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	64	⊢
2	instantiation	49, 4	⊢
	: , : , :
3	instantiation	5, 6, 7, 8	, , ,  ⊢
	: , : , : , :
4	instantiation	49, 9	⊢
	: , : , :
5	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
6	instantiation	10, 11, 119, 12, 74, 16, 67, 21, 22	, , ,  ⊢
	: , : , : , : , : , : , :
7	instantiation	18, 55, 114, 13, 56, 14, 15, 74, 16, 67, 21, 22, 17*	, , ,  ⊢
	: , : , : , : , : , :
8	instantiation	18, 119, 114, 19, 20, 28, 67, 21, 22, 23*	, , ,  ⊢
	: , : , : , : , : , :
9	instantiation	24, 74, 92, 88, 25*	⊢
	: , :
10	theorem		⊢
	proveit.numbers.addition.leftward_commutation
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
12	instantiation	26	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
14	instantiation	90	⊢
	: , :
15	instantiation	27	⊢
	: , : , : , :
16	instantiation	72, 28	⊢
	:
17	instantiation	64, 29, 30, 31*	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.addition.association
19	instantiation	90	⊢
	: , :
20	instantiation	90	⊢
	: , :
21	instantiation	117, 107, 32	⊢
	: , : , :
22	instantiation	37, 92, 33	⊢
	: , :
23	instantiation	52, 34, 82*	⊢
	: , :
24	theorem		⊢
	proveit.numbers.division.div_as_mult
25	instantiation	64, 35, 36	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
28	instantiation	37, 73, 74	⊢
	: , :
29	instantiation	49, 38	⊢
	: , : , :
30	instantiation	52, 39	⊢
	: , :
31	instantiation	40, 116, 41, 111, 42*, 43*, 44*	⊢
	: , : , : , :
32	instantiation	117, 99, 45	⊢
	: , : , :
33	instantiation	117, 107, 46	⊢
	: , : , :
34	instantiation	54, 55, 114, 119, 56, 47, 103, 67, 48*	⊢
	: , : , : , : , : , :
35	instantiation	49, 50	⊢
	: , : , :
36	instantiation	51, 74, 73	⊢
	: , :
37	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
38	instantiation	52, 53	⊢
	: , :
39	instantiation	54, 55, 114, 119, 56, 57, 103, 58, 74, 59*	⊢
	: , : , : , : , : , :
40	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
41	instantiation	60, 116	⊢
	:
42	instantiation	61, 103, 62	⊢
	:
43	instantiation	63, 103, 92, 88	⊢
	: , :
44	instantiation	64, 65, 66	⊢
	: , : , :
45	assumption		⊢
46	assumption		⊢
47	instantiation	90	⊢
	: , :
48	instantiation	91, 67	⊢
	:
49	axiom		⊢
	proveit.logic.equality.substitution
50	instantiation	68, 69, 75, 70*	⊢
	: , :
51	theorem		⊢
	proveit.numbers.multiplication.commutation
52	theorem		⊢
	proveit.logic.equality.equals_reversal
53	instantiation	71, 73, 74	⊢
	: , :
54	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
55	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
56	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
57	instantiation	90	⊢
	: , :
58	instantiation	72, 73	⊢
	:
59	instantiation	91, 74	⊢
	:
60	theorem		⊢
	proveit.numbers.negation.int_closure
61	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
62	instantiation	98, 75	⊢
	:
63	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
64	axiom		⊢
	proveit.logic.equality.equals_transitivity
65	instantiation	76, 114, 77, 78, 79, 80	⊢
	: , : , : , :
66	instantiation	81, 103, 92, 82	⊢
	: , : , :
67	instantiation	117, 107, 83	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
69	instantiation	117, 84, 85	⊢
	: , : , :
70	instantiation	86, 92	⊢
	:
71	theorem		⊢
	proveit.numbers.negation.neg_times_pos
72	theorem		⊢
	proveit.numbers.negation.complex_closure
73	instantiation	87, 103, 92, 88	⊢
	: , :
74	instantiation	117, 107, 89	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
76	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
77	instantiation	90	⊢
	: , :
78	instantiation	90	⊢
	: , :
79	instantiation	91, 92	⊢
	:
80	instantiation	93, 103, 94*	⊢
	: , :
81	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
82	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
83	instantiation	117, 99, 95	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
85	instantiation	117, 96, 97	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
87	theorem		⊢
	proveit.numbers.division.div_complex_closure
88	instantiation	98, 110	⊢
	:
89	instantiation	117, 99, 100	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
91	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
92	instantiation	117, 107, 101	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.negation.pos_times_neg
94	instantiation	102, 103	⊢
	:
95	assumption		⊢
96	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
97	instantiation	117, 104, 105	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
100	assumption		⊢
101	instantiation	117, 112, 106	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
103	instantiation	117, 107, 108	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
105	instantiation	117, 109, 110	⊢
	: , : , :
106	instantiation	117, 115, 111	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
108	instantiation	117, 112, 113	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
110	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
111	instantiation	117, 118, 114	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
113	instantiation	117, 115, 116	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
115	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
116	instantiation	117, 118, 119	⊢
	: , : , :
117	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
118	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
119	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements