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