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, 5, 6, 7, 8, 9	,  ⊢
	: , : , : , : , : , :
1	reference	84	⊢
2	reference	150	⊢
3	reference	145	⊢
4	reference	85	⊢
5	instantiation	101	⊢
	: , :
6	reference	86	⊢
7	instantiation	19, 14, 10	⊢
	: , :
8	instantiation	35, 11, 12, 13	⊢
	: , :
9	instantiation	19, 14, 15	,  ⊢
	: , :
10	instantiation	70, 16, 17	⊢
	: , : , :
11	instantiation	148, 111, 18	⊢
	: , : , :
12	instantiation	19, 94, 20	⊢
	: , :
13	instantiation	21, 22, 23	⊢
	: , : , :
14	instantiation	148, 111, 24	⊢
	: , : , :
15	instantiation	25, 26	,  ⊢
	:
16	instantiation	98, 73, 27	⊢
	: , :
17	instantiation	59, 28, 29	⊢
	: , : , :
18	instantiation	148, 122, 30	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
20	instantiation	35, 68, 94, 45	⊢
	: , :
21	theorem		⊢
	proveit.logic.equality.sub_left_side_into
22	instantiation	31, 105, 32	⊢
	: , :
23	instantiation	65, 33	⊢
	: , : , :
24	instantiation	148, 114, 34	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.negation.complex_closure
26	instantiation	35, 36, 37, 38	,  ⊢
	: , :
27	instantiation	70, 39, 40	⊢
	: , : , :
28	instantiation	84, 150, 74, 85, 41, 86, 73, 99, 64, 100	⊢
	: , : , : , : , : , :
29	instantiation	84, 85, 145, 74, 86, 75, 41, 94, 89, 99, 64, 100	⊢
	: , : , : , : , : , :
30	instantiation	148, 129, 144	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
32	instantiation	148, 42, 43	⊢
	: , : , :
33	instantiation	44, 68, 94, 45, 46*	⊢
	: , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
35	theorem		⊢
	proveit.numbers.division.div_complex_closure
36	instantiation	70, 47, 48	,  ⊢
	: , : , :
37	instantiation	148, 111, 49	⊢
	: , : , :
38	instantiation	55, 50	⊢
	:
39	instantiation	98, 51, 100	⊢
	: , :
40	instantiation	84, 85, 145, 150, 86, 52, 99, 64, 100	⊢
	: , : , : , : , : , :
41	instantiation	90	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
43	instantiation	53, 110, 54	⊢
	: , :
44	theorem		⊢
	proveit.numbers.division.div_as_mult
45	instantiation	55, 128	⊢
	:
46	instantiation	59, 56, 57	⊢
	: , : , :
47	instantiation	98, 73, 58	,  ⊢
	: , :
48	instantiation	59, 60, 61	,  ⊢
	: , : , :
49	instantiation	148, 122, 62	⊢
	: , : , :
50	instantiation	63, 145, 142	⊢
	: , :
51	instantiation	98, 99, 64	⊢
	: , :
52	instantiation	101	⊢
	: , :
53	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
54	instantiation	148, 127, 147	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
56	instantiation	65, 66	⊢
	: , : , :
57	instantiation	67, 68, 69	⊢
	: , :
58	instantiation	70, 71, 72	,  ⊢
	: , : , :
59	axiom		⊢
	proveit.logic.equality.equals_transitivity
60	instantiation	84, 150, 74, 85, 76, 86, 73, 99, 100, 88	,  ⊢
	: , : , : , : , : , :
61	instantiation	84, 85, 145, 74, 86, 75, 76, 94, 89, 99, 100, 88	,  ⊢
	: , : , : , : , : , :
62	instantiation	148, 129, 138	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
64	instantiation	148, 111, 77	⊢
	: , : , :
65	axiom		⊢
	proveit.logic.equality.substitution
66	instantiation	78, 79, 126, 80*	⊢
	: , :
67	theorem		⊢
	proveit.numbers.multiplication.commutation
68	instantiation	148, 111, 81	⊢
	: , : , :
69	instantiation	148, 111, 82	⊢
	: , : , :
70	theorem		⊢
	proveit.logic.equality.sub_right_side_into
71	instantiation	98, 83, 88	,  ⊢
	: , :
72	instantiation	84, 85, 145, 150, 86, 87, 99, 100, 88	,  ⊢
	: , : , : , : , : , :
73	instantiation	98, 94, 89	⊢
	: , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
75	instantiation	101	⊢
	: , :
76	instantiation	90	⊢
	: , : , :
77	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
78	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
79	instantiation	148, 91, 92	⊢
	: , : , :
80	instantiation	93, 94	⊢
	:
81	instantiation	95, 96, 147	⊢
	: , : , :
82	instantiation	148, 122, 97	⊢
	: , : , :
83	instantiation	98, 99, 100	⊢
	: , :
84	theorem		⊢
	proveit.numbers.multiplication.disassociation
85	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
86	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
87	instantiation	101	⊢
	: , :
88	instantiation	148, 111, 102	⊢
	: , : , :
89	instantiation	148, 111, 103	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
91	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
92	instantiation	148, 104, 105	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
94	instantiation	148, 111, 106	⊢
	: , : , :
95	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
96	instantiation	107, 108	⊢
	: , :
97	instantiation	148, 109, 110	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
99	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
100	instantiation	148, 111, 112	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
102	instantiation	148, 122, 113	⊢
	: , : , :
103	instantiation	148, 114, 115	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
105	instantiation	148, 116, 117	⊢
	: , : , :
106	instantiation	148, 122, 118	⊢
	: , : , :
107	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
109	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
110	instantiation	119, 120, 121	⊢
	: , :
111	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
112	instantiation	148, 122, 123	⊢
	: , : , :
113	instantiation	148, 129, 124	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
115	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
116	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
117	instantiation	148, 125, 128	⊢
	: , : , :
118	instantiation	148, 129, 141	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
120	instantiation	148, 127, 126	⊢
	: , : , :
121	instantiation	148, 127, 128	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
123	instantiation	148, 129, 130	⊢
	: , : , :
124	instantiation	148, 132, 131	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
126	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
127	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
128	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
129	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
130	instantiation	148, 132, 133	⊢
	: , : , :
131	assumption		⊢
132	instantiation	134, 135, 136	⊢
	: , :
133	assumption		⊢
134	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
135	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
136	instantiation	137, 138, 139	⊢
	: , :
137	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
138	instantiation	140, 141, 142	⊢
	: , :
139	instantiation	143, 144	⊢
	:
140	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
141	instantiation	148, 149, 145	⊢
	: , : , :
142	instantiation	148, 146, 147	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.negation.int_closure
144	instantiation	148, 149, 150	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
146	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
147	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
148	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
149	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
150	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements