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