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