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