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	generalization	1	⊢
1	instantiation	2, 3	⊢
	: , : , :
2	axiom		⊢
	proveit.core_expr_types.conditionals.conditional_substitution
3	deduction	4	⊢
4	instantiation	77, 5, 6	⊢
	: , : , :
5	instantiation	49, 7	⊢
	: , : , :
6	instantiation	8, 35, 9, 27, 10*	⊢
	: , : , :
7	instantiation	11, 12, 13, 14, 15, 16	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
9	instantiation	17, 54	⊢
	:
10	instantiation	77, 18, 19	⊢
	: , : , :
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
13	instantiation	111	⊢
	: , :
14	instantiation	111	⊢
	: , :
15	instantiation	49, 20	⊢
	: , : , :
16	instantiation	21	⊢
	:
17	theorem		⊢
	proveit.numbers.negation.complex_closure
18	instantiation	49, 22	⊢
	: , : , :
19	instantiation	23, 24	⊢
	:
20	instantiation	49, 25	⊢
	: , : , :
21	axiom		⊢
	proveit.logic.equality.equals_reflexivity
22	instantiation	26, 54, 27, 28	⊢
	: , :
23	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
24	instantiation	138, 115, 29	⊢
	: , : , :
25	instantiation	77, 30, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
27	instantiation	86, 32, 33	⊢
	: , : , :
28	instantiation	66, 90, 140, 99, 34, 100, 103, 104, 109, 110, 102	⊢
	: , : , : , : , : , : , :
29	instantiation	138, 118, 35	⊢
	: , : , :
30	instantiation	49, 36	⊢
	: , : , :
31	instantiation	77, 37, 38	⊢
	: , : , :
32	instantiation	108, 89, 39	⊢
	: , :
33	instantiation	77, 40, 41	⊢
	: , : , :
34	instantiation	105	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
36	instantiation	98, 67, 125, 99, 68, 42, 100, 103, 104, 109, 110, 72, 102	⊢
	: , : , : , : , : , :
37	instantiation	77, 43, 44	⊢
	: , : , :
38	instantiation	45, 54	⊢
	:
39	instantiation	86, 46, 47	⊢
	: , : , :
40	instantiation	98, 140, 90, 99, 48, 100, 89, 109, 102, 110	⊢
	: , : , : , : , : , :
41	instantiation	98, 99, 125, 90, 100, 91, 48, 103, 104, 109, 102, 110	⊢
	: , : , : , : , : , :
42	instantiation	111	⊢
	: , :
43	instantiation	49, 50	⊢
	: , : , :
44	instantiation	51, 52, 53, 54, 55*	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.division.frac_one_denom
46	instantiation	108, 56, 110	⊢
	: , :
47	instantiation	98, 99, 125, 140, 100, 57, 109, 102, 110	⊢
	: , : , : , : , : , :
48	instantiation	105	⊢
	: , : , :
49	axiom		⊢
	proveit.logic.equality.substitution
50	instantiation	77, 58, 59	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.division.frac_cancel_left
52	instantiation	138, 61, 60	⊢
	: , : , :
53	instantiation	138, 61, 62	⊢
	: , : , :
54	instantiation	86, 63, 64	⊢
	: , : , :
55	instantiation	65, 72	⊢
	:
56	instantiation	108, 109, 102	⊢
	: , :
57	instantiation	111	⊢
	: , :
58	instantiation	66, 99, 67, 140, 100, 68, 103, 104, 109, 110, 72, 102	⊢
	: , : , : , : , : , : , :
59	instantiation	69, 140, 70, 99, 71, 100, 72, 103, 104, 109, 110, 102	⊢
	: , : , : , : , : , :
60	instantiation	138, 74, 73	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
62	instantiation	138, 74, 75	⊢
	: , : , :
63	instantiation	108, 89, 76	⊢
	: , :
64	instantiation	77, 78, 79	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
66	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
68	instantiation	80	⊢
	: , : , : , :
69	theorem		⊢
	proveit.numbers.multiplication.association
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
71	instantiation	81	⊢
	: , : , : , : , :
72	instantiation	138, 115, 82	⊢
	: , : , :
73	instantiation	138, 84, 83	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
75	instantiation	138, 84, 85	⊢
	: , : , :
76	instantiation	86, 87, 88	⊢
	: , : , :
77	axiom		⊢
	proveit.logic.equality.equals_transitivity
78	instantiation	98, 140, 90, 99, 92, 100, 89, 109, 110, 102	⊢
	: , : , : , : , : , :
79	instantiation	98, 99, 125, 90, 100, 91, 92, 103, 104, 109, 110, 102	⊢
	: , : , : , : , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
81	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
82	instantiation	93, 94, 135	⊢
	: , : , :
83	instantiation	138, 95, 135	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
85	instantiation	138, 95, 96	⊢
	: , : , :
86	theorem		⊢
	proveit.logic.equality.sub_right_side_into
87	instantiation	108, 97, 102	⊢
	: , :
88	instantiation	98, 99, 125, 140, 100, 101, 109, 110, 102	⊢
	: , : , : , : , : , :
89	instantiation	108, 103, 104	⊢
	: , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
91	instantiation	111	⊢
	: , :
92	instantiation	105	⊢
	: , : , :
93	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
94	instantiation	106, 107	⊢
	: , :
95	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
96	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
97	instantiation	108, 109, 110	⊢
	: , :
98	theorem		⊢
	proveit.numbers.multiplication.disassociation
99	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
100	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
101	instantiation	111	⊢
	: , :
102	instantiation	138, 115, 112	⊢
	: , : , :
103	instantiation	138, 115, 113	⊢
	: , : , :
104	instantiation	138, 115, 114	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
106	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
108	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
109	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
110	instantiation	138, 115, 116	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
112	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
113	instantiation	138, 120, 117	⊢
	: , : , :
114	instantiation	138, 118, 119	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
116	instantiation	138, 120, 121	⊢
	: , : , :
117	instantiation	138, 123, 122	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
120	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
121	instantiation	138, 123, 124	⊢
	: , : , :
122	instantiation	138, 139, 125	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
124	instantiation	138, 126, 127	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
126	instantiation	128, 129, 130	⊢
	: , :
127	assumption		⊢
128	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
129	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
130	instantiation	131, 132, 133	⊢
	: , :
131	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
132	instantiation	138, 134, 135	⊢
	: , : , :
133	instantiation	136, 137	⊢
	:
134	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
135	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
136	theorem		⊢
	proveit.numbers.negation.int_closure
137	instantiation	138, 139, 140	⊢
	: , : , :
138	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
139	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
140	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements