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.division.frac_cancel_left
2	instantiation	230, 5, 6	⊢
	: , : , :
3	instantiation	190, 7, 8	⊢
	:
4	instantiation	230, 222, 9	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
6	instantiation	230, 10, 11	⊢
	: , : , :
7	instantiation	230, 222, 19	⊢
	: , : , :
8	instantiation	12, 13	⊢
	: , :
9	instantiation	14, 15	⊢
	:
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
11	instantiation	230, 16, 17	⊢
	: , : , :
12	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
13	instantiation	18, 51, 19, 20	⊢
	: , :
14	theorem		⊢
	proveit.trigonometry.real_closure
15	instantiation	79, 21, 22	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
17	instantiation	230, 23, 212	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
19	instantiation	24, 51, 194, 26	⊢
	: , : , :
20	instantiation	25, 51, 194, 26	⊢
	: , : , :
21	instantiation	107, 27, 120	⊢
	: , :
22	instantiation	83, 138, 232, 225, 139, 28, 143, 96, 97	⊢
	: , : , : , : , : , :
23	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
26	instantiation	29, 30	⊢
	:
27	instantiation	107, 170, 119	⊢
	: , :
28	instantiation	213	⊢
	: , :
29	theorem		⊢
	proveit.trigonometry.sine_pos_interval
30	instantiation	31, 51, 119, 32, 33	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOO
32	instantiation	230, 146, 37	⊢
	: , : , :
33	instantiation	34, 35, 36	⊢
	: , :
34	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
35	instantiation	106, 37	⊢
	:
36	instantiation	38, 39, 40	⊢
	: , : , :
37	instantiation	41, 145, 147	⊢
	: , :
38	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
39	instantiation	79, 42, 60	⊢
	: , : , :
40	instantiation	90, 88, 43, 44, 45*, 46*	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
42	instantiation	47, 48, 49	⊢
	: , : , :
43	instantiation	107, 108, 51	⊢
	: , :
44	instantiation	50, 108, 51, 119, 82, 52	⊢
	: , : , :
45	instantiation	180, 53, 54	⊢
	: , : , :
46	instantiation	55, 56, 57*	⊢
	: , :
47	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
48	instantiation	58, 59, 60	⊢
	: , : , :
49	instantiation	61, 119, 62, 175, 63, 64, 65*, 66*	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
52	instantiation	67, 157	⊢
	:
53	instantiation	121, 68	⊢
	: , : , :
54	instantiation	69, 70	⊢
	:
55	theorem		⊢
	proveit.logic.equality.equals_reversal
56	instantiation	71, 138, 232, 225, 139, 72, 87, 96	⊢
	: , : , : , : , : , :
57	instantiation	180, 73, 74	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.equality.sub_left_side_into
59	instantiation	75, 225, 145, 147, 76, 77*	⊢
	: , : , : , : , : , :
60	instantiation	121, 78	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
62	instantiation	107, 170, 120	⊢
	: , :
63	instantiation	79, 80, 81	⊢
	: , : , :
64	instantiation	154, 82	⊢
	: , :
65	instantiation	83, 225, 232, 138, 84, 139, 96, 143, 97	⊢
	: , : , : , : , : , :
66	instantiation	85, 96, 87	⊢
	: , :
67	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
68	instantiation	86, 87	⊢
	:
69	theorem		⊢
	proveit.numbers.addition.elim_zero_left
70	instantiation	230, 222, 88	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
72	instantiation	213	⊢
	: , :
73	instantiation	121, 89	⊢
	: , : , :
74	instantiation	214, 96	⊢
	:
75	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_factor_bound
76	instantiation	90, 169, 223, 91, 92, 93*, 94*	⊢
	: , : , :
77	instantiation	95, 225, 96, 97	⊢
	: , : , : , :
78	instantiation	180, 98, 99	⊢
	: , : , :
79	theorem		⊢
	proveit.logic.equality.sub_right_side_into
80	instantiation	100, 101, 102	⊢
	: , :
81	instantiation	103, 212, 104, 143, 191, 105*	⊢
	: , :
82	instantiation	106, 145	⊢
	:
83	theorem		⊢
	proveit.numbers.multiplication.disassociation
84	instantiation	213	⊢
	: , :
85	theorem		⊢
	proveit.numbers.multiplication.commutation
86	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
87	instantiation	230, 222, 175	⊢
	: , : , :
88	instantiation	107, 108, 119	⊢
	: , :
89	instantiation	109, 221, 229, 110*	⊢
	: , : , : , :
90	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
91	instantiation	230, 226, 111	⊢
	: , : , :
92	instantiation	112, 223, 170, 194, 113, 114	⊢
	: , : , :
93	instantiation	115, 149, 216, 116	⊢
	: , : , :
94	instantiation	180, 117, 118	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
96	instantiation	230, 222, 119	⊢
	: , : , :
97	instantiation	230, 222, 120	⊢
	: , : , :
98	instantiation	121, 122	⊢
	: , : , :
99	instantiation	123, 191	⊢
	:
100	theorem		⊢
	proveit.numbers.absolute_value.weak_upper_bound
101	instantiation	124, 152, 175, 153	⊢
	: , : , :
102	instantiation	154, 125	⊢
	: , :
103	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
104	instantiation	213	⊢
	: , :
105	instantiation	126, 127	⊢
	:
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
107	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
108	instantiation	230, 226, 128	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
110	instantiation	180, 129, 130	⊢
	: , : , :
111	instantiation	230, 228, 131	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
113	instantiation	132, 223, 194, 133, 134, 135, 136*	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
115	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
116	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
117	instantiation	137, 138, 232, 225, 139, 140, 143, 149, 141	⊢
	: , : , : , : , : , :
118	instantiation	142, 149, 143, 144	⊢
	: , : , :
119	instantiation	230, 146, 145	⊢
	: , : , :
120	instantiation	230, 146, 147	⊢
	: , : , :
121	axiom		⊢
	proveit.logic.equality.substitution
122	instantiation	148, 149, 191, 150*	⊢
	: , :
123	theorem		⊢
	proveit.numbers.absolute_value.abs_even
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
125	instantiation	151, 152, 175, 153	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
127	instantiation	154, 155	⊢
	: , :
128	instantiation	230, 156, 157	⊢
	: , : , :
129	instantiation	198, 232, 158, 159, 160, 161	⊢
	: , : , : , :
130	instantiation	162, 163, 164	⊢
	:
131	instantiation	230, 231, 165	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
133	instantiation	188, 189, 167	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
135	instantiation	166, 167	⊢
	:
136	instantiation	168, 216	⊢
	:
137	theorem		⊢
	proveit.numbers.addition.disassociation
138	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
139	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
140	instantiation	213	⊢
	: , :
141	instantiation	230, 222, 169	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
143	instantiation	230, 222, 170	⊢
	: , : , :
144	instantiation	171	⊢
	:
145	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
146	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
147	instantiation	172, 173	⊢
	:
148	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
149	instantiation	230, 222, 194	⊢
	: , : , :
150	instantiation	214, 191	⊢
	:
151	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
152	instantiation	174, 175	⊢
	:
153	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
154	theorem		⊢
	proveit.numbers.ordering.relax_less
155	instantiation	176, 205	⊢
	:
156	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
157	instantiation	177, 178, 179	⊢
	: , :
158	instantiation	213	⊢
	: , :
159	instantiation	213	⊢
	: , :
160	instantiation	180, 181, 182	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
162	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
163	instantiation	230, 222, 183	⊢
	: , : , :
164	instantiation	211, 184	⊢
	:
165	instantiation	185, 186, 225	⊢
	: , :
166	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
167	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
168	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
169	instantiation	230, 226, 187	⊢
	: , : , :
170	instantiation	188, 189, 205	⊢
	: , : , :
171	axiom		⊢
	proveit.logic.equality.equals_reflexivity
172	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
173	instantiation	190, 191, 192	⊢
	:
174	theorem		⊢
	proveit.numbers.negation.real_closure
175	instantiation	193, 194, 223, 195	⊢
	: , :
176	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
177	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
178	instantiation	230, 197, 196	⊢
	: , : , :
179	instantiation	230, 197, 212	⊢
	: , : , :
180	axiom		⊢
	proveit.logic.equality.equals_transitivity
181	instantiation	198, 232, 199, 200, 201, 202	⊢
	: , : , : , :
182	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
183	instantiation	230, 226, 203	⊢
	: , : , :
184	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
185	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
186	instantiation	230, 204, 205	⊢
	: , : , :
187	instantiation	230, 228, 206	⊢
	: , : , :
188	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
189	instantiation	207, 208	⊢
	: , :
190	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
191	instantiation	230, 222, 209	⊢
	: , : , :
192	assumption		⊢
193	theorem		⊢
	proveit.numbers.division.div_real_closure
194	instantiation	230, 226, 210	⊢
	: , : , :
195	instantiation	211, 212	⊢
	:
196	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
197	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
198	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
199	instantiation	213	⊢
	: , :
200	instantiation	213	⊢
	: , :
201	instantiation	214, 216	⊢
	:
202	instantiation	215, 216	⊢
	:
203	instantiation	230, 228, 217	⊢
	: , : , :
204	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
205	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
206	instantiation	218, 221	⊢
	:
207	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
208	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
209	instantiation	219, 220	⊢
	:
210	instantiation	230, 228, 221	⊢
	: , : , :
211	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
212	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
213	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
214	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
215	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
216	instantiation	230, 222, 223	⊢
	: , : , :
217	instantiation	230, 231, 224	⊢
	: , : , :
218	theorem		⊢
	proveit.numbers.negation.int_closure
219	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
220	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
221	instantiation	230, 231, 225	⊢
	: , : , :
222	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
223	instantiation	230, 226, 227	⊢
	: , : , :
224	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
225	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
226	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
227	instantiation	230, 228, 229	⊢
	: , : , :
228	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
229	instantiation	230, 231, 232	⊢
	: , : , :
230	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
231	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
232	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements