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	59, 2, 3	,  ⊢
	: , : , :
2	instantiation	4, 85, 150, 86, 8, 7, 9	,  ⊢
	: , : , : , : , : , : , :
3	instantiation	5, 150, 145, 85, 6, 86, 7, 8, 9	,  ⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
5	theorem		⊢
	proveit.numbers.multiplication.association
6	instantiation	101	⊢
	: , :
7	instantiation	35, 10, 11, 12	⊢
	: , :
8	instantiation	17, 14, 13	⊢
	: , :
9	instantiation	17, 14, 15	,  ⊢
	: , :
10	instantiation	148, 111, 16	⊢
	: , : , :
11	instantiation	17, 94, 18	⊢
	: , :
12	instantiation	19, 20, 21	⊢
	: , : , :
13	instantiation	70, 22, 23	⊢
	: , : , :
14	instantiation	148, 111, 24	⊢
	: , : , :
15	instantiation	25, 26	,  ⊢
	:
16	instantiation	148, 122, 27	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
18	instantiation	35, 67, 94, 42	⊢
	: , :
19	theorem		⊢
	proveit.logic.equality.sub_left_side_into
20	instantiation	28, 105, 29	⊢
	: , :
21	instantiation	64, 30	⊢
	: , : , :
22	instantiation	98, 73, 31	⊢
	: , :
23	instantiation	59, 32, 33	⊢
	: , : , :
24	instantiation	148, 114, 34	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.negation.complex_closure
26	instantiation	35, 36, 37, 38	,  ⊢
	: , :
27	instantiation	148, 129, 144	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
29	instantiation	148, 39, 40	⊢
	: , : , :
30	instantiation	41, 67, 94, 42, 43*	⊢
	: , :
31	instantiation	70, 44, 45	⊢
	: , : , :
32	instantiation	84, 150, 74, 85, 46, 86, 73, 99, 69, 100	⊢
	: , : , : , : , : , :
33	instantiation	84, 85, 145, 74, 86, 75, 46, 94, 89, 99, 69, 100	⊢
	: , : , : , : , : , :
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	53, 50	⊢
	:
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
40	instantiation	51, 110, 52	⊢
	: , :
41	theorem		⊢
	proveit.numbers.division.div_as_mult
42	instantiation	53, 128	⊢
	:
43	instantiation	59, 54, 55	⊢
	: , : , :
44	instantiation	98, 56, 100	⊢
	: , :
45	instantiation	84, 85, 145, 150, 86, 57, 99, 69, 100	⊢
	: , : , : , : , : , :
46	instantiation	90	⊢
	: , : , :
47	instantiation	98, 73, 58	,  ⊢
	: , :
48	instantiation	59, 60, 61	,  ⊢
	: , : , :
49	instantiation	148, 122, 62	⊢
	: , : , :
50	instantiation	63, 145, 142	⊢
	: , :
51	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
52	instantiation	148, 127, 147	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
54	instantiation	64, 65	⊢
	: , : , :
55	instantiation	66, 67, 68	⊢
	: , :
56	instantiation	98, 99, 69	⊢
	: , :
57	instantiation	101	⊢
	: , :
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	axiom		⊢
	proveit.logic.equality.substitution
65	instantiation	77, 78, 126, 79*	⊢
	: , :
66	theorem		⊢
	proveit.numbers.multiplication.commutation
67	instantiation	148, 111, 80	⊢
	: , : , :
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.numbers.exponentiation.neg_power_as_div
78	instantiation	148, 91, 92	⊢
	: , : , :
79	instantiation	93, 94	⊢
	:
80	instantiation	95, 96, 147	⊢
	: , : , :
81	instantiation	148, 122, 97	⊢
	: , : , :
82	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
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