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