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