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, 8, 9*	⊢
	: , : , : , : , : , :
1	reference	15	⊢
2	reference	78	⊢
3	reference	61	⊢
4	reference	80	⊢
5	instantiation	71	⊢
	: , :
6	reference	62	⊢
7	instantiation	97, 91, 10	⊢
	: , : , :
8	reference	89	⊢
9	instantiation	46, 11, 12	⊢
	: , : , :
10	instantiation	97, 93, 13	⊢
	: , : , :
11	instantiation	58, 14	⊢
	: , : , :
12	instantiation	15, 78, 61, 99, 80, 16, 17, 89, 18*	⊢
	: , : , : , : , : , :
13	instantiation	97, 95, 19	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.add_9_1
15	theorem		⊢
	proveit.numbers.addition.association
16	instantiation	71	⊢
	: , :
17	instantiation	97, 91, 20	⊢
	: , : , :
18	instantiation	46, 21, 22	⊢
	: , : , :
19	instantiation	97, 98, 79	⊢
	: , : , :
20	instantiation	97, 93, 23	⊢
	: , : , :
21	instantiation	58, 24	⊢
	: , : , :
22	instantiation	29, 99, 78, 55, 25, 26*, 27*	⊢
	: , : , : , :
23	instantiation	97, 95, 28	⊢
	: , : , :
24	instantiation	29, 99, 78, 55, 56, 30, 31*, 32*	⊢
	: , : , : , :
25	instantiation	33, 92, 34, 35, 36, 74*, 37*	⊢
	: , : , :
26	instantiation	60, 61, 78, 62, 44, 80, 45	⊢
	: , : , : , : , : , : , :
27	instantiation	46, 38, 39	⊢
	: , : , :
28	instantiation	97, 40, 41	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.md_nine_add_one
30	instantiation	50, 42	⊢
	:
31	instantiation	60, 61, 78, 43, 44, 80, 45	⊢
	: , : , : , : , : , : , :
32	instantiation	46, 47, 48	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
35	instantiation	97, 93, 49	⊢
	: , : , :
36	instantiation	50, 51	⊢
	:
37	theorem		⊢
	proveit.numbers.numerals.decimals.add_8_1
38	instantiation	58, 52	⊢
	: , : , :
39	instantiation	60, 61, 78, 53, 63, 80, 64	⊢
	: , : , : , : , : , : , :
40	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
41	instantiation	54, 99, 55, 56, 57	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
43	instantiation	71	⊢
	: , :
44	instantiation	72, 78	⊢
	: , :
45	instantiation	73, 74	⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.equals_transitivity
47	instantiation	58, 59	⊢
	: , : , :
48	instantiation	60, 61, 78, 62, 63, 80, 64	⊢
	: , : , : , : , : , : , :
49	instantiation	97, 95, 65	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
51	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
52	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
53	instantiation	71	⊢
	: , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.deci_sequence_is_nat_pos
55	instantiation	67, 66, 69	⊢
	: , : , :
56	instantiation	67, 68, 69	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
58	axiom		⊢
	proveit.logic.equality.substitution
59	instantiation	70, 89	⊢
	:
60	theorem		⊢
	proveit.core_expr_types.tuples.tuple_portion_substitution
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
62	instantiation	71	⊢
	: , :
63	instantiation	72, 78	⊢
	: , :
64	instantiation	73, 74	⊢
	: , : , :
65	instantiation	97, 98, 75	⊢
	: , : , :
66	instantiation	77, 99, 75, 76	⊢
	: , : , : , : , :
67	theorem		⊢
	proveit.logic.equality.sub_left_side_into
68	instantiation	77, 78, 79, 80, 81	⊢
	: , : , : , : , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.N_leq_9_enumSet
70	theorem		⊢
	proveit.numbers.addition.elim_zero_left
71	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
72	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
73	axiom		⊢
	proveit.core_expr_types.tuples.empty_range_def
74	instantiation	82, 83, 84	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
76	instantiation	85	⊢
	: , : , : , : , : , : , : , :
77	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
78	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
79	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
80	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
81	instantiation	86	⊢
	: , : , : , : , : , : , : , : , :
82	theorem		⊢
	proveit.logic.equality.sub_right_side_into
83	instantiation	87, 89	⊢
	:
84	instantiation	88, 89, 90	⊢
	: , :
85	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_8_typical_eq
86	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_9_typical_eq
87	theorem		⊢
	proveit.numbers.addition.elim_zero_right
88	theorem		⊢
	proveit.numbers.addition.commutation
89	instantiation	97, 91, 92	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
91	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
92	instantiation	97, 93, 94	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
94	instantiation	97, 95, 96	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
96	instantiation	97, 98, 99	⊢
	: , : , :
97	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
98	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements