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	deduction	1	⊢
1	instantiation	74, 2, 3	⊢
	: , : , :
2	instantiation	46, 4	⊢
	: , : , :
3	instantiation	5, 32, 6, 24, 7*	⊢
	: , : , :
4	instantiation	8, 9, 10, 11, 12, 13	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
6	instantiation	14, 51	⊢
	:
7	instantiation	74, 15, 16	⊢
	: , : , :
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
10	instantiation	108	⊢
	: , :
11	instantiation	108	⊢
	: , :
12	instantiation	46, 17	⊢
	: , : , :
13	instantiation	18	⊢
	:
14	theorem		⊢
	proveit.numbers.negation.complex_closure
15	instantiation	46, 19	⊢
	: , : , :
16	instantiation	20, 21	⊢
	:
17	instantiation	46, 22	⊢
	: , : , :
18	axiom		⊢
	proveit.logic.equality.equals_reflexivity
19	instantiation	23, 51, 24, 25	⊢
	: , :
20	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
21	instantiation	135, 112, 26	⊢
	: , : , :
22	instantiation	74, 27, 28	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
24	instantiation	83, 29, 30	⊢
	: , : , :
25	instantiation	63, 87, 137, 96, 31, 97, 100, 101, 106, 107, 99	⊢
	: , : , : , : , : , : , :
26	instantiation	135, 115, 32	⊢
	: , : , :
27	instantiation	46, 33	⊢
	: , : , :
28	instantiation	74, 34, 35	⊢
	: , : , :
29	instantiation	105, 86, 36	⊢
	: , :
30	instantiation	74, 37, 38	⊢
	: , : , :
31	instantiation	102	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
33	instantiation	95, 64, 122, 96, 65, 39, 97, 100, 101, 106, 107, 69, 99	⊢
	: , : , : , : , : , :
34	instantiation	74, 40, 41	⊢
	: , : , :
35	instantiation	42, 51	⊢
	:
36	instantiation	83, 43, 44	⊢
	: , : , :
37	instantiation	95, 137, 87, 96, 45, 97, 86, 106, 99, 107	⊢
	: , : , : , : , : , :
38	instantiation	95, 96, 122, 87, 97, 88, 45, 100, 101, 106, 99, 107	⊢
	: , : , : , : , : , :
39	instantiation	108	⊢
	: , :
40	instantiation	46, 47	⊢
	: , : , :
41	instantiation	48, 49, 50, 51, 52*	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.division.frac_one_denom
43	instantiation	105, 53, 107	⊢
	: , :
44	instantiation	95, 96, 122, 137, 97, 54, 106, 99, 107	⊢
	: , : , : , : , : , :
45	instantiation	102	⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.substitution
47	instantiation	74, 55, 56	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.division.frac_cancel_left
49	instantiation	135, 58, 57	⊢
	: , : , :
50	instantiation	135, 58, 59	⊢
	: , : , :
51	instantiation	83, 60, 61	⊢
	: , : , :
52	instantiation	62, 69	⊢
	:
53	instantiation	105, 106, 99	⊢
	: , :
54	instantiation	108	⊢
	: , :
55	instantiation	63, 96, 64, 137, 97, 65, 100, 101, 106, 107, 69, 99	⊢
	: , : , : , : , : , : , :
56	instantiation	66, 137, 67, 96, 68, 97, 69, 100, 101, 106, 107, 99	⊢
	: , : , : , : , : , :
57	instantiation	135, 71, 70	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
59	instantiation	135, 71, 72	⊢
	: , : , :
60	instantiation	105, 86, 73	⊢
	: , :
61	instantiation	74, 75, 76	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
63	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
65	instantiation	77	⊢
	: , : , : , :
66	theorem		⊢
	proveit.numbers.multiplication.association
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
68	instantiation	78	⊢
	: , : , : , : , :
69	instantiation	135, 112, 79	⊢
	: , : , :
70	instantiation	135, 81, 80	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
72	instantiation	135, 81, 82	⊢
	: , : , :
73	instantiation	83, 84, 85	⊢
	: , : , :
74	axiom		⊢
	proveit.logic.equality.equals_transitivity
75	instantiation	95, 137, 87, 96, 89, 97, 86, 106, 107, 99	⊢
	: , : , : , : , : , :
76	instantiation	95, 96, 122, 87, 97, 88, 89, 100, 101, 106, 107, 99	⊢
	: , : , : , : , : , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
78	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
79	instantiation	90, 91, 132	⊢
	: , : , :
80	instantiation	135, 92, 132	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
82	instantiation	135, 92, 93	⊢
	: , : , :
83	theorem		⊢
	proveit.logic.equality.sub_right_side_into
84	instantiation	105, 94, 99	⊢
	: , :
85	instantiation	95, 96, 122, 137, 97, 98, 106, 107, 99	⊢
	: , : , : , : , : , :
86	instantiation	105, 100, 101	⊢
	: , :
87	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
88	instantiation	108	⊢
	: , :
89	instantiation	102	⊢
	: , : , :
90	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
91	instantiation	103, 104	⊢
	: , :
92	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
93	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
94	instantiation	105, 106, 107	⊢
	: , :
95	theorem		⊢
	proveit.numbers.multiplication.disassociation
96	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
97	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
98	instantiation	108	⊢
	: , :
99	instantiation	135, 112, 109	⊢
	: , : , :
100	instantiation	135, 112, 110	⊢
	: , : , :
101	instantiation	135, 112, 111	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
103	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
104	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
105	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
106	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
107	instantiation	135, 112, 113	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
109	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
110	instantiation	135, 117, 114	⊢
	: , : , :
111	instantiation	135, 115, 116	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
113	instantiation	135, 117, 118	⊢
	: , : , :
114	instantiation	135, 120, 119	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
116	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
117	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
118	instantiation	135, 120, 121	⊢
	: , : , :
119	instantiation	135, 136, 122	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
121	instantiation	135, 123, 124	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
123	instantiation	125, 126, 127	⊢
	: , :
124	assumption		⊢
125	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
126	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
127	instantiation	128, 129, 130	⊢
	: , :
128	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
129	instantiation	135, 131, 132	⊢
	: , : , :
130	instantiation	133, 134	⊢
	:
131	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
132	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
133	theorem		⊢
	proveit.numbers.negation.int_closure
134	instantiation	135, 136, 137	⊢
	: , : , :
135	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
136	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
137	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements