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