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	, , ,  ⊢
	: , : , :
1	reference	100	⊢
2	instantiation	122, 4	,  ⊢
	: , : , :
3	instantiation	100, 5, 6	, ,  ⊢
	: , : , :
4	instantiation	7, 8, 75, 92, 9, 10, 11*	,  ⊢
	: , : , :
5	instantiation	100, 12, 13	, ,  ⊢
	: , : , :
6	instantiation	100, 14, 15	, ,  ⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
8	instantiation	148, 141, 16	⊢
	: , : , :
9	instantiation	17, 18	⊢
	:
10	assumption		⊢
11	instantiation	19, 98, 97, 140, 20*, 21*	⊢
	: , : , :
12	instantiation	100, 22, 23	, ,  ⊢
	: , : , :
13	instantiation	38, 24, 25, 26	, ,  ⊢
	: , : , : , :
14	instantiation	42, 136, 135, 57, 104, 59, 60, 61, 62	, ,  ⊢
	: , : , : , : , : , : , :
15	instantiation	51, 43, 135, 150, 44, 27, 28, 104, 61, 59, 60, 62, 29*	, ,  ⊢
	: , : , : , : , : , :
16	instantiation	148, 144, 30	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_if_in_rational_nonzero
18	instantiation	148, 31, 49	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.exponentiation.neg_power_of_quotient
20	instantiation	32, 133	⊢
	:
21	instantiation	32, 94	⊢
	:
22	instantiation	56, 43, 150, 136, 44, 34, 54, 59, 60, 33	, ,  ⊢
	: , : , : , : , : , :
23	instantiation	56, 150, 135, 43, 34, 35, 44, 54, 59, 60, 53, 62	, ,  ⊢
	: , : , : , : , : , :
24	instantiation	36, 43, 150, 136, 44, 37, 54, 59, 60, 53, 62	, ,  ⊢
	: , : , : , : , : , : , :
25	instantiation	38, 39, 40, 41	, ,  ⊢
	: , : , : , :
26	instantiation	42, 43, 150, 136, 44, 45, 59, 60, 61, 104, 62	, ,  ⊢
	: , : , : , : , : , : , :
27	instantiation	93	⊢
	: , :
28	instantiation	63	⊢
	: , : , :
29	instantiation	46, 104, 96, 99, 98, 90*, 47*	⊢
	: , : , : , :
30	instantiation	148, 48, 49	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
32	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
33	instantiation	50, 53, 62	⊢
	: , :
34	instantiation	63	⊢
	: , : , :
35	instantiation	93	⊢
	: , :
36	theorem		⊢
	proveit.numbers.multiplication.rightward_commutation
37	instantiation	63	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
39	instantiation	51, 135, 136, 57, 52, 59, 60, 53, 54, 62	, ,  ⊢
	: , : , : , : , : , :
40	instantiation	122, 55	⊢
	: , : , :
41	instantiation	56, 135, 136, 57, 58, 59, 60, 61, 104, 62	, ,  ⊢
	: , : , : , : , : , :
42	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
43	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
44	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
45	instantiation	63	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.division.prod_of_fracs
47	instantiation	100, 64, 65	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
49	instantiation	66, 67, 68	⊢
	: , :
50	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
51	theorem		⊢
	proveit.numbers.multiplication.association
52	instantiation	93	⊢
	: , :
53	instantiation	72, 133, 94, 73	⊢
	: , :
54	instantiation	72, 104, 133, 69	⊢
	: , :
55	instantiation	87, 70, 71	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.multiplication.disassociation
57	instantiation	93	⊢
	: , :
58	instantiation	93	⊢
	: , :
59	assumption		⊢
60	assumption		⊢
61	instantiation	72, 96, 94, 73	⊢
	: , :
62	instantiation	74, 75, 76	⊢
	: , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
64	instantiation	77, 135, 78, 79, 80, 81	⊢
	: , : , : , :
65	instantiation	82, 98, 99, 94, 83*, 84*, 85*	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
67	instantiation	148, 86, 138	⊢
	: , : , :
68	instantiation	148, 86, 137	⊢
	: , : , :
69	instantiation	91, 137	⊢
	:
70	instantiation	87, 88, 89	⊢
	: , : , :
71	instantiation	122, 90	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.division.div_complex_closure
73	instantiation	91, 138	⊢
	:
74	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
75	assumption		⊢
76	instantiation	148, 141, 92	⊢
	: , : , :
77	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
78	instantiation	93	⊢
	: , :
79	instantiation	93	⊢
	: , :
80	instantiation	132, 104	⊢
	:
81	instantiation	131, 94	⊢
	:
82	theorem		⊢
	proveit.numbers.division.frac_cancel_left
83	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
84	instantiation	132, 94	⊢
	:
85	instantiation	103, 94	⊢
	:
86	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
87	theorem		⊢
	proveit.logic.equality.sub_right_side_into
88	instantiation	95, 96, 104, 97, 98, 99	⊢
	: , : , : , : , :
89	instantiation	100, 101, 102	⊢
	: , : , :
90	instantiation	103, 104	⊢
	:
91	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
92	instantiation	105, 107	⊢
	:
93	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
94	instantiation	148, 141, 106	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
96	instantiation	148, 141, 107	⊢
	: , : , :
97	instantiation	148, 110, 108	⊢
	: , : , :
98	instantiation	148, 110, 109	⊢
	: , : , :
99	instantiation	148, 110, 111	⊢
	: , : , :
100	axiom		⊢
	proveit.logic.equality.equals_transitivity
101	instantiation	122, 112	⊢
	: , : , :
102	instantiation	122, 113	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.division.frac_one_denom
104	instantiation	148, 141, 114	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.negation.real_closure
106	instantiation	148, 144, 115	⊢
	: , : , :
107	instantiation	148, 144, 116	⊢
	: , : , :
108	instantiation	148, 119, 117	⊢
	: , : , :
109	instantiation	148, 119, 118	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
111	instantiation	148, 119, 120	⊢
	: , : , :
112	instantiation	122, 121	⊢
	: , : , :
113	instantiation	122, 123	⊢
	: , : , :
114	instantiation	148, 144, 124	⊢
	: , : , :
115	instantiation	148, 146, 125	⊢
	: , : , :
116	instantiation	148, 146, 126	⊢
	: , : , :
117	instantiation	148, 129, 127	⊢
	: , : , :
118	instantiation	148, 129, 128	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
120	instantiation	148, 129, 130	⊢
	: , : , :
121	instantiation	131, 133	⊢
	:
122	axiom		⊢
	proveit.logic.equality.substitution
123	instantiation	132, 133	⊢
	:
124	instantiation	148, 146, 134	⊢
	: , : , :
125	instantiation	148, 149, 135	⊢
	: , : , :
126	instantiation	148, 149, 136	⊢
	: , : , :
127	instantiation	148, 139, 137	⊢
	: , : , :
128	instantiation	148, 139, 138	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
130	instantiation	148, 139, 140	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
132	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
133	instantiation	148, 141, 142	⊢
	: , : , :
134	instantiation	148, 149, 143	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
136	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
137	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
138	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
139	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
140	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
141	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
142	instantiation	148, 144, 145	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
144	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
145	instantiation	148, 146, 147	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
147	instantiation	148, 149, 150	⊢
	: , : , :
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.nat3
*equality replacement requirements