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.booleans.conjunction.and_if_both
2	axiom		⊢
	proveit.logic.booleans.true_axiom
3	generalization	4	,  ⊢
4	instantiation	80, 5, 6	, , ,  ⊢
	: , : , :
5	instantiation	34, 7, 8	, , ,  ⊢
	: , : , :
6	instantiation	46, 9	, ,  ⊢
	: , :
7	instantiation	34, 10, 11	, , ,  ⊢
	: , : , :
8	instantiation	28, 12, 13, 14, 15*	, ,  ⊢
	: , : , : , :
9	instantiation	34, 16, 17	, ,  ⊢
	: , : , :
10	instantiation	18, 19, 20	, , ,  ⊢
	: , : , :
11	instantiation	21, 101, 146, 102, 110, 122, 115, 22*, 23*	,  ⊢
	: , : , : , : , : , :
12	instantiation	25, 24	, ,  ⊢
	: , : , :
13	instantiation	25, 26	, ,  ⊢
	: , : , :
14	instantiation	46, 27	, ,  ⊢
	: , :
15	instantiation	28, 29, 30, 31	,  ⊢
	: , : , : , :
16	instantiation	46, 32	, ,  ⊢
	: , :
17	instantiation	33, 128, 127	⊢
	: , :
18	theorem		⊢
	proveit.logic.equality.sub_left_side_into
19	instantiation	34, 35, 36	,  ⊢
	: , : , :
20	instantiation	37, 38, 39, 115, 40*, 41*	, ,  ⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
22	instantiation	84, 115	,  ⊢
	:
23	instantiation	42, 122, 113, 75, 43*, 44*	,  ⊢
	: , : , :
24	instantiation	46, 45	, ,  ⊢
	: , :
25	axiom		⊢
	proveit.logic.equality.substitution
26	instantiation	46, 47	, ,  ⊢
	: , :
27	instantiation	48, 146, 149, 101, 49, 102, 50, 83, 85	, ,  ⊢
	: , : , : , : , : , :
28	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
29	instantiation	92, 101, 149, 146, 102, 51, 110, 105, 85	,  ⊢
	: , : , : , : , : , :
30	instantiation	92, 149, 101, 51, 52, 102, 110, 105, 115, 106	,  ⊢
	: , : , : , : , : , :
31	instantiation	53, 146, 101, 102, 110, 115, 106	,  ⊢
	: , : , : , : , : , : , : , :
32	instantiation	68, 110, 73, 71, 72, 54*	, ,  ⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.commutation
34	theorem		⊢
	proveit.logic.equality.sub_right_side_into
35	instantiation	55, 56, 133, 57, 58*	⊢
	: , : , : , :
36	assumption		⊢
37	theorem		⊢
	proveit.numbers.division.frac_cancel_left
38	instantiation	59, 71, 72	,  ⊢
	:
39	instantiation	147, 60, 61	⊢
	: , : , :
40	instantiation	62, 71	⊢
	:
41	instantiation	63, 115	,  ⊢
	:
42	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
43	instantiation	64, 122	⊢
	:
44	instantiation	80, 65, 66	⊢
	: , : , :
45	instantiation	68, 110, 83, 71, 72, 67*	, ,  ⊢
	: , : , :
46	theorem		⊢
	proveit.logic.equality.equals_reversal
47	instantiation	68, 110, 85, 71, 72, 69*	, ,  ⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
49	instantiation	114	⊢
	: , :
50	instantiation	70, 110, 71, 72	,  ⊢
	: , :
51	instantiation	114	⊢
	: , :
52	instantiation	114	⊢
	: , :
53	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
54	instantiation	84, 73	,  ⊢
	:
55	axiom		⊢
	proveit.numbers.summation.sum_split_last
56	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
57	instantiation	74, 75	⊢
	:
58	instantiation	80, 76, 77	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
61	instantiation	147, 78, 79	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
63	theorem		⊢
	proveit.numbers.division.frac_one_denom
64	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
65	instantiation	92, 146, 149, 101, 93, 102, 110, 128	⊢
	: , : , : , : , : , :
66	instantiation	80, 81, 82	⊢
	: , : , :
67	instantiation	84, 83	,  ⊢
	:
68	theorem		⊢
	proveit.numbers.division.mult_frac_left
69	instantiation	84, 85	,  ⊢
	:
70	theorem		⊢
	proveit.numbers.division.div_complex_closure
71	instantiation	126, 110, 86	⊢
	: , :
72	instantiation	87, 88	⊢
	: , :
73	instantiation	126, 110, 89	,  ⊢
	: , :
74	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
75	instantiation	90, 146, 101, 102, 145, 91	⊢
	: , : , : , : , :
76	instantiation	92, 101, 149, 146, 102, 93, 128, 110, 94	⊢
	: , : , : , : , : , :
77	instantiation	95, 110, 128, 96	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
79	instantiation	147, 97, 98	⊢
	: , : , :
80	axiom		⊢
	proveit.logic.equality.equals_transitivity
81	instantiation	99, 146, 101, 102, 110, 128	⊢
	: , : , : , : , : , : , :
82	instantiation	100, 101, 149, 146, 102, 103, 110, 128, 104*	⊢
	: , : , : , : , : , :
83	instantiation	126, 110, 105	,  ⊢
	: , :
84	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
85	instantiation	126, 115, 106	,  ⊢
	: , :
86	instantiation	116, 122	⊢
	:
87	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
88	instantiation	107, 108	⊢
	: , :
89	instantiation	116, 109	,  ⊢
	:
90	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
91	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
92	theorem		⊢
	proveit.numbers.addition.disassociation
93	instantiation	114	⊢
	: , :
94	instantiation	116, 110	⊢
	:
95	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
96	instantiation	111	⊢
	:
97	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
98	instantiation	147, 112, 113	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.addition.leftward_commutation
100	theorem		⊢
	proveit.numbers.addition.association
101	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
102	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
103	instantiation	114	⊢
	: , :
104	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
105	instantiation	116, 115	,  ⊢
	:
106	instantiation	116, 117	,  ⊢
	:
107	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
108	assumption		⊢
109	instantiation	121, 122, 118	,  ⊢
	: , :
110	instantiation	147, 131, 119	⊢
	: , : , :
111	axiom		⊢
	proveit.logic.equality.equals_reflexivity
112	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
113	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
114	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
115	instantiation	121, 122, 120	,  ⊢
	: , :
116	theorem		⊢
	proveit.numbers.negation.complex_closure
117	instantiation	121, 122, 123	,  ⊢
	: , :
118	instantiation	126, 128, 127	⊢
	: , :
119	instantiation	147, 134, 124	⊢
	: , : , :
120	instantiation	147, 131, 125	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
122	assumption		⊢
123	instantiation	126, 127, 128	⊢
	: , :
124	instantiation	147, 141, 140	⊢
	: , : , :
125	instantiation	147, 134, 129	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
127	instantiation	147, 131, 130	⊢
	: , : , :
128	instantiation	147, 131, 132	⊢
	: , : , :
129	instantiation	147, 141, 133	⊢
	: , : , :
130	instantiation	147, 134, 135	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
132	instantiation	136, 137, 145	⊢
	: , : , :
133	instantiation	138, 139, 140	⊢
	: , :
134	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
135	instantiation	147, 141, 142	⊢
	: , : , :
136	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
137	instantiation	143, 144	⊢
	: , :
138	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
139	instantiation	147, 148, 145	⊢
	: , : , :
140	instantiation	147, 148, 146	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
142	instantiation	147, 148, 149	⊢
	: , : , :
143	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
144	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_within_real
145	assumption		⊢
146	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
147	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
148	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
149	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements