		⊢
	proveit.numbers.addition.leftward_commutation
38	theorem		⊢
	proveit.numbers.addition.association
39	instantiation	135	⊢
	: , :
40	instantiation	184, 155, 51	⊢
	: , : , :
41	instantiation	52, 119, 146, 53	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
43	instantiation	184, 61, 54	⊢
	: , : , :
44	instantiation	55, 56	⊢
	:
45	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
46	instantiation	184, 174, 57	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
48	instantiation	109, 58, 59	⊢
	: , : , :
49	instantiation	79	⊢
	:
50	instantiation	60, 67	⊢
	: , :
51	instantiation	184, 147, 80	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
53	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
54	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
55	theorem		⊢
	proveit.numbers.negation.int_closure
56	instantiation	184, 61, 87	⊢
	: , : , :
57	instantiation	184, 181, 62	⊢
	: , : , :
58	instantiation	107, 63	⊢
	: , : , :
59	instantiation	109, 64, 65	⊢
	: , : , :
60	theorem		⊢
	proveit.logic.equality.equals_reversal
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
62	instantiation	95, 66	⊢
	:
63	instantiation	107, 67	⊢
	: , : , :
64	instantiation	68, 121, 183, 186, 122, 69, 77, 72, 70	⊢
	: , : , : , : , : , :
65	instantiation	71, 77, 72, 73	⊢
	: , : , :
66	instantiation	102, 159, 74, 104	⊢
	: , :
67	instantiation	107, 75	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.addition.disassociation
69	instantiation	135	⊢
	: , :
70	instantiation	76, 77	⊢
	:
71	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
72	instantiation	184, 155, 78	⊢
	: , : , :
73	instantiation	79	⊢
	:
74	instantiation	112, 159, 80	⊢
	: , :
75	instantiation	107, 81	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.negation.complex_closure
77	instantiation	184, 155, 82	⊢
	: , : , :
78	instantiation	184, 174, 83	⊢
	: , : , :
79	axiom		⊢
	proveit.logic.equality.equals_reflexivity
80	instantiation	157, 158, 106, 91	⊢
	: , :
81	instantiation	107, 84	⊢
	: , : , :
82	instantiation	85, 86, 87	⊢
	: , : , :
83	instantiation	184, 181, 88	⊢
	: , : , :
84	instantiation	89, 119, 90, 91, 92*	⊢
	: , :
85	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
86	instantiation	93, 94	⊢
	: , :
87	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
88	instantiation	95, 96	⊢
	:
89	theorem		⊢
	proveit.numbers.division.div_as_mult
90	instantiation	184, 155, 97	⊢
	: , : , :
91	instantiation	98, 99	⊢
	:
92	instantiation	109, 100, 101	⊢
	: , : , :
93	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
94	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
95	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
96	instantiation	102, 159, 103, 104	⊢
	: , :
97	instantiation	184, 147, 106	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
99	instantiation	184, 105, 106	⊢
	: , : , :
100	instantiation	107, 108	⊢
	: , : , :
101	instantiation	109, 110, 111	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
103	instantiation	112, 159, 113	⊢
	: , :
104	instantiation	130, 114	⊢
	: , :
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
106	instantiation	126, 159, 141	⊢
	: , :
107	axiom		⊢
	proveit.logic.equality.substitution
108	instantiation	115, 146, 138, 149, 160, 116, 117*	⊢
	: , : , :
109	axiom		⊢
	proveit.logic.equality.equals_transitivity
110	instantiation	118, 186, 183, 121, 123, 122, 119, 124, 125	⊢
	: , : , : , : , : , :
111	instantiation	120, 121, 183, 122, 123, 124, 125	⊢
	: , : , : , :
112	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
113	instantiation	126, 148, 127	⊢
	: , :
114	instantiation	128, 186, 183, 129	⊢
	: , :
115	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
116	instantiation	130, 131	⊢
	: , :
117	instantiation	132, 133, 178, 134*	⊢
	: , :
118	theorem		⊢
	proveit.numbers.multiplication.disassociation
119	instantiation	184, 155, 165	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
121	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
122	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
123	instantiation	135	⊢
	: , :
124	instantiation	184, 155, 136	⊢
	: , : , :
125	instantiation	137, 138, 139	⊢
	: , :
126	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
127	instantiation	140, 141, 149	⊢
	: , :
128	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
129	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
130	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
131	instantiation	142, 164, 151, 152	⊢
	: , :
132	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
133	instantiation	184, 143, 144	⊢
	: , : , :
134	instantiation	145, 146	⊢
	:
135	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
136	instantiation	184, 147, 148	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
138	instantiation	184, 155, 151	⊢
	: , : , :
139	instantiation	184, 155, 149	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
141	instantiation	150, 151, 152	⊢
	:
142	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
143	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
144	instantiation	184, 153, 154	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
146	instantiation	184, 155, 156	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
148	instantiation	157, 158, 159, 160	⊢
	: , :
149	instantiation	161, 165	⊢
	:
150	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
151	instantiation	162, 164, 165, 166	⊢
	: , : , :
152	instantiation	163, 164, 165, 166	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
154	instantiation	184, 167, 168	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
156	instantiation	184, 174, 169	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
158	instantiation	184, 171, 170	⊢
	: , : , :
159	instantiation	184, 171, 172	⊢
	: , : , :
160	instantiation	173, 180	⊢
	:
161	theorem		⊢
	proveit.numbers.negation.real_closure
162	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
163	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
164	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
165	instantiation	184, 174, 175	⊢
	: , : , :
166	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
167	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
168	instantiation	184, 176, 180	⊢
	: , : , :
169	instantiation	184, 181, 177	⊢
	: , : , :
170	instantiation	184, 179, 178	⊢
	: , : , :
171	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
172	instantiation	184, 179, 180	⊢
	: , : , :
173	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
174	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
175	instantiation	184, 181, 182	⊢
	: , : , :
176	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
177	instantiation	184, 185, 183	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
179	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
180	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
181	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
182	instantiation	184, 185, 186	⊢
	: , : , :
183	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
184	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
185	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
186	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements