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	theorem		⊢
	proveit.logic.sets.inclusion.transitivity_subset_subset
2	instantiation	6, 4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8	⊢
	: , : , :
4	instantiation	13, 123, 20, 21, 9	⊢
	: , : , : , : , :
5	instantiation	10, 11, 12	⊢
	: , : , :
6	theorem		⊢
	proveit.logic.equality.sub_left_side_into
7	instantiation	13, 120, 117, 24, 14	⊢
	: , : , : , : , :
8	instantiation	18, 120, 117, 19, 24, 22	⊢
	: , : , : , : , : , : , :
9	instantiation	23, 123, 20, 15, 16	⊢
	: , : , :
10	axiom		⊢
	proveit.logic.equality.equals_transitivity
11	instantiation	18, 117, 123, 17	⊢
	: , : , : , : , : , : , :
12	instantiation	18, 123, 19, 20, 21, 22	⊢
	: , : , : , : , : , : , :
13	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
14	instantiation	23, 120, 24, 25, 26, 27, 28, 29	⊢
	: , : , :
15	instantiation	38, 30	⊢
	: , :
16	instantiation	38, 31	⊢
	: , :
17	instantiation	32	⊢
	: , :
18	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
19	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
20	instantiation	32	⊢
	: , :
21	instantiation	32	⊢
	: , :
22	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
24	instantiation	33	⊢
	: , : , : , : , :
25	instantiation	38, 34	⊢
	: , :
26	instantiation	38, 35	⊢
	: , :
27	instantiation	38, 36	⊢
	: , :
28	instantiation	38, 37	⊢
	: , :
29	instantiation	38, 39	⊢
	: , :
30	instantiation	46, 117, 120, 40	⊢
	: , :
31	instantiation	46, 119, 120, 41	⊢
	: , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
34	instantiation	46, 117, 47, 42	⊢
	: , :
35	instantiation	46, 123, 47, 43	⊢
	: , :
36	instantiation	46, 119, 47, 44	⊢
	: , :
37	instantiation	46, 118, 47, 45	⊢
	: , :
38	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
39	instantiation	46, 120, 47, 48	⊢
	: , :
40	instantiation	62, 99, 63, 100, 57, 53*, 49*	⊢
	: , : , :
41	instantiation	62, 101, 63, 104, 64, 58*, 50*	⊢
	: , : , :
42	instantiation	62, 99, 63, 51, 52, 53*, 54*	⊢
	: , : , :
43	instantiation	62, 104, 63, 102, 55, 56*, 87*	⊢
	: , : , :
44	instantiation	62, 101, 63, 100, 57, 58*, 80*	⊢
	: , : , :
45	instantiation	62, 100, 63, 101, 59, 60*, 61*	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat7
48	instantiation	62, 102, 63, 104, 64, 65*, 66*	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
50	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
51	instantiation	121, 109, 67	⊢
	: , : , :
52	instantiation	82, 68	⊢
	:
53	instantiation	86, 69, 70	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.add_6_1
55	instantiation	82, 71	⊢
	:
56	instantiation	86, 72, 73	⊢
	: , : , :
57	instantiation	82, 74	⊢
	:
58	instantiation	86, 75, 76	⊢
	: , : , :
59	instantiation	82, 77	⊢
	:
60	instantiation	86, 78, 79	⊢
	: , : , :
61	instantiation	86, 80, 81	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
64	instantiation	82, 83	⊢
	:
65	instantiation	86, 84, 85	⊢
	: , : , :
66	instantiation	86, 87, 88	⊢
	: , : , :
67	instantiation	121, 115, 89	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
69	instantiation	93, 90	⊢
	:
70	instantiation	95, 90, 94	⊢
	: , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
72	instantiation	93, 97	⊢
	:
73	instantiation	95, 97, 94	⊢
	: , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
75	instantiation	93, 92	⊢
	:
76	instantiation	95, 92, 94	⊢
	: , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
78	instantiation	93, 91	⊢
	:
79	instantiation	95, 91, 94	⊢
	: , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_3
81	instantiation	95, 91, 92	⊢
	: , :
82	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
83	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
84	instantiation	93, 96	⊢
	:
85	instantiation	95, 96, 94	⊢
	: , :
86	theorem		⊢
	proveit.logic.equality.sub_right_side_into
87	theorem		⊢
	proveit.numbers.numerals.decimals.add_5_2
88	instantiation	95, 96, 97	⊢
	: , :
89	instantiation	121, 122, 98	⊢
	: , : , :
90	instantiation	121, 103, 99	⊢
	: , : , :
91	instantiation	121, 103, 100	⊢
	: , : , :
92	instantiation	121, 103, 101	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.addition.elim_zero_right
94	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
95	theorem		⊢
	proveit.numbers.addition.commutation
96	instantiation	121, 103, 102	⊢
	: , : , :
97	instantiation	121, 103, 104	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
99	instantiation	121, 109, 105	⊢
	: , : , :
100	instantiation	121, 109, 106	⊢
	: , : , :
101	instantiation	121, 109, 107	⊢
	: , : , :
102	instantiation	121, 109, 108	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
104	instantiation	121, 109, 110	⊢
	: , : , :
105	instantiation	121, 115, 111	⊢
	: , : , :
106	instantiation	121, 115, 112	⊢
	: , : , :
107	instantiation	121, 115, 113	⊢
	: , : , :
108	instantiation	121, 115, 114	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
110	instantiation	121, 115, 116	⊢
	: , : , :
111	instantiation	121, 122, 117	⊢
	: , : , :
112	instantiation	121, 122, 118	⊢
	: , : , :
113	instantiation	121, 122, 119	⊢
	: , : , :
114	instantiation	121, 122, 120	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
116	instantiation	121, 122, 123	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
118	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
119	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
120	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
121	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
122	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
123	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements