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	reference	81	⊢
2	instantiation	109, 3, 4	⊢
	: , : , :
3	instantiation	81, 5	⊢
	: , : , :
4	instantiation	6, 161, 162, 33, 7*	⊢
	: , : , :
5	modus ponens	8, 9	⊢
6	theorem		⊢
	proveit.numbers.summation.trivial_sum
7	instantiation	109, 10, 87	⊢
	: , : , :
8	instantiation	11, 128	⊢
	: , : , : , : , : , :
9	generalization	12	⊢
10	instantiation	81, 13	⊢
	: , : , :
11	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
12	instantiation	14, 15	⊢
	: , : , :
13	instantiation	109, 16, 17	⊢
	: , : , :
14	axiom		⊢
	proveit.core_expr_types.conditionals.conditional_substitution
15	deduction	18	⊢
16	instantiation	81, 19	⊢
	: , : , :
17	instantiation	20, 21, 22, 23	⊢
	: , : , : , :
18	instantiation	109, 24, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.negation.negated_zero
20	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
21	instantiation	26, 131, 157, 132, 30, 27, 104, 31, 28, 33	⊢
	: , : , : , : , : , :
22	instantiation	29, 157, 172, 30, 104, 31, 33	⊢
	: , : , : , :
23	instantiation	32, 33, 104, 34	⊢
	: , : , :
24	instantiation	81, 35	⊢
	: , : , :
25	instantiation	36, 67, 37, 59, 38*	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.disassociation
27	instantiation	143	⊢
	: , :
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
29	theorem		⊢
	proveit.numbers.addition.elim_zero_any
30	instantiation	143	⊢
	: , :
31	instantiation	170, 147, 39	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
33	instantiation	170, 147, 40	⊢
	: , : , :
34	instantiation	53	⊢
	:
35	instantiation	41, 42, 43, 44, 45, 46	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
37	instantiation	47, 86	⊢
	:
38	instantiation	109, 48, 49	⊢
	: , : , :
39	instantiation	170, 152, 50	⊢
	: , : , :
40	instantiation	170, 152, 51	⊢
	: , : , :
41	theorem		⊢
	proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
43	instantiation	143	⊢
	: , :
44	instantiation	143	⊢
	: , :
45	instantiation	81, 52	⊢
	: , : , :
46	instantiation	53	⊢
	:
47	theorem		⊢
	proveit.numbers.negation.complex_closure
48	instantiation	81, 54	⊢
	: , : , :
49	instantiation	55, 56	⊢
	:
50	instantiation	170, 155, 165	⊢
	: , : , :
51	instantiation	170, 155, 169	⊢
	: , : , :
52	instantiation	81, 57	⊢
	: , : , :
53	axiom		⊢
	proveit.logic.equality.equals_reflexivity
54	instantiation	58, 86, 59, 60	⊢
	: , :
55	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
56	instantiation	170, 147, 61	⊢
	: , : , :
57	instantiation	109, 62, 63	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
59	instantiation	118, 64, 65	⊢
	: , : , :
60	instantiation	98, 122, 172, 131, 66, 132, 135, 136, 141, 142, 134	⊢
	: , : , : , : , : , : , :
61	instantiation	170, 150, 67	⊢
	: , : , :
62	instantiation	81, 68	⊢
	: , : , :
63	instantiation	109, 69, 70	⊢
	: , : , :
64	instantiation	140, 121, 71	⊢
	: , :
65	instantiation	109, 72, 73	⊢
	: , : , :
66	instantiation	137	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
68	instantiation	130, 99, 157, 131, 100, 74, 132, 135, 136, 141, 142, 104, 134	⊢
	: , : , : , : , : , :
69	instantiation	109, 75, 76	⊢
	: , : , :
70	instantiation	77, 86	⊢
	:
71	instantiation	118, 78, 79	⊢
	: , : , :
72	instantiation	130, 172, 122, 131, 80, 132, 121, 141, 134, 142	⊢
	: , : , : , : , : , :
73	instantiation	130, 131, 157, 122, 132, 123, 80, 135, 136, 141, 134, 142	⊢
	: , : , : , : , : , :
74	instantiation	143	⊢
	: , :
75	instantiation	81, 82	⊢
	: , : , :
76	instantiation	83, 84, 85, 86, 87*	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.division.frac_one_denom
78	instantiation	140, 88, 142	⊢
	: , :
79	instantiation	130, 131, 157, 172, 132, 89, 141, 134, 142	⊢
	: , : , : , : , : , :
80	instantiation	137	⊢
	: , : , :
81	axiom		⊢
	proveit.logic.equality.substitution
82	instantiation	109, 90, 91	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.division.frac_cancel_left
84	instantiation	170, 93, 92	⊢
	: , : , :
85	instantiation	170, 93, 94	⊢
	: , : , :
86	instantiation	118, 95, 96	⊢
	: , : , :
87	instantiation	97, 104	⊢
	:
88	instantiation	140, 141, 134	⊢
	: , :
89	instantiation	143	⊢
	: , :
90	instantiation	98, 131, 99, 172, 132, 100, 135, 136, 141, 142, 104, 134	⊢
	: , : , : , : , : , : , :
91	instantiation	101, 172, 102, 131, 103, 132, 104, 135, 136, 141, 142, 134	⊢
	: , : , : , : , : , :
92	instantiation	170, 106, 105	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
94	instantiation	170, 106, 107	⊢
	: , : , :
95	instantiation	140, 121, 108	⊢
	: , :
96	instantiation	109, 110, 111	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
98	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
100	instantiation	112	⊢
	: , : , : , :
101	theorem		⊢
	proveit.numbers.multiplication.association
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
103	instantiation	113	⊢
	: , : , : , : , :
104	instantiation	170, 147, 114	⊢
	: , : , :
105	instantiation	170, 116, 115	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
107	instantiation	170, 116, 117	⊢
	: , : , :
108	instantiation	118, 119, 120	⊢
	: , : , :
109	axiom		⊢
	proveit.logic.equality.equals_transitivity
110	instantiation	130, 172, 122, 131, 124, 132, 121, 141, 142, 134	⊢
	: , : , : , : , : , :
111	instantiation	130, 131, 157, 122, 132, 123, 124, 135, 136, 141, 142, 134	⊢
	: , : , : , : , : , :
112	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
113	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
114	instantiation	125, 126, 167	⊢
	: , : , :
115	instantiation	170, 127, 167	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
117	instantiation	170, 127, 128	⊢
	: , : , :
118	theorem		⊢
	proveit.logic.equality.sub_right_side_into
119	instantiation	140, 129, 134	⊢
	: , :
120	instantiation	130, 131, 157, 172, 132, 133, 141, 142, 134	⊢
	: , : , : , : , : , :
121	instantiation	140, 135, 136	⊢
	: , :
122	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
123	instantiation	143	⊢
	: , :
124	instantiation	137	⊢
	: , : , :
125	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
126	instantiation	138, 139	⊢
	: , :
127	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
128	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
129	instantiation	140, 141, 142	⊢
	: , :
130	theorem		⊢
	proveit.numbers.multiplication.disassociation
131	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
132	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
133	instantiation	143	⊢
	: , :
134	instantiation	170, 147, 144	⊢
	: , : , :
135	instantiation	170, 147, 145	⊢
	: , : , :
136	instantiation	170, 147, 146	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
138	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
139	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
140	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
141	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
142	instantiation	170, 147, 148	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
144	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
145	instantiation	170, 152, 149	⊢
	: , : , :
146	instantiation	170, 150, 151	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
148	instantiation	170, 152, 153	⊢
	: , : , :
149	instantiation	170, 155, 154	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
151	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
152	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
153	instantiation	170, 155, 156	⊢
	: , : , :
154	instantiation	170, 171, 157	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
156	instantiation	170, 158, 159	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
158	instantiation	160, 161, 162	⊢
	: , :
159	assumption		⊢
160	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
161	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
162	instantiation	163, 164, 165	⊢
	: , :
163	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
164	instantiation	170, 166, 167	⊢
	: , : , :
165	instantiation	168, 169	⊢
	:
166	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
167	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
168	theorem		⊢
	proveit.numbers.negation.int_closure
169	instantiation	170, 171, 172	⊢
	: , : , :
170	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
171	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
172	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements