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