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	,  ⊢
	: , : , :
1	reference	141	⊢
2	instantiation	22, 4, 5	,  ⊢
	: , : , :
3	instantiation	127, 6, 7	⊢
	: , : , :
4	instantiation	8, 79, 9, 230, 10, 11*	⊢
	: , : , :
5	instantiation	12, 230, 79, 13, 14, 15*	,  ⊢
	: , : , :
6	instantiation	16, 219, 17, 230, 104*	⊢
	: , : , :
7	instantiation	18, 252, 203, 205, 137, 19, 20, 21*	⊢
	: , : , : , : , : , :
8	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
9	instantiation	177, 64, 63	⊢
	: , :
10	instantiation	22, 23, 24	⊢
	: , : , :
11	instantiation	190, 25, 26	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
13	instantiation	177, 65, 222	⊢
	: , :
14	instantiation	127, 27, 28	⊢
	: , : , :
15	instantiation	190, 29, 30	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.modular.mod_abs_scaled
17	instantiation	177, 32, 31	⊢
	: , :
18	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
19	instantiation	250, 223, 32	⊢
	: , : , :
20	instantiation	250, 223, 220	⊢
	: , : , :
21	instantiation	127, 33, 34	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
23	instantiation	127, 35, 36, 37*	⊢
	: , : , :
24	instantiation	141, 38, 39	⊢
	: , : , :
25	instantiation	202, 252, 247, 203, 40, 205, 42, 43, 41	⊢
	: , : , : , : , : , :
26	instantiation	207, 42, 43, 44	⊢
	: , : , :
27	assumption		⊢
28	axiom		⊢
	proveit.physics.quantum.QPE._best_floor_def
29	instantiation	202, 203, 247, 252, 205, 45, 47, 206, 208	⊢
	: , : , : , : , : , :
30	instantiation	46, 208, 47, 210	⊢
	: , : , :
31	instantiation	140, 220	⊢
	:
32	instantiation	48, 154, 219, 97	⊢
	: , :
33	instantiation	127, 49, 50	⊢
	: , : , :
34	instantiation	86, 51, 52, 53	⊢
	: , : , : , :
35	instantiation	54, 80, 96, 101, 55*	⊢
	: , : , :
36	instantiation	61, 110, 145	⊢
	: , :
37	instantiation	56, 57, 101, 58, 59*	⊢
	: , :
38	instantiation	74, 60	⊢
	: , :
39	instantiation	61, 62, 144	⊢
	: , :
40	instantiation	221	⊢
	: , :
41	instantiation	250, 223, 63	⊢
	: , : , :
42	instantiation	250, 223, 79	⊢
	: , : , :
43	instantiation	250, 223, 64	⊢
	: , : , :
44	instantiation	225	⊢
	:
45	instantiation	221	⊢
	: , :
46	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
47	instantiation	250, 223, 65	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.division.div_real_closure
49	instantiation	66, 208, 139, 67, 150	⊢
	: , : , : , : , :
50	instantiation	190, 68, 69	⊢
	: , : , :
51	instantiation	146, 70	⊢
	: , : , :
52	instantiation	146, 71	⊢
	: , : , :
53	instantiation	136, 139	⊢
	:
54	theorem		⊢
	proveit.numbers.modular.mod_abs_of_difference_bound
55	instantiation	190, 72, 73	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.modular.mod_abs_x_reduce_to_abs_x
57	instantiation	177, 157, 126	⊢
	: , :
58	instantiation	74, 75	⊢
	: , :
59	instantiation	76, 77, 78*	⊢
	:
60	instantiation	112, 229, 230, 173	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.addition.commutation
62	instantiation	250, 223, 117	⊢
	: , : , :
63	instantiation	140, 79	⊢
	:
64	instantiation	95, 80, 219, 97	⊢
	: , :
65	instantiation	250, 236, 81	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
67	instantiation	250, 164, 82	⊢
	: , : , :
68	instantiation	146, 83	⊢
	: , : , :
69	instantiation	146, 84	⊢
	: , : , :
70	instantiation	167, 208	⊢
	:
71	instantiation	167, 139	⊢
	:
72	instantiation	146, 85	⊢
	: , : , :
73	instantiation	86, 87, 88, 89	⊢
	: , : , : , :
74	theorem		⊢
	proveit.numbers.ordering.relax_less
75	instantiation	90, 91, 92	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
77	instantiation	93, 94	⊢
	: , :
78	instantiation	105, 145, 144	⊢
	: , :
79	instantiation	95, 96, 219, 97	⊢
	: , :
80	instantiation	177, 154, 126	⊢
	: , :
81	instantiation	250, 98, 99	⊢
	: , : , :
82	instantiation	250, 100, 101	⊢
	: , : , :
83	instantiation	190, 102, 103	⊢
	: , : , :
84	instantiation	146, 104	⊢
	: , : , :
85	instantiation	105, 139, 145	⊢
	: , :
86	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
87	instantiation	202, 203, 247, 252, 205, 107, 139, 110, 106	⊢
	: , : , : , : , : , :
88	instantiation	202, 247, 203, 107, 108, 205, 139, 110, 125, 145	⊢
	: , : , : , : , : , :
89	instantiation	109, 203, 252, 205, 139, 110, 145, 111	⊢
	: , : , : , : , : , : , : , :
90	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
91	instantiation	112, 229, 230, 113	⊢
	: , : , :
92	instantiation	141, 114, 115	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.addition.subtraction.nonpos_difference
94	instantiation	116, 201	⊢
	:
95	theorem		⊢
	proveit.numbers.modular.mod_abs_real_closure
96	instantiation	177, 154, 117	⊢
	: , :
97	instantiation	118, 182, 119	⊢
	: , :
98	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
99	instantiation	120, 182, 121	⊢
	: , :
100	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
101	instantiation	122, 159, 224	⊢
	: , :
102	instantiation	146, 123	⊢
	: , : , :
103	instantiation	167, 137	⊢
	:
104	instantiation	166, 137	⊢
	:
105	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_subtract
106	instantiation	124, 125, 145	⊢
	: , :
107	instantiation	221	⊢
	: , :
108	instantiation	221	⊢
	: , :
109	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
110	instantiation	250, 223, 126	⊢
	: , : , :
111	instantiation	225	⊢
	:
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
113	instantiation	127, 128, 129	⊢
	: , : , :
114	instantiation	130, 197	⊢
	:
115	instantiation	190, 131, 132	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.rounding.floor_x_le_x
117	instantiation	140, 157	⊢
	:
118	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
119	instantiation	250, 195, 133	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
121	instantiation	226, 134, 135	⊢
	: , :
122	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
123	instantiation	136, 137	⊢
	:
124	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
125	instantiation	138, 139	⊢
	:
126	instantiation	140, 201	⊢
	:
127	theorem		⊢
	proveit.logic.equality.sub_right_side_into
128	instantiation	141, 173, 142	⊢
	: , : , :
129	instantiation	143, 144, 145	⊢
	: , :
130	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
131	instantiation	146, 147	⊢
	: , : , :
132	instantiation	148, 149, 150, 168, 151*, 152*	⊢
	: , : , :
133	instantiation	250, 213, 249	⊢
	: , : , :
134	instantiation	250, 169, 249	⊢
	: , : , :
135	instantiation	245, 153	⊢
	:
136	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
137	instantiation	250, 223, 219	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.negation.complex_closure
139	instantiation	250, 223, 154	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.negation.real_closure
141	theorem		⊢
	proveit.logic.equality.sub_left_side_into
142	instantiation	155, 156	⊢
	:
143	theorem		⊢
	proveit.numbers.absolute_value.abs_diff_reversal
144	instantiation	250, 223, 201	⊢
	: , : , :
145	instantiation	250, 223, 157	⊢
	: , : , :
146	axiom		⊢
	proveit.logic.equality.substitution
147	instantiation	158, 159, 224, 230, 160, 161, 162*	⊢
	: , : , : , :
148	theorem		⊢
	proveit.numbers.division.frac_cancel_left
149	instantiation	250, 164, 163	⊢
	: , : , :
150	instantiation	250, 164, 165	⊢
	: , : , :
151	instantiation	166, 181	⊢
	:
152	instantiation	167, 168	⊢
	:
153	instantiation	250, 169, 170	⊢
	: , : , :
154	instantiation	250, 236, 171	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
156	instantiation	172, 229, 230, 173	⊢
	: , : , :
157	instantiation	250, 236, 174	⊢
	: , : , :
158	theorem		⊢
	proveit.numbers.exponentiation.exp_factored_real
159	instantiation	250, 175, 176	⊢
	: , : , :
160	instantiation	177, 224, 222	⊢
	: , :
161	instantiation	178, 179	⊢
	: , :
162	instantiation	180, 181	⊢
	:
163	instantiation	250, 183, 182	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
165	instantiation	250, 183, 184	⊢
	: , : , :
166	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
167	theorem		⊢
	proveit.numbers.division.frac_one_denom
168	instantiation	250, 223, 185	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
170	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
171	instantiation	250, 244, 186	⊢
	: , : , :
172	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
173	instantiation	187, 201	⊢
	:
174	instantiation	250, 244, 188	⊢
	: , : , :
175	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
176	instantiation	250, 189, 212	⊢
	: , : , :
177	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
178	theorem		⊢
	proveit.logic.equality.equals_reversal
179	instantiation	190, 191, 192	⊢
	: , : , :
180	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
181	instantiation	250, 223, 193	⊢
	: , : , :
182	instantiation	250, 195, 194	⊢
	: , : , :
183	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
184	instantiation	250, 195, 196	⊢
	: , : , :
185	instantiation	233, 234, 197	⊢
	: , : , :
186	instantiation	250, 198, 199	⊢
	: , : , :
187	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
188	instantiation	200, 201	⊢
	:
189	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
190	axiom		⊢
	proveit.logic.equality.equals_transitivity
191	instantiation	202, 252, 247, 203, 204, 205, 208, 209, 206	⊢
	: , : , : , : , : , :
192	instantiation	207, 208, 209, 210	⊢
	: , : , :
193	instantiation	250, 236, 211	⊢
	: , : , :
194	instantiation	250, 213, 212	⊢
	: , : , :
195	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
196	instantiation	250, 213, 214	⊢
	: , : , :
197	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
198	instantiation	215, 216, 217	⊢
	: , :
199	assumption		⊢
200	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
201	instantiation	218, 219, 220	⊢
	: , :
202	theorem		⊢
	proveit.numbers.addition.disassociation
203	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
204	instantiation	221	⊢
	: , :
205	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
206	instantiation	250, 223, 222	⊢
	: , : , :
207	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
208	instantiation	250, 223, 230	⊢
	: , : , :
209	instantiation	250, 223, 224	⊢
	: , : , :
210	instantiation	225	⊢
	:
211	instantiation	250, 244, 242	⊢
	: , : , :
212	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
213	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
214	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
215	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
216	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
217	instantiation	226, 235, 238	⊢
	: , :
218	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
219	instantiation	250, 236, 227	⊢
	: , : , :
220	instantiation	228, 229, 230, 231	⊢
	: , : , :
221	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
222	instantiation	250, 236, 232	⊢
	: , : , :
223	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
224	instantiation	233, 234, 249	⊢
	: , : , :
225	axiom		⊢
	proveit.logic.equality.equals_reflexivity
226	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
227	instantiation	250, 244, 235	⊢
	: , : , :
228	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
229	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
230	instantiation	250, 236, 237	⊢
	: , : , :
231	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
232	instantiation	250, 244, 238	⊢
	: , : , :
233	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
234	instantiation	239, 240	⊢
	: , :
235	instantiation	241, 242, 243	⊢
	: , :
236	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
237	instantiation	250, 244, 246	⊢
	: , : , :
238	instantiation	245, 246	⊢
	:
239	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
240	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
241	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
242	instantiation	250, 251, 247	⊢
	: , : , :
243	instantiation	250, 248, 249	⊢
	: , : , :
244	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
245	theorem		⊢
	proveit.numbers.negation.int_closure
246	instantiation	250, 251, 252	⊢
	: , : , :
247	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
248	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
249	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
250	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
251	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
252	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements