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*, 4*	⊢
	: , : , :
1	reference	53	⊢
2	modus ponens	5, 6	⊢
3	instantiation	7, 131	⊢
	: , :
4	instantiation	7, 131	⊢
	: , :
5	instantiation	8, 123	⊢
	: , : , : , : , : , : , :
6	generalization	9	⊢
7	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
8	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
9	instantiation	12, 10, 11	,  ⊢
	: , : , :
10	instantiation	12, 13, 14	,  ⊢
	: , : , :
11	instantiation	78, 15, 16	,  ⊢
	: , : , :
12	theorem		⊢
	proveit.logic.equality.sub_left_side_into
13	instantiation	17, 85, 18, 19, 20, 21*, 22*	,  ⊢
	: , : , :
14	instantiation	78, 23, 24	,  ⊢
	: , : , :
15	instantiation	53, 25	,  ⊢
	: , : , :
16	instantiation	37, 85, 45	,  ⊢
	: , :
17	theorem		⊢
	proveit.numbers.exponentiation.exp_eq
18	instantiation	26, 27, 31	⊢
	: , :
19	instantiation	26, 27, 34	⊢
	: , :
20	instantiation	28, 117, 101, 29*, 30*	⊢
	: , :
21	instantiation	33, 50, 31, 85, 32*	,  ⊢
	: , : , :
22	instantiation	33, 50, 34, 85, 35*	,  ⊢
	: , : , :
23	instantiation	53, 36	,  ⊢
	: , : , :
24	instantiation	37, 85, 42	,  ⊢
	: , :
25	instantiation	94, 38, 39	,  ⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
27	instantiation	154, 128, 40	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.exp_neg2pi_i_x
29	instantiation	41, 64, 87, 52	⊢
	: , :
30	instantiation	41, 59, 87, 52	⊢
	: , :
31	instantiation	43, 42	⊢
	:
32	instantiation	44, 42, 85	,  ⊢
	: , :
33	theorem		⊢
	proveit.numbers.exponentiation.complex_power_of_complex_power
34	instantiation	43, 45	⊢
	:
35	instantiation	44, 45, 85	,  ⊢
	: , :
36	instantiation	94, 46, 47	,  ⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.multiplication.commutation
38	instantiation	53, 48	,  ⊢
	: , : , :
39	instantiation	55, 49	,  ⊢
	: , :
40	instantiation	154, 134, 50	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
42	instantiation	51, 64, 87, 52	⊢
	: , :
43	theorem		⊢
	proveit.numbers.negation.complex_closure
44	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
45	instantiation	51, 59, 87, 52	⊢
	: , :
46	instantiation	53, 54	,  ⊢
	: , : , :
47	instantiation	55, 56	,  ⊢
	: , :
48	instantiation	94, 57, 58	,  ⊢
	: , : , :
49	instantiation	63, 85, 59, 65, 66, 67*, 68*	,  ⊢
	: , : , : , :
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
51	theorem		⊢
	proveit.numbers.division.div_complex_closure
52	instantiation	60, 151	⊢
	:
53	axiom		⊢
	proveit.logic.equality.substitution
54	instantiation	94, 61, 62	,  ⊢
	: , : , :
55	theorem		⊢
	proveit.logic.equality.equals_reversal
56	instantiation	63, 85, 64, 65, 66, 67*, 68*	,  ⊢
	: , : , : , :
57	instantiation	72, 106, 73, 156, 107, 74, 119, 120, 110, 85, 103	,  ⊢
	: , : , : , : , : , : , :
58	instantiation	75, 156, 76, 106, 69, 107, 85, 119, 120, 110, 103	,  ⊢
	: , : , : , : , : , :
59	instantiation	78, 70, 71	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
61	instantiation	72, 106, 73, 156, 107, 74, 119, 120, 110, 85, 111	,  ⊢
	: , : , : , : , : , : , :
62	instantiation	75, 156, 76, 106, 77, 107, 85, 119, 120, 110, 111	,  ⊢
	: , : , : , : , : , :
63	theorem		⊢
	proveit.numbers.division.prod_of_fracs
64	instantiation	78, 79, 80	⊢
	: , : , :
65	instantiation	154, 82, 81	⊢
	: , : , :
66	instantiation	154, 82, 83	⊢
	: , : , :
67	instantiation	84, 85	⊢
	:
68	instantiation	86, 87	⊢
	:
69	instantiation	92	⊢
	: , : , : , :
70	instantiation	118, 104, 88	⊢
	: , :
71	instantiation	94, 89, 90	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
74	instantiation	91	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.multiplication.association
76	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
77	instantiation	92	⊢
	: , : , : , :
78	theorem		⊢
	proveit.logic.equality.sub_right_side_into
79	instantiation	118, 104, 93	⊢
	: , :
80	instantiation	94, 95, 96	⊢
	: , : , :
81	instantiation	154, 98, 97	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
83	instantiation	154, 98, 99	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.division.frac_one_denom
85	instantiation	154, 128, 100	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
87	instantiation	154, 128, 101	⊢
	: , : , :
88	instantiation	118, 110, 103	⊢
	: , :
89	instantiation	105, 156, 141, 106, 102, 107, 104, 110, 103	⊢
	: , : , : , : , : , :
90	instantiation	105, 106, 141, 107, 108, 102, 119, 120, 110, 103	⊢
	: , : , : , : , : , :
91	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
92	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
93	instantiation	118, 110, 111	⊢
	: , :
94	axiom		⊢
	proveit.logic.equality.equals_transitivity
95	instantiation	105, 156, 141, 106, 109, 107, 104, 110, 111	⊢
	: , : , : , : , : , :
96	instantiation	105, 106, 141, 107, 108, 109, 119, 120, 110, 111	⊢
	: , : , : , : , : , :
97	instantiation	154, 113, 112	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
99	instantiation	154, 113, 114	⊢
	: , : , :
100	instantiation	154, 132, 115	⊢
	: , : , :
101	instantiation	154, 132, 116	⊢
	: , : , :
102	instantiation	121	⊢
	: , :
103	instantiation	154, 128, 117	⊢
	: , : , :
104	instantiation	118, 119, 120	⊢
	: , :
105	theorem		⊢
	proveit.numbers.multiplication.disassociation
106	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
107	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
108	instantiation	121	⊢
	: , :
109	instantiation	121	⊢
	: , :
110	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
111	instantiation	154, 128, 122	⊢
	: , : , :
112	instantiation	154, 124, 123	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
114	instantiation	154, 124, 151	⊢
	: , : , :
115	instantiation	154, 137, 125	⊢
	: , : , :
116	instantiation	154, 137, 148	⊢
	: , : , :
117	instantiation	154, 132, 126	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
119	instantiation	154, 128, 127	⊢
	: , : , :
120	instantiation	154, 128, 129	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
122	instantiation	154, 132, 130	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
124	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
125	instantiation	154, 139, 131	⊢
	: , : , :
126	instantiation	154, 137, 146	⊢
	: , : , :
127	instantiation	154, 132, 133	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
129	instantiation	154, 134, 135	⊢
	: , : , :
130	instantiation	154, 137, 136	⊢
	: , : , :
131	assumption		⊢
132	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
133	instantiation	154, 137, 138	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
135	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
136	instantiation	154, 139, 140	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
138	instantiation	154, 155, 141	⊢
	: , : , :
139	instantiation	142, 143, 144	⊢
	: , :
140	instantiation	145, 146, 151	⊢
	: , :
141	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
142	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
143	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
144	instantiation	147, 148, 149	⊢
	: , :
145	theorem		⊢
	proveit.numbers.modular.mod_natpos_in_interval
146	assumption		⊢
147	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
148	instantiation	154, 150, 151	⊢
	: , : , :
149	instantiation	152, 153	⊢
	:
150	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
151	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
152	theorem		⊢
	proveit.numbers.negation.int_closure
153	instantiation	154, 155, 156	⊢
	: , : , :
154	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
155	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
156	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements