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, 5, 6	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.booleans.disjunction.singular_constructive_dilemma
2	reference	13	⊢
3	instantiation	7	⊢
	: , :
4	instantiation	8, 9, 10	⊢
	: , :
5	deduction	11	⊢
6	theorem		⊢
	proveit.physics.quantum.QPE._best_guarantee_delta_nonzero
7	theorem		⊢
	proveit.logic.equality.not_equals_is_bool
8	theorem		⊢
	proveit.logic.equality.rhs_via_equality
9	instantiation	12, 13	⊢
	:
10	instantiation	226, 14	⊢
	: , : , :
11	instantiation	42, 15, 16	⊢
	: , : , :
12	theorem		⊢
	proveit.logic.booleans.unfold_is_bool
13	instantiation	17	⊢
	: , :
14	instantiation	160, 18	⊢
	: , :
15	instantiation	19, 20, 21, 22, 59	⊢
	: , : , :
16	instantiation	144, 23, 24	⊢
	: , : , :
17	axiom		⊢
	proveit.logic.equality.equality_in_bool
18	instantiation	25	⊢
	: , :
19	theorem		⊢
	proveit.numbers.division.strong_div_from_denom_bound__all_pos
20	instantiation	252, 27, 26	⊢
	: , : , :
21	instantiation	252, 27, 28	⊢
	: , : , :
22	instantiation	29, 30, 31	⊢
	:
23	instantiation	32, 64, 92, 33, 58, 34*	⊢
	: , : , :
24	instantiation	35, 71, 36, 220, 37, 38*	⊢
	: , : , :
25	axiom		⊢
	proveit.logic.equality.not_equals_def
26	instantiation	252, 40, 39	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
28	instantiation	252, 40, 69	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
30	instantiation	41, 72, 193	⊢
	: , :
31	instantiation	42, 43	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.division.strong_div_from_numer_bound__pos_denom
33	instantiation	44, 92, 156, 45, 46, 47*, 48*	⊢
	: , : , :
34	instantiation	49, 50, 51	⊢
	:
35	theorem		⊢
	proveit.numbers.exponentiation.exp_eq_real
36	instantiation	252, 52, 53	⊢
	: , : , :
37	instantiation	54, 66, 205, 82, 55*	⊢
	: , :
38	instantiation	56, 57	⊢
	:
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
41	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
42	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
43	instantiation	129, 58, 59	⊢
	: , :
44	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
45	instantiation	252, 231, 60	⊢
	: , : , :
46	instantiation	158, 61	⊢
	:
47	instantiation	188, 62, 63	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.add_5_4
49	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
50	instantiation	252, 242, 64	⊢
	: , : , :
51	instantiation	249, 69	⊢
	:
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
53	instantiation	65, 66	⊢
	:
54	theorem		⊢
	proveit.numbers.absolute_value.abs_eq
55	instantiation	67, 68	⊢
	:
56	theorem		⊢
	proveit.numbers.exponentiation.exponentiated_one
57	instantiation	252, 242, 71	⊢
	: , : , :
58	instantiation	158, 69	⊢
	:
59	instantiation	70, 71, 112, 72, 73, 74, 75*	⊢
	: , : , :
60	instantiation	252, 247, 76	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
62	instantiation	77, 79	⊢
	:
63	instantiation	78, 79, 80	⊢
	: , :
64	instantiation	252, 231, 81	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
66	instantiation	144, 205, 82	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
68	instantiation	97, 245	⊢
	:
69	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
70	theorem		⊢
	proveit.numbers.exponentiation.exp_pos_less
71	instantiation	252, 231, 83	⊢
	: , : , :
72	instantiation	252, 84, 85	⊢
	: , : , :
73	instantiation	129, 86, 87	⊢
	: , :
74	instantiation	158, 101	⊢
	:
75	instantiation	171, 88, 89, 90	⊢
	: , : , : , :
76	instantiation	252, 244, 91	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.addition.elim_zero_right
78	theorem		⊢
	proveit.numbers.addition.commutation
79	instantiation	252, 242, 92	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
81	instantiation	252, 247, 93	⊢
	: , : , :
82	instantiation	144, 94, 95	⊢
	: , : , :
83	instantiation	252, 247, 96	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
85	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
86	instantiation	97, 132	⊢
	:
87	instantiation	98, 99	⊢
	: , :
88	instantiation	100, 101, 102	⊢
	: , :
89	instantiation	103, 193, 104, 105, 106	⊢
	: , : , : , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_3
91	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
92	instantiation	252, 231, 107	⊢
	: , : , :
93	instantiation	252, 244, 108	⊢
	: , : , :
94	instantiation	188, 109, 145	⊢
	: , : , :
95	instantiation	110, 254, 111	⊢
	: , :
96	instantiation	252, 244, 193	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
98	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_between_3_and_4
100	theorem		⊢
	proveit.numbers.exponentiation.exp_nat_pos_expansion
101	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
102	instantiation	252, 242, 112	⊢
	: , : , :
103	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
104	instantiation	113, 193	⊢
	: , :
105	instantiation	208	⊢
	: , :
106	instantiation	114	⊢
	:
107	instantiation	252, 247, 115	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
109	modus ponens	116, 117	⊢
110	theorem		⊢
	proveit.numbers.modular.int_mod_elimination
111	instantiation	121, 122, 123, 246, 118	⊢
	: , : , :
112	instantiation	252, 231, 119	⊢
	: , : , :
113	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
114	theorem		⊢
	proveit.numbers.numerals.decimals.reduce_2_repeats
115	instantiation	252, 244, 120	⊢
	: , : , :
116	theorem		⊢
	proveit.physics.quantum.QPE._alpha_ideal_case
117	instantiation	121, 122, 123, 138, 124	⊢
	: , : , :
118	instantiation	129, 125, 126	⊢
	: , :
119	instantiation	252, 247, 127	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
121	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
122	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
123	instantiation	128, 248, 164	⊢
	: , :
124	instantiation	129, 130, 131	⊢
	: , :
125	instantiation	188, 130, 145	⊢
	: , : , :
126	instantiation	188, 131, 145	⊢
	: , : , :
127	instantiation	252, 244, 132	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
129	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
130	instantiation	133, 243, 156, 211, 134, 135, 136*	⊢
	: , : , :
131	instantiation	137, 138, 248, 164, 139, 140	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
133	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
134	instantiation	141, 156, 220, 157	⊢
	: , : , :
135	instantiation	142, 148	⊢
	: , :
136	instantiation	143, 236	⊢
	:
137	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
138	instantiation	144, 246, 145	⊢
	: , : , :
139	instantiation	146, 243, 211, 220, 147, 148, 219*	⊢
	: , : , :
140	instantiation	149, 150, 151	⊢
	: , :
141	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
142	theorem		⊢
	proveit.numbers.ordering.relax_less
143	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
144	theorem		⊢
	proveit.logic.equality.sub_left_side_into
145	instantiation	152, 243, 211, 222, 153, 154*	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
147	instantiation	155, 156, 220, 157	⊢
	: , : , :
148	instantiation	158, 254	⊢
	:
149	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
150	instantiation	252, 231, 159	⊢
	: , : , :
151	instantiation	212	⊢
	:
152	theorem		⊢
	proveit.numbers.multiplication.left_mult_eq_real
153	instantiation	160, 161	⊢
	: , :
154	instantiation	188, 162, 163	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
156	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
157	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
158	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
159	instantiation	252, 247, 164	⊢
	: , : , :
160	theorem		⊢
	proveit.logic.equality.equals_reversal
161	instantiation	165, 232, 176, 166, 177, 167*, 168*	⊢
	: , : , :
162	instantiation	188, 169, 170	⊢
	: , : , :
163	instantiation	171, 172, 173, 174	⊢
	: , : , : , :
164	instantiation	175, 237	⊢
	:
165	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
166	instantiation	188, 176, 177	⊢
	: , : , :
167	instantiation	178, 210	⊢
	:
168	instantiation	216, 179, 180	⊢
	: , : , :
169	instantiation	181, 205, 206, 182, 183	⊢
	: , : , : , : , :
170	instantiation	216, 184, 185	⊢
	: , : , :
171	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
172	instantiation	226, 186	⊢
	: , : , :
173	instantiation	226, 187	⊢
	: , : , :
174	instantiation	235, 206	⊢
	:
175	theorem		⊢
	proveit.numbers.negation.int_closure
176	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
177	instantiation	188, 189, 190	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.addition.elim_zero_left
179	instantiation	191, 192, 193, 245, 194, 195, 198, 196, 210	⊢
	: , : , : , : , : , :
180	instantiation	197, 210, 198, 199	⊢
	: , : , :
181	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
182	instantiation	252, 201, 200	⊢
	: , : , :
183	instantiation	252, 201, 202	⊢
	: , : , :
184	instantiation	226, 203	⊢
	: , : , :
185	instantiation	226, 204	⊢
	: , : , :
186	instantiation	228, 205	⊢
	:
187	instantiation	228, 206	⊢
	:
188	theorem		⊢
	proveit.logic.equality.sub_right_side_into
189	instantiation	207, 246	⊢
	:
190	assumption		⊢
191	theorem		⊢
	proveit.numbers.addition.disassociation
192	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
193	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
194	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
195	instantiation	208	⊢
	: , :
196	instantiation	209, 210	⊢
	:
197	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
198	instantiation	252, 242, 211	⊢
	: , : , :
199	instantiation	212	⊢
	:
200	instantiation	252, 214, 213	⊢
	: , : , :
201	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
202	instantiation	252, 214, 215	⊢
	: , : , :
203	instantiation	216, 217, 218	⊢
	: , : , :
204	instantiation	226, 219	⊢
	: , : , :
205	instantiation	252, 242, 220	⊢
	: , : , :
206	instantiation	252, 242, 221	⊢
	: , : , :
207	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
208	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
209	theorem		⊢
	proveit.numbers.negation.complex_closure
210	instantiation	252, 242, 222	⊢
	: , : , :
211	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
212	axiom		⊢
	proveit.logic.equality.equals_reflexivity
213	instantiation	252, 224, 223	⊢
	: , : , :
214	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
215	instantiation	252, 224, 225	⊢
	: , : , :
216	axiom		⊢
	proveit.logic.equality.equals_transitivity
217	instantiation	226, 227	⊢
	: , : , :
218	instantiation	228, 236	⊢
	:
219	instantiation	229, 236	⊢
	:
220	instantiation	252, 231, 230	⊢
	: , : , :
221	instantiation	252, 231, 239	⊢
	: , : , :
222	instantiation	252, 231, 232	⊢
	: , : , :
223	instantiation	252, 233, 254	⊢
	: , : , :
224	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
225	instantiation	252, 233, 234	⊢
	: , : , :
226	axiom		⊢
	proveit.logic.equality.substitution
227	instantiation	235, 236	⊢
	:
228	theorem		⊢
	proveit.numbers.division.frac_one_denom
229	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
230	instantiation	252, 247, 237	⊢
	: , : , :
231	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
232	instantiation	238, 239, 240, 241	⊢
	: , :
233	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
234	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
235	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
236	instantiation	252, 242, 243	⊢
	: , : , :
237	instantiation	252, 244, 245	⊢
	: , : , :
238	theorem		⊢
	proveit.numbers.division.div_rational_closure
239	instantiation	252, 247, 246	⊢
	: , : , :
240	instantiation	252, 247, 248	⊢
	: , : , :
241	instantiation	249, 254	⊢
	:
242	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
243	instantiation	250, 251, 254	⊢
	: , : , :
244	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
245	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
246	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
247	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
248	instantiation	252, 253, 254	⊢
	: , : , :
249	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
250	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
251	instantiation	255, 256	⊢
	: , :
252	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
253	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
254	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
255	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
256	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements