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