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, 10, 11*	⊢
	: , : , : , : , : , :
1	reference	32	⊢
2	reference	95	⊢
3	reference	78	⊢
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
5	reference	97	⊢
6	instantiation	88	⊢
	: , :
7	instantiation	12	⊢
	: , : , :
8	instantiation	114, 108, 13	⊢
	: , : , :
9	instantiation	114, 108, 14	⊢
	: , : , :
10	reference	106	⊢
11	instantiation	63, 15, 16	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
13	instantiation	114, 110, 17	⊢
	: , : , :
14	instantiation	114, 110, 18	⊢
	: , : , :
15	instantiation	75, 19	⊢
	: , : , :
16	instantiation	32, 95, 78, 97, 20, 79, 21, 106, 22*	⊢
	: , : , : , : , : , :
17	instantiation	114, 112, 23	⊢
	: , : , :
18	instantiation	114, 112, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.add_5_4
20	instantiation	88	⊢
	: , :
21	instantiation	114, 108, 25	⊢
	: , : , :
22	instantiation	63, 26, 27	⊢
	: , : , :
23	instantiation	114, 115, 28	⊢
	: , : , :
24	instantiation	114, 115, 29	⊢
	: , : , :
25	instantiation	114, 110, 30	⊢
	: , : , :
26	instantiation	75, 31	⊢
	: , : , :
27	instantiation	32, 95, 78, 116, 97, 33, 34, 106, 35*	⊢
	: , : , : , : , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
30	instantiation	114, 112, 36	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.add_9_1
32	theorem		⊢
	proveit.numbers.addition.association
33	instantiation	88	⊢
	: , :
34	instantiation	114, 108, 37	⊢
	: , : , :
35	instantiation	63, 38, 39	⊢
	: , : , :
36	instantiation	114, 115, 96	⊢
	: , : , :
37	instantiation	114, 110, 40	⊢
	: , : , :
38	instantiation	75, 41	⊢
	: , : , :
39	instantiation	46, 116, 95, 72, 42, 43*, 44*	⊢
	: , : , : , :
40	instantiation	114, 112, 45	⊢
	: , : , :
41	instantiation	46, 116, 95, 72, 73, 47, 48*, 49*	⊢
	: , : , : , :
42	instantiation	50, 109, 51, 52, 53, 91*, 54*	⊢
	: , : , :
43	instantiation	77, 78, 95, 79, 61, 97, 62	⊢
	: , : , : , : , : , : , :
44	instantiation	63, 55, 56	⊢
	: , : , :
45	instantiation	114, 57, 58	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.md_nine_add_one
47	instantiation	67, 59	⊢
	:
48	instantiation	77, 78, 95, 60, 61, 97, 62	⊢
	: , : , : , : , : , : , :
49	instantiation	63, 64, 65	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
52	instantiation	114, 110, 66	⊢
	: , : , :
53	instantiation	67, 68	⊢
	:
54	theorem		⊢
	proveit.numbers.numerals.decimals.add_8_1
55	instantiation	75, 69	⊢
	: , : , :
56	instantiation	77, 78, 95, 70, 80, 97, 81	⊢
	: , : , : , : , : , : , :
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
58	instantiation	71, 116, 72, 73, 74	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
60	instantiation	88	⊢
	: , :
61	instantiation	89, 95	⊢
	: , :
62	instantiation	90, 91	⊢
	: , : , :
63	axiom		⊢
	proveit.logic.equality.equals_transitivity
64	instantiation	75, 76	⊢
	: , : , :
65	instantiation	77, 78, 95, 79, 80, 97, 81	⊢
	: , : , : , : , : , : , :
66	instantiation	114, 112, 82	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
68	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
69	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
70	instantiation	88	⊢
	: , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.deci_sequence_is_nat_pos
72	instantiation	84, 83, 86	⊢
	: , : , :
73	instantiation	84, 85, 86	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
75	axiom		⊢
	proveit.logic.equality.substitution
76	instantiation	87, 106	⊢
	:
77	theorem		⊢
	proveit.core_expr_types.tuples.tuple_portion_substitution
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
79	instantiation	88	⊢
	: , :
80	instantiation	89, 95	⊢
	: , :
81	instantiation	90, 91	⊢
	: , : , :
82	instantiation	114, 115, 92	⊢
	: , : , :
83	instantiation	94, 116, 92, 93	⊢
	: , : , : , : , :
84	theorem		⊢
	proveit.logic.equality.sub_left_side_into
85	instantiation	94, 95, 96, 97, 98	⊢
	: , : , : , : , :
86	theorem		⊢
	proveit.numbers.numerals.decimals.N_leq_9_enumSet
87	theorem		⊢
	proveit.numbers.addition.elim_zero_left
88	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
89	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
90	axiom		⊢
	proveit.core_expr_types.tuples.empty_range_def
91	instantiation	99, 100, 101	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
93	instantiation	102	⊢
	: , : , : , : , : , : , : , :
94	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
95	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
96	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
97	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
98	instantiation	103	⊢
	: , : , : , : , : , : , : , : , :
99	theorem		⊢
	proveit.logic.equality.sub_right_side_into
100	instantiation	104, 106	⊢
	:
101	instantiation	105, 106, 107	⊢
	: , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_8_typical_eq
103	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_9_typical_eq
104	theorem		⊢
	proveit.numbers.addition.elim_zero_right
105	theorem		⊢
	proveit.numbers.addition.commutation
106	instantiation	114, 108, 109	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
108	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
109	instantiation	114, 110, 111	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
111	instantiation	114, 112, 113	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
113	instantiation	114, 115, 116	⊢
	: , : , :
114	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
115	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
116	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements