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	reference	75	⊢
2	instantiation	4, 162, 5	⊢
	: , :
3	instantiation	137, 209	⊢
	:
4	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
5	instantiation	6, 7, 8	⊢
	:
6	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
7	instantiation	9, 10, 11	⊢
	: , :
8	instantiation	12, 13	⊢
	: , :
9	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
10	instantiation	215, 14, 98	⊢
	: , : , :
11	instantiation	215, 15, 16	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
13	instantiation	41, 17, 18	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
15	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
16	instantiation	19, 205	⊢
	:
17	axiom		⊢
	proveit.physics.quantum.QPE._n_ge_two
18	instantiation	56, 60, 162, 20, 21, 22*, 23*	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.negation.int_neg_closure
20	instantiation	75, 25, 162	⊢
	: , :
21	instantiation	24, 162, 25, 26, 132	⊢
	: , : , :
22	instantiation	143, 27, 28	⊢
	: , : , :
23	instantiation	143, 29, 30	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
25	instantiation	75, 77, 115	⊢
	: , :
26	instantiation	41, 31, 32	⊢
	: , : , :
27	instantiation	89, 217, 188, 90, 47, 91, 149, 95, 48	⊢
	: , : , : , : , : , :
28	instantiation	94, 149, 95, 65	⊢
	: , : , :
29	instantiation	122, 33	⊢
	: , : , :
30	instantiation	34, 35, 36, 37	⊢
	: , : , : , :
31	instantiation	38, 214, 54, 39, 40*	⊢
	: , :
32	instantiation	41, 42, 43	⊢
	: , : , :
33	instantiation	89, 90, 188, 217, 91, 64, 67, 93, 149	⊢
	: , : , : , : , : , :
34	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
35	instantiation	89, 90, 45, 217, 91, 46, 67, 93, 149, 44	⊢
	: , : , : , : , : , :
36	instantiation	89, 45, 188, 90, 46, 47, 91, 67, 93, 149, 95, 48	⊢
	: , : , : , : , : , :
37	instantiation	143, 49, 50	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.rounding.ceil_of_real_above_int
39	instantiation	51, 197, 71, 52	⊢
	: , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
41	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
42	instantiation	53, 54, 166, 55	⊢
	: , :
43	instantiation	56, 115, 57, 77, 58, 59*	⊢
	: , : , :
44	instantiation	215, 177, 60	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
46	instantiation	61	⊢
	: , : , :
47	instantiation	168	⊢
	: , :
48	instantiation	62, 149	⊢
	:
49	instantiation	63, 188, 217, 90, 64, 91, 67, 93, 149, 95, 65	⊢
	: , : , : , : , : , : , : , :
50	instantiation	66, 95, 67, 97	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.logarithms.log_base_large_a_greater_one
52	instantiation	68, 189, 69	⊢
	: , :
53	theorem		⊢
	proveit.numbers.rounding.ceil_increasing_less_eq
54	instantiation	172, 197, 71, 174	⊢
	: , :
55	instantiation	70, 197, 71, 173, 72, 189	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
57	instantiation	75, 138, 116	⊢
	: , :
58	axiom		⊢
	proveit.physics.quantum.QPE._t_req
59	instantiation	143, 73, 74	⊢
	: , : , :
60	instantiation	75, 138, 76	⊢
	: , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
62	theorem		⊢
	proveit.numbers.negation.complex_closure
63	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
64	instantiation	168	⊢
	: , :
65	instantiation	117	⊢
	:
66	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
67	instantiation	215, 177, 77	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
69	instantiation	78, 162, 79, 80, 81, 82*, 83*	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less_eq
71	instantiation	215, 199, 84	⊢
	: , : , :
72	instantiation	85, 162, 156, 86, 87, 88*	⊢
	: , : , :
73	instantiation	89, 90, 188, 217, 91, 92, 95, 96, 93	⊢
	: , : , : , : , : , :
74	instantiation	94, 95, 96, 97	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
76	instantiation	137, 162	⊢
	:
77	instantiation	152, 153, 98	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
79	instantiation	99, 156, 208	⊢
	: , :
80	instantiation	215, 211, 100	⊢
	: , : , :
81	instantiation	101, 156, 208, 209, 102, 103	⊢
	: , : , :
82	instantiation	143, 104, 105	⊢
	: , : , :
83	instantiation	143, 106, 107	⊢
	: , : , :
84	instantiation	183, 108, 200	⊢
	: , :
85	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
86	instantiation	215, 109, 180	⊢
	: , : , :
87	instantiation	110, 111, 195, 197, 112	⊢
	: , : , :
88	instantiation	124, 178, 214, 125*, 113*, 114*	⊢
	: , : , : , :
89	theorem		⊢
	proveit.numbers.addition.disassociation
90	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
91	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
92	instantiation	168	⊢
	: , :
93	instantiation	215, 177, 115	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
95	instantiation	215, 177, 138	⊢
	: , : , :
96	instantiation	215, 177, 116	⊢
	: , : , :
97	instantiation	117	⊢
	:
98	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
99	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
100	instantiation	118, 167, 212	⊢
	: , :
101	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
102	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
103	instantiation	119, 176	⊢
	:
104	instantiation	122, 120	⊢
	: , : , :
105	instantiation	121, 149	⊢
	:
106	instantiation	122, 123	⊢
	: , : , :
107	instantiation	124, 214, 178, 125*, 126*, 133*	⊢
	: , : , : , :
108	instantiation	215, 204, 127	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
110	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
111	instantiation	215, 128, 129	⊢
	: , : , :
112	instantiation	130, 162, 202, 209, 131, 132, 133*	⊢
	: , : , :
113	instantiation	143, 134, 135	⊢
	: , : , :
114	instantiation	136, 149	⊢
	:
115	instantiation	137, 138	⊢
	:
116	instantiation	215, 211, 139	⊢
	: , : , :
117	axiom		⊢
	proveit.logic.equality.equals_reflexivity
118	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
119	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
120	instantiation	140, 141	⊢
	:
121	theorem		⊢
	proveit.numbers.addition.elim_zero_left
122	axiom		⊢
	proveit.logic.equality.substitution
123	instantiation	169, 141	⊢
	:
124	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
125	instantiation	142, 149	⊢
	:
126	instantiation	143, 144, 145	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
128	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
129	instantiation	215, 146, 217	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
131	instantiation	147, 208, 209, 210	⊢
	: , : , :
132	instantiation	148, 188	⊢
	:
133	instantiation	169, 149	⊢
	:
134	instantiation	157, 188, 150, 151, 161, 160	⊢
	: , : , : , :
135	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
136	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
137	theorem		⊢
	proveit.numbers.negation.real_closure
138	instantiation	152, 153, 154	⊢
	: , : , :
139	instantiation	215, 213, 155	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
141	instantiation	215, 177, 156	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.division.frac_one_denom
143	axiom		⊢
	proveit.logic.equality.equals_transitivity
144	instantiation	157, 188, 158, 159, 160, 161	⊢
	: , : , : , :
145	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_4
146	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
147	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
148	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
149	instantiation	215, 177, 162	⊢
	: , : , :
150	instantiation	168	⊢
	: , :
151	instantiation	168	⊢
	: , :
152	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
153	instantiation	163, 164	⊢
	: , :
154	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
155	instantiation	165, 166	⊢
	:
156	instantiation	215, 211, 167	⊢
	: , : , :
157	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
158	instantiation	168	⊢
	: , :
159	instantiation	168	⊢
	: , :
160	instantiation	169, 170	⊢
	:
161	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
162	instantiation	215, 211, 171	⊢
	: , : , :
163	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
164	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
165	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
166	instantiation	172, 197, 173, 174	⊢
	: , :
167	instantiation	215, 175, 176	⊢
	: , : , :
168	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
169	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
170	instantiation	215, 177, 209	⊢
	: , : , :
171	instantiation	215, 213, 178	⊢
	: , : , :
172	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
173	instantiation	179, 197, 180	⊢
	: , :
174	instantiation	181, 182	⊢
	: , :
175	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
176	instantiation	183, 190, 200	⊢
	: , :
177	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
178	instantiation	215, 216, 188	⊢
	: , : , :
179	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
180	instantiation	184, 185, 195, 186	⊢
	: , :
181	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
182	instantiation	187, 217, 188, 189	⊢
	: , :
183	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
184	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
185	instantiation	215, 199, 190	⊢
	: , : , :
186	instantiation	191, 192	⊢
	:
187	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
188	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
189	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
190	instantiation	215, 204, 193	⊢
	: , : , :
191	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
192	instantiation	215, 194, 195	⊢
	: , : , :
193	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
194	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
195	instantiation	196, 197, 198	⊢
	: , :
196	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
197	instantiation	215, 199, 200	⊢
	: , : , :
198	instantiation	201, 202, 203	⊢
	:
199	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
200	instantiation	215, 204, 205	⊢
	: , : , :
201	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
202	instantiation	206, 208, 209, 210	⊢
	: , : , :
203	instantiation	207, 208, 209, 210	⊢
	: , : , :
204	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
205	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
206	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
207	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
208	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
209	instantiation	215, 211, 212	⊢
	: , : , :
210	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
211	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
212	instantiation	215, 213, 214	⊢
	: , : , :
213	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
214	instantiation	215, 216, 217	⊢
	: , : , :
215	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
216	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
217	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements