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