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.exponentiation.exp_monotonicity_large_base_less_eq
2	reference	132	⊢
3	instantiation	46, 31, 92	⊢
	: , :
4	reference	158	⊢
5	instantiation	15, 7, 8	⊢
	: , : , :
6	instantiation	9, 10, 11, 125	⊢
	: , : , : , :
7	instantiation	12, 183, 27, 13, 14*	⊢
	: , :
8	instantiation	15, 16, 17	⊢
	: , : , :
9	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
10	instantiation	18, 174, 121	⊢
	: , :
11	instantiation	19, 157, 20, 21, 22	⊢
	: , : , : , :
12	theorem		⊢
	proveit.numbers.rounding.ceil_of_real_above_int
13	instantiation	23, 166, 44, 24, 158, 25*	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
15	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
16	instantiation	26, 27, 139, 28	⊢
	: , :
17	instantiation	29, 92, 30, 31, 32, 33*	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.exponentiation.exp_nat_pos_expansion
19	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
20	instantiation	34, 157	⊢
	: , :
21	instantiation	133	⊢
	: , :
22	instantiation	35	⊢
	:
23	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less
24	instantiation	36, 132, 37, 38, 39, 40*, 41*	⊢
	: , : , :
25	instantiation	42, 166	⊢
	:
26	theorem		⊢
	proveit.numbers.rounding.ceil_increasing_less_eq
27	instantiation	144, 166, 44, 146	⊢
	: , :
28	instantiation	43, 166, 44, 145, 45, 158	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
30	instantiation	46, 113, 93	⊢
	: , :
31	instantiation	127, 128, 47	⊢
	: , : , :
32	axiom		⊢
	proveit.physics.quantum.QPE._t_req
33	instantiation	108, 48, 49	⊢
	: , : , :
34	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
35	theorem		⊢
	proveit.numbers.numerals.decimals.reduce_2_repeats
36	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
37	instantiation	50, 115, 177	⊢
	: , :
38	instantiation	184, 180, 51	⊢
	: , : , :
39	instantiation	52, 115, 177, 178, 53, 54	⊢
	: , : , :
40	instantiation	108, 55, 56	⊢
	: , : , :
41	instantiation	108, 57, 58	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.logarithms.log_eq_1
43	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less_eq
44	instantiation	153, 59, 166, 83	⊢
	: , :
45	instantiation	60, 132, 61, 62, 63, 64*	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
47	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
48	instantiation	65, 66, 157, 186, 67, 68, 71, 72, 69	⊢
	: , : , : , : , : , :
49	instantiation	70, 71, 72, 73	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
51	instantiation	74, 131, 181	⊢
	: , :
52	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
53	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
54	instantiation	75, 141	⊢
	:
55	instantiation	78, 76	⊢
	: , : , :
56	instantiation	77, 121	⊢
	:
57	instantiation	78, 79	⊢
	: , : , :
58	instantiation	88, 183, 148, 89*, 80*, 106*	⊢
	: , : , : , :
59	instantiation	184, 168, 81	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
61	instantiation	82, 178, 132, 83	⊢
	: , :
62	instantiation	184, 84, 150	⊢
	: , : , :
63	instantiation	85, 86, 164, 166, 87	⊢
	: , : , :
64	instantiation	88, 148, 183, 89*, 90*, 91*	⊢
	: , : , : , :
65	theorem		⊢
	proveit.numbers.addition.disassociation
66	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
67	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
68	instantiation	133	⊢
	: , :
69	instantiation	184, 143, 92	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
71	instantiation	184, 143, 113	⊢
	: , : , :
72	instantiation	184, 143, 93	⊢
	: , : , :
73	instantiation	94	⊢
	:
74	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
75	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
76	instantiation	95, 96	⊢
	:
77	theorem		⊢
	proveit.numbers.addition.elim_zero_left
78	axiom		⊢
	proveit.logic.equality.substitution
79	instantiation	134, 96	⊢
	:
80	instantiation	108, 97, 98	⊢
	: , : , :
81	instantiation	184, 173, 99	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.division.div_real_closure
83	instantiation	100, 174	⊢
	:
84	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
85	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
86	instantiation	184, 101, 102	⊢
	: , : , :
87	instantiation	103, 132, 171, 178, 104, 105, 106*	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
89	instantiation	107, 121	⊢
	:
90	instantiation	108, 109, 110	⊢
	: , : , :
91	instantiation	111, 121	⊢
	:
92	instantiation	112, 113	⊢
	:
93	instantiation	184, 180, 114	⊢
	: , : , :
94	axiom		⊢
	proveit.logic.equality.equals_reflexivity
95	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
96	instantiation	184, 143, 115	⊢
	: , : , :
97	instantiation	122, 157, 116, 117, 126, 125	⊢
	: , : , : , :
98	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_4
99	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
100	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
102	instantiation	184, 118, 186	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
104	instantiation	119, 177, 178, 179	⊢
	: , : , :
105	instantiation	120, 157	⊢
	:
106	instantiation	134, 121	⊢
	:
107	theorem		⊢
	proveit.numbers.division.frac_one_denom
108	axiom		⊢
	proveit.logic.equality.equals_transitivity
109	instantiation	122, 157, 123, 124, 125, 126	⊢
	: , : , : , :
110	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
111	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
112	theorem		⊢
	proveit.numbers.negation.real_closure
113	instantiation	127, 128, 129	⊢
	: , : , :
114	instantiation	184, 182, 130	⊢
	: , : , :
115	instantiation	184, 180, 131	⊢
	: , : , :
116	instantiation	133	⊢
	: , :
117	instantiation	133	⊢
	: , :
118	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
120	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
121	instantiation	184, 143, 132	⊢
	: , : , :
122	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
123	instantiation	133	⊢
	: , :
124	instantiation	133	⊢
	: , :
125	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
126	instantiation	134, 135	⊢
	:
127	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
128	instantiation	136, 137	⊢
	: , :
129	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
130	instantiation	138, 139	⊢
	:
131	instantiation	184, 140, 141	⊢
	: , : , :
132	instantiation	184, 180, 142	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
134	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
135	instantiation	184, 143, 178	⊢
	: , : , :
136	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
137	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
138	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
139	instantiation	144, 166, 145, 146	⊢
	: , :
140	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
141	instantiation	147, 159, 169	⊢
	: , :
142	instantiation	184, 182, 148	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
144	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
145	instantiation	149, 166, 150	⊢
	: , :
146	instantiation	151, 152	⊢
	: , :
147	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
148	instantiation	184, 185, 157	⊢
	: , : , :
149	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
150	instantiation	153, 154, 164, 155	⊢
	: , :
151	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
152	instantiation	156, 186, 157, 158	⊢
	: , :
153	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
154	instantiation	184, 168, 159	⊢
	: , : , :
155	instantiation	160, 161	⊢
	:
156	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
157	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
158	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
159	instantiation	184, 173, 162	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
161	instantiation	184, 163, 164	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
163	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
164	instantiation	165, 166, 167	⊢
	: , :
165	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
166	instantiation	184, 168, 169	⊢
	: , : , :
167	instantiation	170, 171, 172	⊢
	:
168	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
169	instantiation	184, 173, 174	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
171	instantiation	175, 177, 178, 179	⊢
	: , : , :
172	instantiation	176, 177, 178, 179	⊢
	: , : , :
173	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
174	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
175	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
176	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
177	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
178	instantiation	184, 180, 181	⊢
	: , : , :
179	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
180	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
181	instantiation	184, 182, 183	⊢
	: , : , :
182	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
183	instantiation	184, 185, 186	⊢
	: , : , :
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