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, 4, 5, 6*, 7*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	instantiation	8, 57	⊢
	:
3	instantiation	9, 56, 137	⊢
	: , :
4	instantiation	159, 155, 10	⊢
	: , : , :
5	instantiation	11, 56, 137, 99, 123, 12	⊢
	: , : , :
6	instantiation	13, 14, 15, 16	⊢
	: , : , : , :
7	instantiation	58, 17, 18	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.negation.real_closure
9	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
10	instantiation	19, 64, 110	⊢
	: , :
11	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
12	instantiation	20, 80	⊢
	:
13	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
14	instantiation	58, 21, 22	⊢
	: , : , :
15	instantiation	23	⊢
	:
16	instantiation	24, 28	⊢
	: , :
17	instantiation	30, 25	⊢
	: , : , :
18	instantiation	26, 158, 119, 27, 96, 28*, 29*	⊢
	: , : , : , :
19	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
20	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
21	instantiation	30, 31	⊢
	: , : , :
22	instantiation	32, 33	⊢
	:
23	axiom		⊢
	proveit.logic.equality.equals_reflexivity
24	theorem		⊢
	proveit.logic.equality.equals_reversal
25	instantiation	100, 41	⊢
	:
26	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
27	instantiation	159, 34, 35	⊢
	: , : , :
28	instantiation	36, 86, 37, 83	⊢
	: , :
29	instantiation	58, 38, 39	⊢
	: , : , :
30	axiom		⊢
	proveit.logic.equality.substitution
31	instantiation	40, 41	⊢
	:
32	theorem		⊢
	proveit.numbers.addition.elim_zero_left
33	instantiation	42, 43	⊢
	:
34	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
35	instantiation	44, 45	⊢
	:
36	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
37	instantiation	159, 153, 46	⊢
	: , : , :
38	instantiation	66, 67, 47, 48, 49, 50	⊢
	: , : , : , :
39	instantiation	51, 52, 53, 86, 54*, 55*	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
41	instantiation	159, 153, 56	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.negation.complex_closure
43	instantiation	159, 153, 57	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.negation.int_neg_closure
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
46	instantiation	159, 155, 82	⊢
	: , : , :
47	instantiation	84	⊢
	: , :
48	instantiation	84	⊢
	: , :
49	instantiation	58, 59, 60	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.mult_6_3
51	theorem		⊢
	proveit.numbers.division.frac_cancel_left
52	instantiation	159, 62, 61	⊢
	: , : , :
53	instantiation	159, 62, 63	⊢
	: , : , :
54	instantiation	100, 73	⊢
	:
55	theorem		⊢
	proveit.numbers.numerals.decimals.mult_9_2
56	instantiation	159, 155, 64	⊢
	: , : , :
57	instantiation	159, 155, 65	⊢
	: , : , :
58	axiom		⊢
	proveit.logic.equality.equals_transitivity
59	instantiation	66, 67, 68, 69, 70, 71	⊢
	: , : , : , :
60	instantiation	72, 73, 101, 74, 75	⊢
	: , : , :
61	instantiation	159, 77, 76	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
63	instantiation	159, 77, 78	⊢
	: , : , :
64	instantiation	159, 79, 80	⊢
	: , : , :
65	instantiation	81, 110, 82, 83	⊢
	: , :
66	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
68	instantiation	84	⊢
	: , :
69	instantiation	84	⊢
	: , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.mult_5_3
71	instantiation	85, 101, 86, 87*	⊢
	: , :
72	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
73	instantiation	159, 153, 88	⊢
	: , : , :
74	instantiation	159, 153, 89	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.numerals.decimals.add_9_6
76	instantiation	159, 91, 90	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
78	instantiation	159, 91, 92	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
80	instantiation	93, 94, 95	⊢
	: , :
81	theorem		⊢
	proveit.numbers.division.div_rational_closure
82	instantiation	159, 157, 96	⊢
	: , : , :
83	instantiation	97, 98	⊢
	:
84	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
85	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
86	instantiation	159, 153, 99	⊢
	: , : , :
87	instantiation	100, 101	⊢
	:
88	instantiation	159, 155, 102	⊢
	: , : , :
89	instantiation	159, 155, 103	⊢
	: , : , :
90	instantiation	159, 104, 135	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
92	instantiation	159, 104, 105	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
94	instantiation	159, 107, 106	⊢
	: , : , :
95	instantiation	159, 107, 108	⊢
	: , : , :
96	instantiation	159, 160, 109	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
98	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
99	instantiation	159, 155, 110	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
101	instantiation	159, 153, 111	⊢
	: , : , :
102	instantiation	159, 157, 112	⊢
	: , : , :
103	instantiation	159, 157, 113	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
105	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
106	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
107	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
108	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
109	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
110	instantiation	159, 157, 114	⊢
	: , : , :
111	instantiation	159, 155, 115	⊢
	: , : , :
112	instantiation	159, 160, 116	⊢
	: , : , :
113	instantiation	159, 117, 118	⊢
	: , : , :
114	instantiation	159, 160, 133	⊢
	: , : , :
115	instantiation	159, 157, 119	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
117	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
118	instantiation	120, 133, 121, 122, 123	⊢
	: , : , :
119	instantiation	159, 160, 124	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.numerals.decimals.deci_sequence_is_nat_pos
121	instantiation	126, 133, 125	⊢
	:
122	instantiation	126, 161, 127	⊢
	:
123	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
124	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
125	instantiation	130, 128, 129	⊢
	: , :
126	theorem		⊢
	proveit.numbers.numerals.decimals.n_in_digits
127	instantiation	130, 131, 132	⊢
	: , :
128	instantiation	143, 133	⊢
	:
129	instantiation	134, 135	⊢
	:
130	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
131	instantiation	143, 161	⊢
	:
132	instantiation	136, 154, 137, 138, 139, 140*, 141*	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
134	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
135	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
136	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
137	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
138	instantiation	159, 155, 142	⊢
	: , : , :
139	instantiation	143, 152	⊢
	:
140	instantiation	144, 145, 146	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_5
142	instantiation	159, 157, 147	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
144	theorem		⊢
	proveit.logic.equality.sub_right_side_into
145	instantiation	148, 150	⊢
	:
146	instantiation	149, 150, 151	⊢
	: , :
147	instantiation	159, 160, 152	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.addition.elim_zero_right
149	theorem		⊢
	proveit.numbers.addition.commutation
150	instantiation	159, 153, 154	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
152	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
153	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
154	instantiation	159, 155, 156	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
156	instantiation	159, 157, 158	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
158	instantiation	159, 160, 161	⊢
	: , : , :
159	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
160	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
161	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
*equality replacement requirements