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	35	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 128, 89, 7, 43, 8*, 9*	⊢
	: , : , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	74, 10	⊢
	:
6	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
7	instantiation	129, 11, 12	⊢
	: , : , :
8	instantiation	13, 63, 14, 15	⊢
	: , :
9	instantiation	35, 16, 17	⊢
	: , : , :
10	instantiation	129, 123, 18	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
12	instantiation	19, 20	⊢
	:
13	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
14	instantiation	129, 123, 21	⊢
	: , : , :
15	instantiation	22, 23	⊢
	:
16	instantiation	44, 45, 24, 25, 26, 27	⊢
	: , : , : , :
17	instantiation	28, 29, 30, 63, 31*, 32*	⊢
	: , : , :
18	instantiation	129, 125, 33	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.negation.int_neg_closure
20	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
21	instantiation	129, 125, 34	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
24	instantiation	61	⊢
	: , :
25	instantiation	61	⊢
	: , :
26	instantiation	35, 36, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.mult_6_3
28	theorem		⊢
	proveit.numbers.division.frac_cancel_left
29	instantiation	129, 39, 38	⊢
	: , : , :
30	instantiation	129, 39, 40	⊢
	: , : , :
31	instantiation	74, 51	⊢
	:
32	theorem		⊢
	proveit.numbers.numerals.decimals.mult_9_2
33	instantiation	129, 41, 42	⊢
	: , : , :
34	instantiation	129, 127, 43	⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.equals_transitivity
36	instantiation	44, 45, 46, 47, 48, 49	⊢
	: , : , : , :
37	instantiation	50, 51, 75, 52, 53	⊢
	: , : , :
38	instantiation	129, 55, 54	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
40	instantiation	129, 55, 56	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
42	instantiation	57, 58, 59	⊢
	: , :
43	instantiation	129, 130, 60	⊢
	: , : , :
44	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
46	instantiation	61	⊢
	: , :
47	instantiation	61	⊢
	: , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.mult_5_3
49	instantiation	62, 75, 63, 64*	⊢
	: , :
50	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
51	instantiation	129, 123, 65	⊢
	: , : , :
52	instantiation	129, 123, 66	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.add_9_6
54	instantiation	129, 68, 67	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
56	instantiation	129, 68, 69	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
58	instantiation	129, 71, 70	⊢
	: , : , :
59	instantiation	129, 71, 72	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
61	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
62	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
63	instantiation	129, 123, 73	⊢
	: , : , :
64	instantiation	74, 75	⊢
	:
65	instantiation	129, 125, 76	⊢
	: , : , :
66	instantiation	129, 125, 77	⊢
	: , : , :
67	instantiation	129, 78, 105	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
69	instantiation	129, 78, 79	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
72	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
73	instantiation	129, 125, 80	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
75	instantiation	129, 123, 81	⊢
	: , : , :
76	instantiation	129, 127, 82	⊢
	: , : , :
77	instantiation	129, 127, 83	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
79	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
80	instantiation	129, 127, 84	⊢
	: , : , :
81	instantiation	129, 125, 85	⊢
	: , : , :
82	instantiation	129, 130, 86	⊢
	: , : , :
83	instantiation	129, 87, 88	⊢
	: , : , :
84	instantiation	129, 130, 103	⊢
	: , : , :
85	instantiation	129, 127, 89	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
87	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
88	instantiation	90, 103, 91, 92, 93	⊢
	: , : , :
89	instantiation	129, 130, 94	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.deci_sequence_is_nat_pos
91	instantiation	96, 103, 95	⊢
	:
92	instantiation	96, 131, 97	⊢
	:
93	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
94	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
95	instantiation	100, 98, 99	⊢
	: , :
96	theorem		⊢
	proveit.numbers.numerals.decimals.n_in_digits
97	instantiation	100, 101, 102	⊢
	: , :
98	instantiation	113, 103	⊢
	:
99	instantiation	104, 105	⊢
	:
100	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
101	instantiation	113, 131	⊢
	:
102	instantiation	106, 124, 107, 108, 109, 110*, 111*	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
104	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
105	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
106	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
108	instantiation	129, 125, 112	⊢
	: , : , :
109	instantiation	113, 122	⊢
	:
110	instantiation	114, 115, 116	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_5
112	instantiation	129, 127, 117	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
114	theorem		⊢
	proveit.logic.equality.sub_right_side_into
115	instantiation	118, 120	⊢
	:
116	instantiation	119, 120, 121	⊢
	: , :
117	instantiation	129, 130, 122	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.addition.elim_zero_right
119	theorem		⊢
	proveit.numbers.addition.commutation
120	instantiation	129, 123, 124	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
122	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
123	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
124	instantiation	129, 125, 126	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
126	instantiation	129, 127, 128	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
128	instantiation	129, 130, 131	⊢
	: , : , :
129	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
130	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
131	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
*equality replacement requirements