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	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	89, 4, 5	,  ⊢
	: , : , :
3	instantiation	121, 6, 7	⊢
	: , : , :
4	instantiation	89, 8, 9	⊢
	: , : , :
5	assumption		⊢
6	instantiation	136, 10	⊢
	: , : , :
7	instantiation	11, 38, 148, 86, 12*	⊢
	: , :
8	instantiation	13, 160, 14, 15, 16*	⊢
	: , : , : , :
9	instantiation	17, 163, 166, 125, 127, 126, 34, 130, 141	⊢
	: , : , : , : , : , :
10	instantiation	39, 163, 166, 125, 127, 126, 148, 130, 141	⊢
	: , : , : , : , : , :
11	theorem		⊢
	proveit.numbers.division.div_as_mult
12	instantiation	121, 18, 19	⊢
	: , : , :
13	axiom		⊢
	proveit.numbers.summation.sum_split_last
14	instantiation	20, 108, 160	⊢
	: , :
15	instantiation	21, 149, 22, 142, 23, 24*	⊢
	: , : , :
16	instantiation	121, 25, 26	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.association
18	instantiation	136, 27	⊢
	: , : , :
19	instantiation	121, 28, 29	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
21	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
23	instantiation	30, 152	⊢
	:
24	instantiation	89, 31, 32	⊢
	: , : , :
25	instantiation	136, 33	⊢
	: , : , :
26	instantiation	124, 163, 166, 125, 127, 126, 34, 130, 141	⊢
	: , : , : , : , : , :
27	instantiation	35, 102, 144, 36*	⊢
	: , :
28	instantiation	37, 38, 79	⊢
	: , :
29	instantiation	39, 163, 166, 125, 40, 126, 79, 55, 56, 41*, 42*	⊢
	: , : , : , : , : , :
30	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
31	instantiation	43, 141	⊢
	:
32	instantiation	44, 141, 45	⊢
	: , :
33	instantiation	46, 146, 47, 48, 49, 50	⊢
	: , : , :
34	modus ponens	51, 52	⊢
35	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
36	instantiation	53, 148	⊢
	:
37	theorem		⊢
	proveit.numbers.multiplication.commutation
38	instantiation	54, 55, 56	⊢
	: , :
39	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
40	instantiation	139	⊢
	: , :
41	instantiation	92, 57, 58, 59	⊢
	: , : , : , :
42	instantiation	121, 60, 61	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.addition.elim_zero_right
44	theorem		⊢
	proveit.numbers.addition.commutation
45	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
46	theorem		⊢
	proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
47	instantiation	139	⊢
	: , :
48	instantiation	139	⊢
	: , :
49	instantiation	136, 62	⊢
	: , : , :
50	instantiation	143	⊢
	:
51	instantiation	63	⊢
	: , : , :
52	generalization	64	⊢
53	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
54	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
55	instantiation	65, 148, 130	⊢
	: , :
56	instantiation	65, 148, 141	⊢
	: , :
57	instantiation	69, 163, 166, 125, 66, 126, 79, 148, 130	⊢
	: , : , : , : , : , :
58	instantiation	121, 67, 68	⊢
	: , : , :
59	instantiation	135, 130	⊢
	:
60	instantiation	69, 163, 166, 125, 70, 126, 79, 148, 141	⊢
	: , : , : , : , : , :
61	instantiation	121, 71, 76	⊢
	: , : , :
62	modus ponens	72, 73	⊢
63	theorem		⊢
	proveit.numbers.summation.summation_complex_closure
64	instantiation	164, 153, 74	,  ⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
66	instantiation	139	⊢
	: , :
67	instantiation	75, 125, 166, 163, 126, 78, 79, 148, 130	⊢
	: , : , : , : , : , :
68	instantiation	136, 76	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.multiplication.disassociation
70	instantiation	139	⊢
	: , :
71	instantiation	77, 166, 125, 78, 126, 79, 148	⊢
	: , : , : , :
72	instantiation	80, 144	⊢
	: , : , : , : , : , :
73	generalization	81	⊢
74	instantiation	164, 158, 82	,  ⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.multiplication.association
76	instantiation	89, 83, 84	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
78	instantiation	139	⊢
	: , :
79	instantiation	85, 141, 148, 86	⊢
	: , :
80	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
81	instantiation	136, 87	⊢
	: , : , :
82	instantiation	164, 161, 88	,  ⊢
	: , : , :
83	instantiation	89, 90, 91	⊢
	: , : , :
84	instantiation	92, 93, 94, 95	⊢
	: , : , : , :
85	theorem		⊢
	proveit.numbers.division.div_complex_closure
86	instantiation	96, 146	⊢
	:
87	instantiation	136, 97	⊢
	: , : , :
88	instantiation	164, 98, 99	,  ⊢
	: , : , :
89	theorem		⊢
	proveit.logic.equality.sub_right_side_into
90	instantiation	100, 141, 101, 102	⊢
	: , : , : , : , :
91	instantiation	121, 103, 104	⊢
	: , : , :
92	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
93	instantiation	136, 105	⊢
	: , : , :
94	instantiation	136, 105	⊢
	: , : , :
95	instantiation	147, 141	⊢
	:
96	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
97	instantiation	136, 106	⊢
	: , : , :
98	instantiation	107, 160, 108	⊢
	: , :
99	assumption		⊢
100	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
101	instantiation	164, 110, 109	⊢
	: , : , :
102	instantiation	164, 110, 111	⊢
	: , : , :
103	instantiation	136, 112	⊢
	: , : , :
104	instantiation	136, 113	⊢
	: , : , :
105	instantiation	138, 141	⊢
	:
106	instantiation	121, 114, 115	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
108	instantiation	164, 116, 152	⊢
	: , : , :
109	instantiation	164, 118, 117	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
111	instantiation	164, 118, 119	⊢
	: , : , :
112	instantiation	136, 120	⊢
	: , : , :
113	instantiation	121, 122, 123	⊢
	: , : , :
114	instantiation	124, 125, 166, 163, 126, 127, 130, 141, 128	⊢
	: , : , : , : , : , :
115	instantiation	129, 141, 130, 131	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
117	instantiation	164, 133, 132	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
119	instantiation	164, 133, 134	⊢
	: , : , :
120	instantiation	135, 148	⊢
	:
121	axiom		⊢
	proveit.logic.equality.equals_transitivity
122	instantiation	136, 137	⊢
	: , : , :
123	instantiation	138, 148	⊢
	:
124	theorem		⊢
	proveit.numbers.addition.disassociation
125	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
126	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
127	instantiation	139	⊢
	: , :
128	instantiation	140, 141	⊢
	:
129	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
130	instantiation	164, 153, 142	⊢
	: , : , :
131	instantiation	143	⊢
	:
132	instantiation	164, 145, 144	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
134	instantiation	164, 145, 146	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
136	axiom		⊢
	proveit.logic.equality.substitution
137	instantiation	147, 148	⊢
	:
138	theorem		⊢
	proveit.numbers.division.frac_one_denom
139	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
140	theorem		⊢
	proveit.numbers.negation.complex_closure
141	instantiation	164, 153, 149	⊢
	: , : , :
142	instantiation	150, 151, 152	⊢
	: , : , :
143	axiom		⊢
	proveit.logic.equality.equals_reflexivity
144	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
145	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
146	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
147	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
148	instantiation	164, 153, 154	⊢
	: , : , :
149	instantiation	164, 158, 155	⊢
	: , : , :
150	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
151	instantiation	156, 157	⊢
	: , :
152	assumption		⊢
153	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
154	instantiation	164, 158, 159	⊢
	: , : , :
155	instantiation	164, 161, 160	⊢
	: , : , :
156	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
157	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
158	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
159	instantiation	164, 161, 162	⊢
	: , : , :
160	instantiation	164, 165, 163	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
162	instantiation	164, 165, 166	⊢
	: , : , :
163	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
164	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
165	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
166	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements