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	,  ⊢
	: , :
1	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
2	instantiation	18, 3, 4	,  ⊢
	: , : , :
3	instantiation	18, 5, 6	,  ⊢
	: , : , :
4	instantiation	203, 7	⊢
	: , : , :
5	instantiation	8, 9	,  ⊢
	: , :
6	instantiation	203, 10	⊢
	: , : , :
7	instantiation	203, 11	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
9	instantiation	12, 13, 14, 15*	,  ⊢
	:
10	instantiation	203, 22	⊢
	: , : , :
11	instantiation	135, 38, 16, 17	⊢
	: , : , : , :
12	theorem		⊢
	proveit.numbers.exponentiation.unit_complex_polar_num_neq_one
13	instantiation	132, 53, 44	⊢
	: , : , :
14	instantiation	18, 19, 20	,  ⊢
	: , : , :
15	instantiation	37, 21	⊢
	: , :
16	instantiation	37, 27	⊢
	: , :
17	instantiation	37, 22	⊢
	: , :
18	theorem		⊢
	proveit.logic.equality.sub_left_side_into
19	instantiation	23, 24, 214, 25	,  ⊢
	: , :
20	instantiation	135, 26, 27, 28	⊢
	: , : , : , :
21	instantiation	203, 29	⊢
	: , : , :
22	instantiation	203, 30	⊢
	: , : , :
23	theorem		⊢
	proveit.physics.quantum.QPE._non_int_delta_b_diff
24	instantiation	31, 150, 237, 151	⊢
	: , : , : , : , :
25	assumption		⊢
26	instantiation	67, 32, 33, 34, 35*	⊢
	: , :
27	instantiation	36, 93, 114	⊢
	: , :
28	instantiation	37, 38	⊢
	: , :
29	instantiation	192, 39, 40	⊢
	: , : , :
30	instantiation	192, 41, 42	⊢
	: , : , :
31	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
32	instantiation	132, 43, 44	⊢
	: , : , :
33	instantiation	240, 218, 60	⊢
	: , : , :
34	instantiation	45, 239, 54, 160, 46	⊢
	: , :
35	instantiation	192, 47, 48	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.commutation
37	theorem		⊢
	proveit.logic.equality.equals_reversal
38	instantiation	203, 49	⊢
	: , : , :
39	instantiation	104, 150, 239, 237, 151, 54, 212, 172, 50, 108	⊢
	: , : , : , : , : , : , :
40	instantiation	105, 237, 99, 150, 86, 151, 50, 212, 172, 108	⊢
	: , : , : , : , : , :
41	instantiation	203, 51	⊢
	: , : , :
42	instantiation	52, 150, 239, 151, 152, 186, 153, 154, 128*	⊢
	: , : , : , : , :
43	instantiation	240, 218, 53	⊢
	: , : , :
44	instantiation	148, 150, 239, 237, 151, 54, 212, 172, 108	⊢
	: , : , : , : , : , :
45	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
46	instantiation	240, 177, 144	⊢
	: , : , :
47	instantiation	203, 55	⊢
	: , : , :
48	instantiation	192, 56, 57	⊢
	: , : , :
49	instantiation	203, 58	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
51	instantiation	203, 59	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
53	instantiation	182, 60, 122	⊢
	: , :
54	instantiation	173	⊢
	: , :
55	instantiation	61, 212, 172, 139, 131, 124, 62*	⊢
	: , : , :
56	instantiation	192, 63, 64	⊢
	: , : , :
57	instantiation	192, 65, 66	⊢
	: , : , :
58	instantiation	67, 153, 68, 69, 70*	⊢
	: , :
59	instantiation	71, 186, 115, 72*	⊢
	: , :
60	instantiation	182, 219, 188	⊢
	: , :
61	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
62	instantiation	73, 160, 210, 74*	⊢
	: , :
63	instantiation	192, 75, 76	⊢
	: , : , :
64	instantiation	192, 77, 78	⊢
	: , : , :
65	instantiation	149, 150, 99, 151, 101, 172, 108, 107	⊢
	: , : , : , :
66	instantiation	192, 79, 80	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.division.div_as_mult
68	instantiation	240, 218, 81	⊢
	: , : , :
69	instantiation	157, 96	⊢
	:
70	instantiation	82, 212, 129, 139, 131, 83*	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
72	instantiation	202, 115	⊢
	:
73	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
74	instantiation	145, 212	⊢
	:
75	instantiation	148, 150, 99, 237, 151, 86, 212, 172, 108, 84	⊢
	: , : , : , : , : , :
76	instantiation	148, 99, 239, 150, 86, 85, 151, 212, 172, 108, 102, 107	⊢
	: , : , : , : , : , :
77	instantiation	104, 150, 99, 237, 151, 86, 212, 172, 108, 102, 107	⊢
	: , : , : , : , : , : , :
78	instantiation	192, 87, 88	⊢
	: , : , :
79	instantiation	192, 89, 90	⊢
	: , : , :
80	instantiation	91, 237, 239, 150, 92, 151, 186, 93, 114, 94*, 95*	⊢
	: , : , : , : , : , :
81	instantiation	155, 156, 96	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
83	instantiation	111, 115, 186, 97*	⊢
	: , :
84	instantiation	98, 102, 107	⊢
	: , :
85	instantiation	173	⊢
	: , :
86	instantiation	116	⊢
	: , : , :
87	instantiation	105, 150, 239, 99, 151, 100, 101, 102, 212, 172, 108, 107	⊢
	: , : , : , : , : , :
88	instantiation	203, 103	⊢
	: , : , :
89	instantiation	104, 237, 150, 151, 172, 108, 107	⊢
	: , : , : , : , : , : , :
90	instantiation	105, 150, 239, 237, 151, 106, 172, 107, 108, 109*	⊢
	: , : , : , : , : , :
91	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
92	instantiation	173	⊢
	: , :
93	instantiation	110, 112	⊢
	:
94	instantiation	111, 186, 112, 113*	⊢
	: , :
95	instantiation	202, 114	⊢
	:
96	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
97	instantiation	211, 115	⊢
	:
98	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
100	instantiation	173	⊢
	: , :
101	instantiation	116	⊢
	: , : , :
102	instantiation	240, 218, 117	⊢
	: , : , :
103	instantiation	132, 118, 119	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
105	theorem		⊢
	proveit.numbers.multiplication.association
106	instantiation	173	⊢
	: , :
107	instantiation	120, 172, 121	⊢
	: , :
108	instantiation	240, 218, 122	⊢
	: , : , :
109	instantiation	123, 172, 197, 139, 124, 125*, 126*	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.negation.complex_closure
111	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
112	instantiation	240, 218, 166	⊢
	: , : , :
113	instantiation	192, 127, 128	⊢
	: , : , :
114	instantiation	240, 218, 142	⊢
	: , : , :
115	instantiation	240, 218, 129	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
117	instantiation	130, 197, 219, 131	⊢
	: , :
118	instantiation	132, 133, 134	⊢
	: , : , :
119	instantiation	135, 136, 137, 138	⊢
	: , : , : , :
120	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
121	instantiation	240, 218, 139	⊢
	: , : , :
122	instantiation	140, 141, 142	⊢
	: , :
123	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
124	instantiation	143, 144	⊢
	:
125	instantiation	145, 172	⊢
	:
126	instantiation	192, 146, 147	⊢
	: , : , :
127	instantiation	148, 237, 239, 150, 152, 151, 186, 153, 154	⊢
	: , : , : , : , : , :
128	instantiation	149, 150, 239, 151, 152, 153, 154	⊢
	: , : , : , :
129	instantiation	155, 156, 232	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.division.div_real_closure
131	instantiation	157, 231	⊢
	:
132	theorem		⊢
	proveit.logic.equality.sub_right_side_into
133	instantiation	158, 186, 159, 160	⊢
	: , : , : , : , :
134	instantiation	192, 161, 162	⊢
	: , : , :
135	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
136	instantiation	203, 163	⊢
	: , : , :
137	instantiation	203, 163	⊢
	: , : , :
138	instantiation	211, 186	⊢
	:
139	instantiation	240, 225, 164	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
141	instantiation	165, 166	⊢
	:
142	instantiation	167, 168	⊢
	:
143	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
144	instantiation	240, 169, 200	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
146	instantiation	203, 170	⊢
	: , : , :
147	instantiation	171, 172	⊢
	:
148	theorem		⊢
	proveit.numbers.multiplication.disassociation
149	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
150	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
151	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
152	instantiation	173	⊢
	: , :
153	instantiation	240, 218, 183	⊢
	: , : , :
154	instantiation	240, 218, 184	⊢
	: , : , :
155	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
156	instantiation	174, 175	⊢
	: , :
157	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
158	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
159	instantiation	240, 177, 176	⊢
	: , : , :
160	instantiation	240, 177, 178	⊢
	: , : , :
161	instantiation	203, 179	⊢
	: , : , :
162	instantiation	203, 180	⊢
	: , : , :
163	instantiation	205, 186	⊢
	:
164	instantiation	240, 233, 181	⊢
	: , : , :
165	theorem		⊢
	proveit.numbers.negation.real_closure
166	instantiation	182, 183, 184	⊢
	: , :
167	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
168	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
169	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
170	instantiation	185, 186, 187	⊢
	: , :
171	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
172	instantiation	240, 218, 188	⊢
	: , : , :
173	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
174	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
175	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
176	instantiation	240, 190, 189	⊢
	: , : , :
177	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
178	instantiation	240, 190, 216	⊢
	: , : , :
179	instantiation	203, 191	⊢
	: , : , :
180	instantiation	192, 193, 194	⊢
	: , : , :
181	instantiation	235, 229	⊢
	:
182	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
183	instantiation	240, 225, 195	⊢
	: , : , :
184	instantiation	240, 225, 196	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
186	instantiation	240, 218, 197	⊢
	: , : , :
187	instantiation	198	⊢
	:
188	instantiation	240, 199, 200	⊢
	: , : , :
189	instantiation	240, 222, 201	⊢
	: , : , :
190	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
191	instantiation	202, 212	⊢
	:
192	axiom		⊢
	proveit.logic.equality.equals_transitivity
193	instantiation	203, 204	⊢
	: , : , :
194	instantiation	205, 212	⊢
	:
195	instantiation	240, 233, 206	⊢
	: , : , :
196	instantiation	240, 207, 208	⊢
	: , : , :
197	instantiation	240, 225, 209	⊢
	: , : , :
198	axiom		⊢
	proveit.logic.equality.equals_reflexivity
199	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
200	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
201	instantiation	240, 230, 210	⊢
	: , : , :
202	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
203	axiom		⊢
	proveit.logic.equality.substitution
204	instantiation	211, 212	⊢
	:
205	theorem		⊢
	proveit.numbers.division.frac_one_denom
206	instantiation	240, 213, 214	⊢
	: , : , :
207	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
208	instantiation	215, 216, 217	⊢
	: , :
209	instantiation	240, 233, 229	⊢
	: , : , :
210	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
211	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
212	instantiation	240, 218, 219	⊢
	: , : , :
213	instantiation	220, 221, 236	⊢
	: , :
214	assumption		⊢
215	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
216	instantiation	240, 222, 223	⊢
	: , : , :
217	instantiation	235, 224	⊢
	:
218	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
219	instantiation	240, 225, 226	⊢
	: , : , :
220	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
221	instantiation	227, 228, 229	⊢
	: , :
222	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
223	instantiation	240, 230, 231	⊢
	: , : , :
224	instantiation	240, 241, 232	⊢
	: , : , :
225	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
226	instantiation	240, 233, 234	⊢
	: , : , :
227	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
228	instantiation	235, 236	⊢
	:
229	instantiation	240, 238, 237	⊢
	: , : , :
230	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
231	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
232	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
233	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
234	instantiation	240, 238, 239	⊢
	: , : , :
235	theorem		⊢
	proveit.numbers.negation.int_closure
236	instantiation	240, 241, 242	⊢
	: , : , :
237	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
238	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
239	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
240	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
241	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
242	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements