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