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	⊢
	: , :
1	reference	38	⊢
2	instantiation	3, 4, 5, 6	⊢
	: , : , : , :
3	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
4	instantiation	120, 7, 8	⊢
	: , : , :
5	instantiation	100	⊢
	:
6	instantiation	38, 9	⊢
	: , :
7	instantiation	130, 10	⊢
	: , : , :
8	instantiation	109, 136, 11, 12, 13*	⊢
	: , :
9	instantiation	120, 14, 15	⊢
	: , : , :
10	instantiation	120, 16, 17	⊢
	: , : , :
11	instantiation	18, 43, 47	⊢
	: , :
12	instantiation	19, 182, 20, 21, 22	⊢
	: , :
13	instantiation	120, 23, 24	⊢
	: , : , :
14	instantiation	130, 25	⊢
	: , : , :
15	instantiation	130, 26	⊢
	: , : , :
16	instantiation	130, 85	⊢
	: , : , :
17	instantiation	120, 27, 28	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
19	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
20	instantiation	137	⊢
	: , :
21	instantiation	29, 43, 44	⊢
	:
22	instantiation	29, 47, 48	⊢
	:
23	instantiation	130, 30	⊢
	: , : , :
24	instantiation	120, 31, 32	⊢
	: , : , :
25	instantiation	120, 33, 34	⊢
	: , : , :
26	instantiation	120, 35, 36	⊢
	: , : , :
27	instantiation	130, 37	⊢
	: , : , :
28	instantiation	38, 39	⊢
	: , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
30	instantiation	40, 43, 47, 82, 44, 48, 68*, 71*	⊢
	: , : , :
31	instantiation	103, 170, 182, 126, 41, 128, 136, 69, 73	⊢
	: , : , : , : , : , :
32	instantiation	115, 126, 182, 128, 41, 69, 73	⊢
	: , : , : , :
33	instantiation	130, 42	⊢
	: , : , :
34	instantiation	109, 136, 43, 44, 45*	⊢
	: , :
35	instantiation	130, 46	⊢
	: , : , :
36	instantiation	109, 136, 47, 48, 49*	⊢
	: , :
37	instantiation	50, 99, 139	⊢
	: , :
38	theorem		⊢
	proveit.logic.equality.equals_reversal
39	instantiation	51, 151, 52, 53	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
41	instantiation	137	⊢
	: , :
42	instantiation	130, 54	⊢
	: , : , :
43	instantiation	55, 151	⊢
	:
44	instantiation	59, 158, 56	⊢
	: , :
45	instantiation	120, 57, 58	⊢
	: , : , :
46	instantiation	130, 98	⊢
	: , : , :
47	instantiation	84, 151, 99	⊢
	: , :
48	instantiation	59, 158, 60	⊢
	: , :
49	instantiation	120, 61, 62	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.addition.commutation
51	theorem		⊢
	proveit.numbers.exponentiation.product_of_pos_powers
52	instantiation	180, 63, 165	⊢
	: , : , :
53	instantiation	180, 63, 133	⊢
	: , : , :
54	instantiation	120, 64, 65	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
56	instantiation	66, 67, 158	⊢
	: , :
57	instantiation	130, 68	⊢
	: , : , :
58	instantiation	72, 69	⊢
	:
59	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
60	instantiation	180, 70, 133	⊢
	: , : , :
61	instantiation	130, 71	⊢
	: , : , :
62	instantiation	72, 73	⊢
	:
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
64	instantiation	120, 74, 75	⊢
	: , : , :
65	instantiation	120, 76, 77	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
67	instantiation	180, 166, 78	⊢
	: , : , :
68	instantiation	81, 151, 147, 82, 110, 79*	⊢
	: , : , :
69	instantiation	84, 151, 80	⊢
	: , :
70	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
71	instantiation	81, 151, 112, 82, 110, 83*	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
73	instantiation	84, 151, 89	⊢
	: , :
74	instantiation	130, 85	⊢
	: , : , :
75	instantiation	130, 86	⊢
	: , : , :
76	instantiation	87, 126, 182, 170, 128, 88, 99, 139, 89	⊢
	: , : , : , : , : , :
77	instantiation	90, 99, 139, 91	⊢
	: , : , :
78	instantiation	180, 174, 177	⊢
	: , : , :
79	instantiation	92, 139, 136, 129*	⊢
	: , :
80	instantiation	180, 159, 93	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
82	instantiation	180, 168, 94	⊢
	: , : , :
83	instantiation	120, 95, 96	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
85	instantiation	109, 124, 151, 110, 97*	⊢
	: , :
86	instantiation	130, 98	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.addition.disassociation
88	instantiation	137	⊢
	: , :
89	instantiation	114, 99	⊢
	:
90	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
91	instantiation	100	⊢
	:
92	theorem		⊢
	proveit.numbers.negation.pos_times_neg
93	instantiation	101, 147	⊢
	:
94	instantiation	180, 175, 102	⊢
	: , : , :
95	instantiation	103, 126, 182, 170, 128, 116, 139, 135, 104	⊢
	: , : , : , : , : , :
96	instantiation	105, 182, 126, 116, 128, 139, 135, 136, 106*	⊢
	: , : , : , : , :
97	instantiation	120, 107, 108	⊢
	: , : , :
98	instantiation	109, 135, 151, 110, 111*	⊢
	: , :
99	instantiation	180, 159, 112	⊢
	: , : , :
100	axiom		⊢
	proveit.logic.equality.equals_reflexivity
101	theorem		⊢
	proveit.numbers.negation.real_closure
102	instantiation	113, 163	⊢
	:
103	theorem		⊢
	proveit.numbers.multiplication.disassociation
104	instantiation	114, 136	⊢
	:
105	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
106	instantiation	115, 182, 126, 116, 128, 139, 135	⊢
	: , : , : , :
107	instantiation	130, 131	⊢
	: , : , :
108	instantiation	120, 117, 118	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.division.div_as_mult
110	instantiation	119, 179	⊢
	:
111	instantiation	120, 121, 122	⊢
	: , : , :
112	instantiation	180, 168, 123	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.negation.int_closure
114	theorem		⊢
	proveit.numbers.negation.complex_closure
115	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
116	instantiation	137	⊢
	: , :
117	instantiation	132, 124, 139	⊢
	: , :
118	instantiation	125, 170, 182, 126, 127, 128, 139, 135, 136, 129*	⊢
	: , : , : , : , : , :
119	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
120	axiom		⊢
	proveit.logic.equality.equals_transitivity
121	instantiation	130, 131	⊢
	: , : , :
122	instantiation	132, 135, 139	⊢
	: , :
123	instantiation	180, 164, 133	⊢
	: , : , :
124	instantiation	134, 135, 136	⊢
	: , :
125	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
126	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
127	instantiation	137	⊢
	: , :
128	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
129	instantiation	138, 139	⊢
	:
130	axiom		⊢
	proveit.logic.equality.substitution
131	instantiation	140, 141, 177, 142*	⊢
	: , :
132	theorem		⊢
	proveit.numbers.multiplication.commutation
133	instantiation	143, 165, 144	⊢
	: , :
134	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
135	instantiation	180, 159, 145	⊢
	: , : , :
136	instantiation	180, 159, 146	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
138	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
139	instantiation	180, 159, 147	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
141	instantiation	180, 148, 149	⊢
	: , : , :
142	instantiation	150, 151	⊢
	:
143	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
144	instantiation	180, 178, 154	⊢
	: , : , :
145	instantiation	152, 153, 154	⊢
	: , : , :
146	instantiation	180, 168, 155	⊢
	: , : , :
147	instantiation	180, 168, 156	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
149	instantiation	180, 157, 158	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
151	instantiation	180, 159, 160	⊢
	: , : , :
152	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
153	instantiation	161, 162	⊢
	: , :
154	assumption		⊢
155	instantiation	180, 175, 163	⊢
	: , : , :
156	instantiation	180, 164, 165	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
158	instantiation	180, 166, 167	⊢
	: , : , :
159	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
160	instantiation	180, 168, 169	⊢
	: , : , :
161	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
162	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
163	instantiation	180, 181, 170	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
165	instantiation	171, 172, 173	⊢
	: , :
166	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
167	instantiation	180, 174, 179	⊢
	: , : , :
168	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
169	instantiation	180, 175, 176	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
171	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
172	instantiation	180, 178, 177	⊢
	: , : , :
173	instantiation	180, 178, 179	⊢
	: , : , :
174	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
175	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
176	instantiation	180, 181, 182	⊢
	: , : , :
177	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
178	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
179	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
180	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
181	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
182	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements