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	⊢
	: , :
1	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
2	instantiation	3, 31, 4, 5	⊢
	: , :
3	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
4	instantiation	6, 31, 174, 8	⊢
	: , : , :
5	instantiation	7, 31, 174, 8	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
7	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
8	instantiation	9, 10	⊢
	:
9	theorem		⊢
	proveit.trigonometry.sine_pos_interval
10	instantiation	11, 31, 99, 12, 13	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOO
12	instantiation	210, 126, 17	⊢
	: , : , :
13	instantiation	14, 15, 16	⊢
	: , :
14	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
15	instantiation	86, 17	⊢
	:
16	instantiation	18, 19, 20	⊢
	: , : , :
17	instantiation	21, 125, 127	⊢
	: , :
18	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
19	instantiation	59, 22, 40	⊢
	: , : , :
20	instantiation	70, 68, 23, 24, 25*, 26*	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
22	instantiation	27, 28, 29	⊢
	: , : , :
23	instantiation	87, 88, 31	⊢
	: , :
24	instantiation	30, 88, 31, 99, 62, 32	⊢
	: , : , :
25	instantiation	160, 33, 34	⊢
	: , : , :
26	instantiation	35, 36, 37*	⊢
	: , :
27	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
28	instantiation	38, 39, 40	⊢
	: , : , :
29	instantiation	41, 99, 42, 155, 43, 44, 45*, 46*	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
32	instantiation	47, 137	⊢
	:
33	instantiation	101, 48	⊢
	: , : , :
34	instantiation	49, 50	⊢
	:
35	theorem		⊢
	proveit.logic.equality.equals_reversal
36	instantiation	51, 118, 212, 205, 119, 52, 67, 76	⊢
	: , : , : , : , : , :
37	instantiation	160, 53, 54	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.equality.sub_left_side_into
39	instantiation	55, 205, 125, 127, 56, 57*	⊢
	: , : , : , : , : , :
40	instantiation	101, 58	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
42	instantiation	87, 150, 100	⊢
	: , :
43	instantiation	59, 60, 61	⊢
	: , : , :
44	instantiation	134, 62	⊢
	: , :
45	instantiation	63, 205, 212, 118, 64, 119, 76, 123, 77	⊢
	: , : , : , : , : , :
46	instantiation	65, 76, 67	⊢
	: , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
48	instantiation	66, 67	⊢
	:
49	theorem		⊢
	proveit.numbers.addition.elim_zero_left
50	instantiation	210, 202, 68	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
52	instantiation	193	⊢
	: , :
53	instantiation	101, 69	⊢
	: , : , :
54	instantiation	194, 76	⊢
	:
55	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_factor_bound
56	instantiation	70, 149, 203, 71, 72, 73*, 74*	⊢
	: , : , :
57	instantiation	75, 205, 76, 77	⊢
	: , : , : , :
58	instantiation	160, 78, 79	⊢
	: , : , :
59	theorem		⊢
	proveit.logic.equality.sub_right_side_into
60	instantiation	80, 81, 82	⊢
	: , :
61	instantiation	83, 192, 84, 123, 171, 85*	⊢
	: , :
62	instantiation	86, 125	⊢
	:
63	theorem		⊢
	proveit.numbers.multiplication.disassociation
64	instantiation	193	⊢
	: , :
65	theorem		⊢
	proveit.numbers.multiplication.commutation
66	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
67	instantiation	210, 202, 155	⊢
	: , : , :
68	instantiation	87, 88, 99	⊢
	: , :
69	instantiation	89, 201, 209, 90*	⊢
	: , : , : , :
70	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
71	instantiation	210, 206, 91	⊢
	: , : , :
72	instantiation	92, 203, 150, 174, 93, 94	⊢
	: , : , :
73	instantiation	95, 129, 196, 96	⊢
	: , : , :
74	instantiation	160, 97, 98	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
76	instantiation	210, 202, 99	⊢
	: , : , :
77	instantiation	210, 202, 100	⊢
	: , : , :
78	instantiation	101, 102	⊢
	: , : , :
79	instantiation	103, 171	⊢
	:
80	theorem		⊢
	proveit.numbers.absolute_value.weak_upper_bound
81	instantiation	104, 132, 155, 133	⊢
	: , : , :
82	instantiation	134, 105	⊢
	: , :
83	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
84	instantiation	193	⊢
	: , :
85	instantiation	106, 107	⊢
	:
86	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
87	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
88	instantiation	210, 206, 108	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
90	instantiation	160, 109, 110	⊢
	: , : , :
91	instantiation	210, 208, 111	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
93	instantiation	112, 203, 174, 113, 114, 115, 116*	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
95	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
96	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
97	instantiation	117, 118, 212, 205, 119, 120, 123, 129, 121	⊢
	: , : , : , : , : , :
98	instantiation	122, 129, 123, 124	⊢
	: , : , :
99	instantiation	210, 126, 125	⊢
	: , : , :
100	instantiation	210, 126, 127	⊢
	: , : , :
101	axiom		⊢
	proveit.logic.equality.substitution
102	instantiation	128, 129, 171, 130*	⊢
	: , :
103	theorem		⊢
	proveit.numbers.absolute_value.abs_even
104	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
105	instantiation	131, 132, 155, 133	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
107	instantiation	134, 135	⊢
	: , :
108	instantiation	210, 136, 137	⊢
	: , : , :
109	instantiation	178, 212, 138, 139, 140, 141	⊢
	: , : , : , :
110	instantiation	142, 143, 144	⊢
	:
111	instantiation	210, 211, 145	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
113	instantiation	168, 169, 147	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
115	instantiation	146, 147	⊢
	:
116	instantiation	148, 196	⊢
	:
117	theorem		⊢
	proveit.numbers.addition.disassociation
118	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
119	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
120	instantiation	193	⊢
	: , :
121	instantiation	210, 202, 149	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
123	instantiation	210, 202, 150	⊢
	: , : , :
124	instantiation	151	⊢
	:
125	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
126	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
127	instantiation	152, 153	⊢
	:
128	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
129	instantiation	210, 202, 174	⊢
	: , : , :
130	instantiation	194, 171	⊢
	:
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
132	instantiation	154, 155	⊢
	:
133	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
134	theorem		⊢
	proveit.numbers.ordering.relax_less
135	instantiation	156, 185	⊢
	:
136	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
137	instantiation	157, 158, 159	⊢
	: , :
138	instantiation	193	⊢
	: , :
139	instantiation	193	⊢
	: , :
140	instantiation	160, 161, 162	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
142	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
143	instantiation	210, 202, 163	⊢
	: , : , :
144	instantiation	191, 164	⊢
	:
145	instantiation	165, 166, 205	⊢
	: , :
146	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
147	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
148	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
149	instantiation	210, 206, 167	⊢
	: , : , :
150	instantiation	168, 169, 185	⊢
	: , : , :
151	axiom		⊢
	proveit.logic.equality.equals_reflexivity
152	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
153	instantiation	170, 171, 172	⊢
	:
154	theorem		⊢
	proveit.numbers.negation.real_closure
155	instantiation	173, 174, 203, 175	⊢
	: , :
156	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
157	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
158	instantiation	210, 177, 176	⊢
	: , : , :
159	instantiation	210, 177, 192	⊢
	: , : , :
160	axiom		⊢
	proveit.logic.equality.equals_transitivity
161	instantiation	178, 212, 179, 180, 181, 182	⊢
	: , : , : , :
162	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
163	instantiation	210, 206, 183	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
165	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
166	instantiation	210, 184, 185	⊢
	: , : , :
167	instantiation	210, 208, 186	⊢
	: , : , :
168	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
169	instantiation	187, 188	⊢
	: , :
170	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
171	instantiation	210, 202, 189	⊢
	: , : , :
172	assumption		⊢
173	theorem		⊢
	proveit.numbers.division.div_real_closure
174	instantiation	210, 206, 190	⊢
	: , : , :
175	instantiation	191, 192	⊢
	:
176	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
177	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
178	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
179	instantiation	193	⊢
	: , :
180	instantiation	193	⊢
	: , :
181	instantiation	194, 196	⊢
	:
182	instantiation	195, 196	⊢
	:
183	instantiation	210, 208, 197	⊢
	: , : , :
184	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
185	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
186	instantiation	198, 201	⊢
	:
187	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
188	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
189	instantiation	199, 200	⊢
	:
190	instantiation	210, 208, 201	⊢
	: , : , :
191	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
192	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
193	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
194	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
195	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
196	instantiation	210, 202, 203	⊢
	: , : , :
197	instantiation	210, 211, 204	⊢
	: , : , :
198	theorem		⊢
	proveit.numbers.negation.int_closure
199	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
200	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
201	instantiation	210, 211, 205	⊢
	: , : , :
202	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
203	instantiation	210, 206, 207	⊢
	: , : , :
204	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
205	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
206	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
207	instantiation	210, 208, 209	⊢
	: , : , :
208	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
209	instantiation	210, 211, 212	⊢
	: , : , :
210	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
211	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
212	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements