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	131	⊢
2	instantiation	39, 3	⊢
	: , :
3	instantiation	4, 5, 6, 7	⊢
	: , : , : , :
4	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
5	instantiation	121, 8, 9	⊢
	: , : , :
6	instantiation	101	⊢
	:
7	instantiation	39, 10	⊢
	: , :
8	instantiation	131, 11	⊢
	: , : , :
9	instantiation	110, 137, 12, 13, 14*	⊢
	: , :
10	instantiation	121, 15, 16	⊢
	: , : , :
11	instantiation	121, 17, 18	⊢
	: , : , :
12	instantiation	19, 44, 48	⊢
	: , :
13	instantiation	20, 183, 21, 22, 23	⊢
	: , :
14	instantiation	121, 24, 25	⊢
	: , : , :
15	instantiation	131, 26	⊢
	: , : , :
16	instantiation	131, 27	⊢
	: , : , :
17	instantiation	131, 86	⊢
	: , : , :
18	instantiation	121, 28, 29	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
20	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
21	instantiation	138	⊢
	: , :
22	instantiation	30, 44, 45	⊢
	:
23	instantiation	30, 48, 49	⊢
	:
24	instantiation	131, 31	⊢
	: , : , :
25	instantiation	121, 32, 33	⊢
	: , : , :
26	instantiation	121, 34, 35	⊢
	: , : , :
27	instantiation	121, 36, 37	⊢
	: , : , :
28	instantiation	131, 38	⊢
	: , : , :
29	instantiation	39, 40	⊢
	: , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
31	instantiation	41, 44, 48, 83, 45, 49, 69*, 72*	⊢
	: , : , :
32	instantiation	104, 171, 183, 127, 42, 129, 137, 70, 74	⊢
	: , : , : , : , : , :
33	instantiation	116, 127, 183, 129, 42, 70, 74	⊢
	: , : , : , :
34	instantiation	131, 43	⊢
	: , : , :
35	instantiation	110, 137, 44, 45, 46*	⊢
	: , :
36	instantiation	131, 47	⊢
	: , : , :
37	instantiation	110, 137, 48, 49, 50*	⊢
	: , :
38	instantiation	51, 100, 140	⊢
	: , :
39	theorem		⊢
	proveit.logic.equality.equals_reversal
40	instantiation	52, 152, 53, 54	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
42	instantiation	138	⊢
	: , :
43	instantiation	131, 55	⊢
	: , : , :
44	instantiation	56, 152	⊢
	:
45	instantiation	60, 159, 57	⊢
	: , :
46	instantiation	121, 58, 59	⊢
	: , : , :
47	instantiation	131, 99	⊢
	: , : , :
48	instantiation	85, 152, 100	⊢
	: , :
49	instantiation	60, 159, 61	⊢
	: , :
50	instantiation	121, 62, 63	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.addition.commutation
52	theorem		⊢
	proveit.numbers.exponentiation.product_of_pos_powers
53	instantiation	181, 64, 166	⊢
	: , : , :
54	instantiation	181, 64, 134	⊢
	: , : , :
55	instantiation	121, 65, 66	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
57	instantiation	67, 68, 159	⊢
	: , :
58	instantiation	131, 69	⊢
	: , : , :
59	instantiation	73, 70	⊢
	:
60	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
61	instantiation	181, 71, 134	⊢
	: , : , :
62	instantiation	131, 72	⊢
	: , : , :
63	instantiation	73, 74	⊢
	:
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
65	instantiation	121, 75, 76	⊢
	: , : , :
66	instantiation	121, 77, 78	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
68	instantiation	181, 167, 79	⊢
	: , : , :
69	instantiation	82, 152, 148, 83, 111, 80*	⊢
	: , : , :
70	instantiation	85, 152, 81	⊢
	: , :
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
72	instantiation	82, 152, 113, 83, 111, 84*	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
74	instantiation	85, 152, 90	⊢
	: , :
75	instantiation	131, 86	⊢
	: , : , :
76	instantiation	131, 87	⊢
	: , : , :
77	instantiation	88, 127, 183, 171, 129, 89, 100, 140, 90	⊢
	: , : , : , : , : , :
78	instantiation	91, 100, 140, 92	⊢
	: , : , :
79	instantiation	181, 175, 178	⊢
	: , : , :
80	instantiation	93, 140, 137, 130*	⊢
	: , :
81	instantiation	181, 160, 94	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
83	instantiation	181, 169, 95	⊢
	: , : , :
84	instantiation	121, 96, 97	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
86	instantiation	110, 125, 152, 111, 98*	⊢
	: , :
87	instantiation	131, 99	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.addition.disassociation
89	instantiation	138	⊢
	: , :
90	instantiation	115, 100	⊢
	:
91	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
92	instantiation	101	⊢
	:
93	theorem		⊢
	proveit.numbers.negation.pos_times_neg
94	instantiation	102, 148	⊢
	:
95	instantiation	181, 176, 103	⊢
	: , : , :
96	instantiation	104, 127, 183, 171, 129, 117, 140, 136, 105	⊢
	: , : , : , : , : , :
97	instantiation	106, 183, 127, 117, 129, 140, 136, 137, 107*	⊢
	: , : , : , : , :
98	instantiation	121, 108, 109	⊢
	: , : , :
99	instantiation	110, 136, 152, 111, 112*	⊢
	: , :
100	instantiation	181, 160, 113	⊢
	: , : , :
101	axiom		⊢
	proveit.logic.equality.equals_reflexivity
102	theorem		⊢
	proveit.numbers.negation.real_closure
103	instantiation	114, 164	⊢
	:
104	theorem		⊢
	proveit.numbers.multiplication.disassociation
105	instantiation	115, 137	⊢
	:
106	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
107	instantiation	116, 183, 127, 117, 129, 140, 136	⊢
	: , : , : , :
108	instantiation	131, 132	⊢
	: , : , :
109	instantiation	121, 118, 119	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.division.div_as_mult
111	instantiation	120, 180	⊢
	:
112	instantiation	121, 122, 123	⊢
	: , : , :
113	instantiation	181, 169, 124	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.negation.int_closure
115	theorem		⊢
	proveit.numbers.negation.complex_closure
116	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
117	instantiation	138	⊢
	: , :
118	instantiation	133, 125, 140	⊢
	: , :
119	instantiation	126, 171, 183, 127, 128, 129, 140, 136, 137, 130*	⊢
	: , : , : , : , : , :
120	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
121	axiom		⊢
	proveit.logic.equality.equals_transitivity
122	instantiation	131, 132	⊢
	: , : , :
123	instantiation	133, 136, 140	⊢
	: , :
124	instantiation	181, 165, 134	⊢
	: , : , :
125	instantiation	135, 136, 137	⊢
	: , :
126	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
127	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
128	instantiation	138	⊢
	: , :
129	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
130	instantiation	139, 140	⊢
	:
131	axiom		⊢
	proveit.logic.equality.substitution
132	instantiation	141, 142, 178, 143*	⊢
	: , :
133	theorem		⊢
	proveit.numbers.multiplication.commutation
134	instantiation	144, 166, 145	⊢
	: , :
135	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
136	instantiation	181, 160, 146	⊢
	: , : , :
137	instantiation	181, 160, 147	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
139	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
140	instantiation	181, 160, 148	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
142	instantiation	181, 149, 150	⊢
	: , : , :
143	instantiation	151, 152	⊢
	:
144	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
145	instantiation	181, 179, 155	⊢
	: , : , :
146	instantiation	153, 154, 155	⊢
	: , : , :
147	instantiation	181, 169, 156	⊢
	: , : , :
148	instantiation	181, 169, 157	⊢
	: , : , :
149	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
150	instantiation	181, 158, 159	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
152	instantiation	181, 160, 161	⊢
	: , : , :
153	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
154	instantiation	162, 163	⊢
	: , :
155	assumption		⊢
156	instantiation	181, 176, 164	⊢
	: , : , :
157	instantiation	181, 165, 166	⊢
	: , : , :
158	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
159	instantiation	181, 167, 168	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
161	instantiation	181, 169, 170	⊢
	: , : , :
162	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
163	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
164	instantiation	181, 182, 171	⊢
	: , : , :
165	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
166	instantiation	172, 173, 174	⊢
	: , :
167	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
168	instantiation	181, 175, 180	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
170	instantiation	181, 176, 177	⊢
	: , : , :
171	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
172	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
173	instantiation	181, 179, 178	⊢
	: , : , :
174	instantiation	181, 179, 180	⊢
	: , : , :
175	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
176	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
177	instantiation	181, 182, 183	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
179	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
180	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
181	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
182	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
183	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements