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	⊢
	: , : , : , :
1	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
2	instantiation	118, 5, 6	⊢
	: , : , :
3	instantiation	98	⊢
	:
4	instantiation	36, 7	⊢
	: , :
5	instantiation	128, 8	⊢
	: , : , :
6	instantiation	107, 134, 9, 10, 11*	⊢
	: , :
7	instantiation	118, 12, 13	⊢
	: , : , :
8	instantiation	118, 14, 15	⊢
	: , : , :
9	instantiation	16, 41, 45	⊢
	: , :
10	instantiation	17, 180, 18, 19, 20	⊢
	: , :
11	instantiation	118, 21, 22	⊢
	: , : , :
12	instantiation	128, 23	⊢
	: , : , :
13	instantiation	128, 24	⊢
	: , : , :
14	instantiation	128, 83	⊢
	: , : , :
15	instantiation	118, 25, 26	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
17	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
18	instantiation	135	⊢
	: , :
19	instantiation	27, 41, 42	⊢
	:
20	instantiation	27, 45, 46	⊢
	:
21	instantiation	128, 28	⊢
	: , : , :
22	instantiation	118, 29, 30	⊢
	: , : , :
23	instantiation	118, 31, 32	⊢
	: , : , :
24	instantiation	118, 33, 34	⊢
	: , : , :
25	instantiation	128, 35	⊢
	: , : , :
26	instantiation	36, 37	⊢
	: , :
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
28	instantiation	38, 41, 45, 80, 42, 46, 66*, 69*	⊢
	: , : , :
29	instantiation	101, 168, 180, 124, 39, 126, 134, 67, 71	⊢
	: , : , : , : , : , :
30	instantiation	113, 124, 180, 126, 39, 67, 71	⊢
	: , : , : , :
31	instantiation	128, 40	⊢
	: , : , :
32	instantiation	107, 134, 41, 42, 43*	⊢
	: , :
33	instantiation	128, 44	⊢
	: , : , :
34	instantiation	107, 134, 45, 46, 47*	⊢
	: , :
35	instantiation	48, 97, 137	⊢
	: , :
36	theorem		⊢
	proveit.logic.equality.equals_reversal
37	instantiation	49, 149, 50, 51	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
39	instantiation	135	⊢
	: , :
40	instantiation	128, 52	⊢
	: , : , :
41	instantiation	53, 149	⊢
	:
42	instantiation	57, 156, 54	⊢
	: , :
43	instantiation	118, 55, 56	⊢
	: , : , :
44	instantiation	128, 96	⊢
	: , : , :
45	instantiation	82, 149, 97	⊢
	: , :
46	instantiation	57, 156, 58	⊢
	: , :
47	instantiation	118, 59, 60	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.addition.commutation
49	theorem		⊢
	proveit.numbers.exponentiation.product_of_pos_powers
50	instantiation	178, 61, 163	⊢
	: , : , :
51	instantiation	178, 61, 131	⊢
	: , : , :
52	instantiation	118, 62, 63	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
54	instantiation	64, 65, 156	⊢
	: , :
55	instantiation	128, 66	⊢
	: , : , :
56	instantiation	70, 67	⊢
	:
57	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
58	instantiation	178, 68, 131	⊢
	: , : , :
59	instantiation	128, 69	⊢
	: , : , :
60	instantiation	70, 71	⊢
	:
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
62	instantiation	118, 72, 73	⊢
	: , : , :
63	instantiation	118, 74, 75	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
65	instantiation	178, 164, 76	⊢
	: , : , :
66	instantiation	79, 149, 145, 80, 108, 77*	⊢
	: , : , :
67	instantiation	82, 149, 78	⊢
	: , :
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
69	instantiation	79, 149, 110, 80, 108, 81*	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
71	instantiation	82, 149, 87	⊢
	: , :
72	instantiation	128, 83	⊢
	: , : , :
73	instantiation	128, 84	⊢
	: , : , :
74	instantiation	85, 124, 180, 168, 126, 86, 97, 137, 87	⊢
	: , : , : , : , : , :
75	instantiation	88, 97, 137, 89	⊢
	: , : , :
76	instantiation	178, 172, 175	⊢
	: , : , :
77	instantiation	90, 137, 134, 127*	⊢
	: , :
78	instantiation	178, 157, 91	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
80	instantiation	178, 166, 92	⊢
	: , : , :
81	instantiation	118, 93, 94	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
83	instantiation	107, 122, 149, 108, 95*	⊢
	: , :
84	instantiation	128, 96	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.addition.disassociation
86	instantiation	135	⊢
	: , :
87	instantiation	112, 97	⊢
	:
88	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
89	instantiation	98	⊢
	:
90	theorem		⊢
	proveit.numbers.negation.pos_times_neg
91	instantiation	99, 145	⊢
	:
92	instantiation	178, 173, 100	⊢
	: , : , :
93	instantiation	101, 124, 180, 168, 126, 114, 137, 133, 102	⊢
	: , : , : , : , : , :
94	instantiation	103, 180, 124, 114, 126, 137, 133, 134, 104*	⊢
	: , : , : , : , :
95	instantiation	118, 105, 106	⊢
	: , : , :
96	instantiation	107, 133, 149, 108, 109*	⊢
	: , :
97	instantiation	178, 157, 110	⊢
	: , : , :
98	axiom		⊢
	proveit.logic.equality.equals_reflexivity
99	theorem		⊢
	proveit.numbers.negation.real_closure
100	instantiation	111, 161	⊢
	:
101	theorem		⊢
	proveit.numbers.multiplication.disassociation
102	instantiation	112, 134	⊢
	:
103	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
104	instantiation	113, 180, 124, 114, 126, 137, 133	⊢
	: , : , : , :
105	instantiation	128, 129	⊢
	: , : , :
106	instantiation	118, 115, 116	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.division.div_as_mult
108	instantiation	117, 177	⊢
	:
109	instantiation	118, 119, 120	⊢
	: , : , :
110	instantiation	178, 166, 121	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.negation.int_closure
112	theorem		⊢
	proveit.numbers.negation.complex_closure
113	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
114	instantiation	135	⊢
	: , :
115	instantiation	130, 122, 137	⊢
	: , :
116	instantiation	123, 168, 180, 124, 125, 126, 137, 133, 134, 127*	⊢
	: , : , : , : , : , :
117	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
118	axiom		⊢
	proveit.logic.equality.equals_transitivity
119	instantiation	128, 129	⊢
	: , : , :
120	instantiation	130, 133, 137	⊢
	: , :
121	instantiation	178, 162, 131	⊢
	: , : , :
122	instantiation	132, 133, 134	⊢
	: , :
123	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
124	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
125	instantiation	135	⊢
	: , :
126	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
127	instantiation	136, 137	⊢
	:
128	axiom		⊢
	proveit.logic.equality.substitution
129	instantiation	138, 139, 175, 140*	⊢
	: , :
130	theorem		⊢
	proveit.numbers.multiplication.commutation
131	instantiation	141, 163, 142	⊢
	: , :
132	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
133	instantiation	178, 157, 143	⊢
	: , : , :
134	instantiation	178, 157, 144	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
136	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
137	instantiation	178, 157, 145	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
139	instantiation	178, 146, 147	⊢
	: , : , :
140	instantiation	148, 149	⊢
	:
141	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
142	instantiation	178, 176, 152	⊢
	: , : , :
143	instantiation	150, 151, 152	⊢
	: , : , :
144	instantiation	178, 166, 153	⊢
	: , : , :
145	instantiation	178, 166, 154	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
147	instantiation	178, 155, 156	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
149	instantiation	178, 157, 158	⊢
	: , : , :
150	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
151	instantiation	159, 160	⊢
	: , :
152	assumption		⊢
153	instantiation	178, 173, 161	⊢
	: , : , :
154	instantiation	178, 162, 163	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
156	instantiation	178, 164, 165	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
158	instantiation	178, 166, 167	⊢
	: , : , :
159	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
160	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
161	instantiation	178, 179, 168	⊢
	: , : , :
162	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
163	instantiation	169, 170, 171	⊢
	: , :
164	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
165	instantiation	178, 172, 177	⊢
	: , : , :
166	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
167	instantiation	178, 173, 174	⊢
	: , : , :
168	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
169	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
170	instantiation	178, 176, 175	⊢
	: , : , :
171	instantiation	178, 176, 177	⊢
	: , : , :
172	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
173	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
174	instantiation	178, 179, 180	⊢
	: , : , :
175	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
176	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
177	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
178	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
179	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
180	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements