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.multiplication.weak_bound_via_right_factor_bound
2	reference	163	⊢
3	instantiation	52, 172, 58	⊢
	: , :
4	instantiation	191, 181, 7	⊢
	: , : , :
5	instantiation	37, 156, 8, 9, 10, 11*	⊢
	: , : , :
6	instantiation	12, 190	⊢
	:
7	instantiation	13, 15, 14	⊢
	: , :
8	instantiation	191, 154, 81	⊢
	: , : , :
9	instantiation	191, 181, 15	⊢
	: , : , :
10	instantiation	16, 163, 73, 17, 136, 18, 19*	⊢
	: , : , :
11	instantiation	116, 20, 21	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
13	theorem		⊢
	proveit.numbers.addition.add_rational_closure_bin
14	instantiation	191, 188, 22	⊢
	: , : , :
15	instantiation	191, 23, 24	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
17	instantiation	52, 40, 38	⊢
	: , :
18	instantiation	25, 26, 27	⊢
	: , : , :
19	instantiation	28, 166, 81, 111	⊢
	: , :
20	instantiation	75, 128, 190, 193, 129, 29, 153, 46, 146	⊢
	: , : , : , : , : , :
21	instantiation	116, 30, 31	⊢
	: , : , :
22	instantiation	191, 32, 33	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
24	instantiation	34, 161, 35	⊢
	: , :
25	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
26	instantiation	36, 73	⊢
	:
27	instantiation	37, 38, 39, 40, 41, 42*	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.exponentiation.exponent_log_with_same_base
29	instantiation	142	⊢
	: , :
30	instantiation	43, 193, 128, 129, 153, 46, 146	⊢
	: , : , : , : , : , : , :
31	instantiation	44, 128, 190, 193, 129, 45, 153, 146, 46, 47*	⊢
	: , : , : , : , : , :
32	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
33	instantiation	48, 185	⊢
	:
34	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
35	instantiation	49, 50, 51	⊢
	: , :
36	theorem		⊢
	proveit.numbers.rounding.ceil_x_ge_x
37	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
38	instantiation	168, 89	⊢
	:
39	instantiation	52, 89, 53	⊢
	: , :
40	instantiation	92, 93, 61	⊢
	: , : , :
41	axiom		⊢
	proveit.physics.quantum.QPE._t_req
42	instantiation	54, 55, 56, 57	⊢
	: , : , : , :
43	theorem		⊢
	proveit.numbers.addition.leftward_commutation
44	theorem		⊢
	proveit.numbers.addition.association
45	instantiation	142	⊢
	: , :
46	instantiation	191, 162, 58	⊢
	: , : , :
47	instantiation	59, 126, 153, 60	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.negation.int_neg_closure
49	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
50	instantiation	191, 68, 61	⊢
	: , : , :
51	instantiation	62, 63	⊢
	:
52	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
53	instantiation	191, 181, 64	⊢
	: , : , :
54	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
55	instantiation	116, 65, 66	⊢
	: , : , :
56	instantiation	86	⊢
	:
57	instantiation	67, 74	⊢
	: , :
58	instantiation	191, 154, 87	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
60	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
61	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
62	theorem		⊢
	proveit.numbers.negation.int_closure
63	instantiation	191, 68, 94	⊢
	: , : , :
64	instantiation	191, 188, 69	⊢
	: , : , :
65	instantiation	114, 70	⊢
	: , : , :
66	instantiation	116, 71, 72	⊢
	: , : , :
67	theorem		⊢
	proveit.logic.equality.equals_reversal
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
69	instantiation	102, 73	⊢
	:
70	instantiation	114, 74	⊢
	: , : , :
71	instantiation	75, 128, 190, 193, 129, 76, 84, 79, 77	⊢
	: , : , : , : , : , :
72	instantiation	78, 84, 79, 80	⊢
	: , : , :
73	instantiation	109, 166, 81, 111	⊢
	: , :
74	instantiation	114, 82	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.addition.disassociation
76	instantiation	142	⊢
	: , :
77	instantiation	83, 84	⊢
	:
78	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
79	instantiation	191, 162, 85	⊢
	: , : , :
80	instantiation	86	⊢
	:
81	instantiation	119, 166, 87	⊢
	: , :
82	instantiation	114, 88	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.negation.complex_closure
84	instantiation	191, 162, 89	⊢
	: , : , :
85	instantiation	191, 181, 90	⊢
	: , : , :
86	axiom		⊢
	proveit.logic.equality.equals_reflexivity
87	instantiation	164, 165, 113, 98	⊢
	: , :
88	instantiation	114, 91	⊢
	: , : , :
89	instantiation	92, 93, 94	⊢
	: , : , :
90	instantiation	191, 188, 95	⊢
	: , : , :
91	instantiation	96, 126, 97, 98, 99*	⊢
	: , :
92	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
93	instantiation	100, 101	⊢
	: , :
94	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
95	instantiation	102, 103	⊢
	:
96	theorem		⊢
	proveit.numbers.division.div_as_mult
97	instantiation	191, 162, 104	⊢
	: , : , :
98	instantiation	105, 106	⊢
	:
99	instantiation	116, 107, 108	⊢
	: , : , :
100	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
102	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
103	instantiation	109, 166, 110, 111	⊢
	: , :
104	instantiation	191, 154, 113	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
106	instantiation	191, 112, 113	⊢
	: , : , :
107	instantiation	114, 115	⊢
	: , : , :
108	instantiation	116, 117, 118	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
110	instantiation	119, 166, 120	⊢
	: , :
111	instantiation	137, 121	⊢
	: , :
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
113	instantiation	133, 166, 148	⊢
	: , :
114	axiom		⊢
	proveit.logic.equality.substitution
115	instantiation	122, 153, 145, 156, 167, 123, 124*	⊢
	: , : , :
116	axiom		⊢
	proveit.logic.equality.equals_transitivity
117	instantiation	125, 193, 190, 128, 130, 129, 126, 131, 132	⊢
	: , : , : , : , : , :
118	instantiation	127, 128, 190, 129, 130, 131, 132	⊢
	: , : , : , :
119	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
120	instantiation	133, 155, 134	⊢
	: , :
121	instantiation	135, 193, 190, 136	⊢
	: , :
122	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
123	instantiation	137, 138	⊢
	: , :
124	instantiation	139, 140, 185, 141*	⊢
	: , :
125	theorem		⊢
	proveit.numbers.multiplication.disassociation
126	instantiation	191, 162, 172	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
128	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
129	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
130	instantiation	142	⊢
	: , :
131	instantiation	191, 162, 143	⊢
	: , : , :
132	instantiation	144, 145, 146	⊢
	: , :
133	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
134	instantiation	147, 148, 156	⊢
	: , :
135	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
136	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
137	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
138	instantiation	149, 171, 158, 159	⊢
	: , :
139	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
140	instantiation	191, 150, 151	⊢
	: , : , :
141	instantiation	152, 153	⊢
	:
142	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
143	instantiation	191, 154, 155	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
145	instantiation	191, 162, 158	⊢
	: , : , :
146	instantiation	191, 162, 156	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
148	instantiation	157, 158, 159	⊢
	:
149	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
150	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
151	instantiation	191, 160, 161	⊢
	: , : , :
152	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
153	instantiation	191, 162, 163	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
155	instantiation	164, 165, 166, 167	⊢
	: , :
156	instantiation	168, 172	⊢
	:
157	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
158	instantiation	169, 171, 172, 173	⊢
	: , : , :
159	instantiation	170, 171, 172, 173	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
161	instantiation	191, 174, 175	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
163	instantiation	191, 181, 176	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
165	instantiation	191, 178, 177	⊢
	: , : , :
166	instantiation	191, 178, 179	⊢
	: , : , :
167	instantiation	180, 187	⊢
	:
168	theorem		⊢
	proveit.numbers.negation.real_closure
169	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
170	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
171	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
172	instantiation	191, 181, 182	⊢
	: , : , :
173	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
174	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
175	instantiation	191, 183, 187	⊢
	: , : , :
176	instantiation	191, 188, 184	⊢
	: , : , :
177	instantiation	191, 186, 185	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
179	instantiation	191, 186, 187	⊢
	: , : , :
180	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
181	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
182	instantiation	191, 188, 189	⊢
	: , : , :
183	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
184	instantiation	191, 192, 190	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
186	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
187	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
188	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
189	instantiation	191, 192, 193	⊢
	: , : , :
190	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
191	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
192	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
193	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements