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