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	47, 4	⊢
	: , : , :
3	instantiation	5, 67, 50, 88, 69, 6, 7, 78, 8*	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.numerals.decimals.add_9_1
5	theorem		⊢
	proveit.numbers.addition.association
6	instantiation	60	⊢
	: , :
7	instantiation	86, 80, 9	⊢
	: , : , :
8	instantiation	35, 10, 11	⊢
	: , : , :
9	instantiation	86, 82, 12	⊢
	: , : , :
10	instantiation	47, 13	⊢
	: , : , :
11	instantiation	18, 88, 67, 44, 14, 15*, 16*	⊢
	: , : , : , :
12	instantiation	86, 84, 17	⊢
	: , : , :
13	instantiation	18, 88, 67, 44, 45, 19, 20*, 21*	⊢
	: , : , : , :
14	instantiation	22, 81, 23, 24, 25, 63*, 26*	⊢
	: , : , :
15	instantiation	49, 50, 67, 51, 33, 69, 34	⊢
	: , : , : , : , : , : , :
16	instantiation	35, 27, 28	⊢
	: , : , :
17	instantiation	86, 29, 30	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.md_nine_add_one
19	instantiation	39, 31	⊢
	:
20	instantiation	49, 50, 67, 32, 33, 69, 34	⊢
	: , : , : , : , : , : , :
21	instantiation	35, 36, 37	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
24	instantiation	86, 82, 38	⊢
	: , : , :
25	instantiation	39, 40	⊢
	:
26	theorem		⊢
	proveit.numbers.numerals.decimals.add_8_1
27	instantiation	47, 41	⊢
	: , : , :
28	instantiation	49, 50, 67, 42, 52, 69, 53	⊢
	: , : , : , : , : , : , :
29	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
30	instantiation	43, 88, 44, 45, 46	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
32	instantiation	60	⊢
	: , :
33	instantiation	61, 67	⊢
	: , :
34	instantiation	62, 63	⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.equals_transitivity
36	instantiation	47, 48	⊢
	: , : , :
37	instantiation	49, 50, 67, 51, 52, 69, 53	⊢
	: , : , : , : , : , : , :
38	instantiation	86, 84, 54	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
41	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
42	instantiation	60	⊢
	: , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.deci_sequence_is_nat_pos
44	instantiation	56, 55, 58	⊢
	: , : , :
45	instantiation	56, 57, 58	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
47	axiom		⊢
	proveit.logic.equality.substitution
48	instantiation	59, 78	⊢
	:
49	theorem		⊢
	proveit.core_expr_types.tuples.tuple_portion_substitution
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
51	instantiation	60	⊢
	: , :
52	instantiation	61, 67	⊢
	: , :
53	instantiation	62, 63	⊢
	: , : , :
54	instantiation	86, 87, 64	⊢
	: , : , :
55	instantiation	66, 88, 64, 65	⊢
	: , : , : , : , :
56	theorem		⊢
	proveit.logic.equality.sub_left_side_into
57	instantiation	66, 67, 68, 69, 70	⊢
	: , : , : , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.N_leq_9_enumSet
59	theorem		⊢
	proveit.numbers.addition.elim_zero_left
60	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
61	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
62	axiom		⊢
	proveit.core_expr_types.tuples.empty_range_def
63	instantiation	71, 72, 73	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
65	instantiation	74	⊢
	: , : , : , : , : , : , : , :
66	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
67	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
69	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
70	instantiation	75	⊢
	: , : , : , : , : , : , : , : , :
71	theorem		⊢
	proveit.logic.equality.sub_right_side_into
72	instantiation	76, 78	⊢
	:
73	instantiation	77, 78, 79	⊢
	: , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_8_typical_eq
75	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_9_typical_eq
76	theorem		⊢
	proveit.numbers.addition.elim_zero_right
77	theorem		⊢
	proveit.numbers.addition.commutation
78	instantiation	86, 80, 81	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
80	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
81	instantiation	86, 82, 83	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
83	instantiation	86, 84, 85	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
85	instantiation	86, 87, 88	⊢
	: , : , :
86	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
87	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
88	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements