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	130	⊢
2	instantiation	25, 4	, , ,  ⊢
	: , : , :
3	instantiation	5, 6, 7, 8, 9*	, , ,  ⊢
	: , :
4	instantiation	130, 10, 11	, , ,  ⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.division.div_as_mult
6	instantiation	37, 12, 13	, , ,  ⊢
	: , : , :
7	instantiation	14, 111	⊢
	:
8	instantiation	15, 111, 106, 95	⊢
	: , :
9	instantiation	130, 16, 17	, , ,  ⊢
	: , : , :
10	instantiation	18, 19, 20, 21	, , ,  ⊢
	: , : , : , :
11	instantiation	65, 66, 167, 68, 34, 72, 74, 111, 73, 83, 76	, , ,  ⊢
	: , : , : , : , : , : , :
12	instantiation	82, 40, 22	, , ,  ⊢
	: , :
13	instantiation	130, 23, 24	, , ,  ⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
15	theorem		⊢
	proveit.numbers.exponentiation.exp_not_eq_zero
16	instantiation	25, 26	⊢
	: , : , :
17	instantiation	130, 27, 28	, , ,  ⊢
	: , : , :
18	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
19	instantiation	130, 29, 30	, , ,  ⊢
	: , : , :
20	instantiation	69, 66, 167, 45, 68, 31, 32, 89, 111, 86, 51, 83, 76, 33*	, , ,  ⊢
	: , : , : , : , : , :
21	instantiation	69, 167, 34, 35, 72, 74, 111, 86, 51, 83, 76, 36*	, , ,  ⊢
	: , : , : , : , : , :
22	instantiation	37, 38, 39	, ,  ⊢
	: , : , :
23	instantiation	61, 172, 150, 66, 41, 68, 40, 111, 83, 76	, , ,  ⊢
	: , : , : , : , : , :
24	instantiation	61, 66, 167, 150, 68, 70, 41, 73, 74, 111, 83, 76	, , ,  ⊢
	: , : , : , : , : , :
25	axiom		⊢
	proveit.logic.equality.substitution
26	instantiation	42, 111, 124, 43, 95, 44*	⊢
	: , : , :
27	instantiation	61, 66, 45, 172, 68, 46, 73, 74, 111, 83, 76, 75	, , ,  ⊢
	: , : , : , : , : , :
28	instantiation	130, 47, 48	, , ,  ⊢
	: , : , :
29	instantiation	65, 172, 149, 49, 89, 111, 86, 83, 51, 76	, , ,  ⊢
	: , : , : , : , : , : , :
30	instantiation	65, 149, 172, 50, 89, 111, 86, 83, 51, 76	, , ,  ⊢
	: , : , : , : , : , : , :
31	instantiation	153	⊢
	: , :
32	instantiation	64	⊢
	: , : , : , : , :
33	instantiation	52, 89, 133, 53*, 148*	⊢
	: , : , :
34	instantiation	153	⊢
	: , :
35	instantiation	153	⊢
	: , :
36	instantiation	54, 86, 160, 55, 56, 57*, 58*, 59*	⊢
	: , : , : , :
37	theorem		⊢
	proveit.logic.equality.sub_right_side_into
38	instantiation	82, 60, 76	, ,  ⊢
	: , :
39	instantiation	61, 66, 167, 172, 68, 62, 111, 83, 76	, ,  ⊢
	: , : , : , : , : , :
40	instantiation	82, 73, 74	⊢
	: , :
41	instantiation	84	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
43	instantiation	107, 163	⊢
	:
44	instantiation	156, 106, 160, 63*	⊢
	: , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
46	instantiation	64	⊢
	: , : , : , : , :
47	instantiation	65, 150, 167, 66, 67, 72, 68, 73, 74, 111, 83, 76, 75	, , ,  ⊢
	: , : , : , : , : , : , :
48	instantiation	69, 167, 70, 71, 72, 73, 74, 111, 75, 83, 76, 77*	, , ,  ⊢
	: , : , : , : , : , :
49	instantiation	78	⊢
	: , : , : , :
50	instantiation	78	⊢
	: , : , : , :
51	instantiation	85, 160, 87, 88	⊢
	: , :
52	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
53	instantiation	110, 89	⊢
	:
54	theorem		⊢
	proveit.numbers.division.prod_of_fracs
55	instantiation	170, 80, 79	⊢
	: , : , :
56	instantiation	170, 80, 81	⊢
	: , : , :
57	instantiation	128, 86	⊢
	:
58	instantiation	159, 86	⊢
	:
59	instantiation	154, 87	⊢
	:
60	instantiation	82, 111, 83	,  ⊢
	: , :
61	theorem		⊢
	proveit.numbers.multiplication.disassociation
62	instantiation	153	⊢
	: , :
63	instantiation	159, 106	⊢
	:
64	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
65	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
66	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
67	instantiation	84	⊢
	: , : , :
68	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
69	theorem		⊢
	proveit.numbers.multiplication.association
70	instantiation	153	⊢
	: , :
71	instantiation	153	⊢
	: , :
72	instantiation	153	⊢
	: , :
73	instantiation	85, 86, 87, 88	⊢
	: , :
74	instantiation	90, 89, 155	⊢
	: , :
75	instantiation	90, 111, 91	⊢
	: , :
76	instantiation	170, 162, 92	⊢
	: , : , :
77	instantiation	93, 111, 163, 94, 95, 96*, 97*	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
79	instantiation	170, 99, 98	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
81	instantiation	170, 99, 100	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
83	instantiation	170, 162, 101	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
85	theorem		⊢
	proveit.numbers.division.div_complex_closure
86	instantiation	170, 162, 102	⊢
	: , : , :
87	instantiation	170, 162, 103	⊢
	: , : , :
88	instantiation	151, 135	⊢
	:
89	instantiation	170, 162, 104	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
91	instantiation	105, 106	⊢
	:
92	assumption		⊢
93	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
94	instantiation	107, 124	⊢
	:
95	instantiation	108, 109	⊢
	:
96	instantiation	110, 111	⊢
	:
97	instantiation	112, 169, 113, 164, 114*, 115*, 116*	⊢
	: , : , : , :
98	instantiation	170, 118, 117	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
100	instantiation	170, 118, 119	⊢
	: , : , :
101	instantiation	170, 140, 120	⊢
	: , : , :
102	instantiation	170, 165, 121	⊢
	: , : , :
103	instantiation	170, 165, 122	⊢
	: , : , :
104	instantiation	170, 140, 123	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.negation.complex_closure
106	instantiation	170, 162, 124	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.negation.real_closure
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
109	instantiation	170, 125, 141	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
111	instantiation	170, 162, 126	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
113	instantiation	127, 169	⊢
	:
114	instantiation	128, 160	⊢
	:
115	instantiation	129, 160, 155, 139	⊢
	: , :
116	instantiation	130, 131, 132	⊢
	: , : , :
117	instantiation	170, 134, 133	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
119	instantiation	170, 134, 135	⊢
	: , : , :
120	assumption		⊢
121	instantiation	170, 168, 136	⊢
	: , : , :
122	instantiation	170, 168, 137	⊢
	: , : , :
123	assumption		⊢
124	instantiation	138, 163, 158, 139	⊢
	: , :
125	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real_nonzero
126	instantiation	170, 140, 141	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.negation.int_closure
128	theorem		⊢
	proveit.numbers.division.frac_one_denom
129	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
130	axiom		⊢
	proveit.logic.equality.equals_transitivity
131	instantiation	142, 167, 143, 144, 145, 146	⊢
	: , : , : , :
132	instantiation	147, 160, 155, 148	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
134	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
135	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
136	instantiation	170, 171, 149	⊢
	: , : , :
137	instantiation	170, 171, 150	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.division.div_real_closure
139	instantiation	151, 152	⊢
	:
140	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
141	assumption		⊢
142	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
143	instantiation	153	⊢
	: , :
144	instantiation	153	⊢
	: , :
145	instantiation	154, 155	⊢
	:
146	instantiation	156, 160, 157*	⊢
	: , :
147	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
148	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
149	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
150	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
151	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
152	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
153	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
154	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
155	instantiation	170, 162, 158	⊢
	: , : , :
156	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
157	instantiation	159, 160	⊢
	:
158	instantiation	170, 165, 161	⊢
	: , : , :
159	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
160	instantiation	170, 162, 163	⊢
	: , : , :
161	instantiation	170, 168, 164	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
163	instantiation	170, 165, 166	⊢
	: , : , :
164	instantiation	170, 171, 167	⊢
	: , : , :
165	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
166	instantiation	170, 168, 169	⊢
	: , : , :
167	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
168	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
169	instantiation	170, 171, 172	⊢
	: , : , :
170	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
171	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
172	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements