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_eq_subset_eq
2	instantiation	4, 108, 112, 5, 6	⊢
	: , : , : , :
3	instantiation	7, 8	⊢
	: , :
4	theorem		⊢
	proveit.logic.sets.enumeration.subset_eq_of_superset
5	instantiation	9	⊢
	: , : , :
6	instantiation	10	⊢
	: , :
7	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
8	instantiation	11, 12, 13	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11	theorem		⊢
	proveit.logic.equality.sub_left_side_into
12	instantiation	14, 109, 106, 20, 15	⊢
	: , : , : , : , :
13	instantiation	16, 109, 106, 17, 20, 18	⊢
	: , : , : , : , : , : , :
14	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
15	instantiation	19, 109, 20, 21, 22, 23, 24, 25	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
17	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
18	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
19	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
20	instantiation	26	⊢
	: , : , : , : , :
21	instantiation	31, 27	⊢
	: , :
22	instantiation	31, 28	⊢
	: , :
23	instantiation	31, 29	⊢
	: , :
24	instantiation	31, 30	⊢
	: , :
25	instantiation	31, 32	⊢
	: , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
27	instantiation	37, 106, 38, 33	⊢
	: , :
28	instantiation	37, 112, 38, 34	⊢
	: , :
29	instantiation	37, 108, 38, 35	⊢
	: , :
30	instantiation	37, 107, 38, 36	⊢
	: , :
31	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
32	instantiation	37, 109, 38, 39	⊢
	: , :
33	instantiation	51, 88, 52, 40, 41, 42*, 43*	⊢
	: , : , :
34	instantiation	51, 93, 52, 91, 44, 45*, 76*	⊢
	: , : , :
35	instantiation	51, 90, 52, 89, 46, 47*, 69*	⊢
	: , : , :
36	instantiation	51, 89, 52, 90, 48, 49*, 50*	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat7
39	instantiation	51, 91, 52, 93, 53, 54*, 55*	⊢
	: , : , :
40	instantiation	110, 98, 56	⊢
	: , : , :
41	instantiation	71, 57	⊢
	:
42	instantiation	75, 58, 59	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.add_6_1
44	instantiation	71, 60	⊢
	:
45	instantiation	75, 61, 62	⊢
	: , : , :
46	instantiation	71, 63	⊢
	:
47	instantiation	75, 64, 65	⊢
	: , : , :
48	instantiation	71, 66	⊢
	:
49	instantiation	75, 67, 68	⊢
	: , : , :
50	instantiation	75, 69, 70	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
53	instantiation	71, 72	⊢
	:
54	instantiation	75, 73, 74	⊢
	: , : , :
55	instantiation	75, 76, 77	⊢
	: , : , :
56	instantiation	110, 104, 78	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
58	instantiation	82, 79	⊢
	:
59	instantiation	84, 79, 83	⊢
	: , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
61	instantiation	82, 86	⊢
	:
62	instantiation	84, 86, 83	⊢
	: , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
64	instantiation	82, 81	⊢
	:
65	instantiation	84, 81, 83	⊢
	: , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
67	instantiation	82, 80	⊢
	:
68	instantiation	84, 80, 83	⊢
	: , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_3
70	instantiation	84, 80, 81	⊢
	: , :
71	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
72	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
73	instantiation	82, 85	⊢
	:
74	instantiation	84, 85, 83	⊢
	: , :
75	theorem		⊢
	proveit.logic.equality.sub_right_side_into
76	theorem		⊢
	proveit.numbers.numerals.decimals.add_5_2
77	instantiation	84, 85, 86	⊢
	: , :
78	instantiation	110, 111, 87	⊢
	: , : , :
79	instantiation	110, 92, 88	⊢
	: , : , :
80	instantiation	110, 92, 89	⊢
	: , : , :
81	instantiation	110, 92, 90	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.addition.elim_zero_right
83	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
84	theorem		⊢
	proveit.numbers.addition.commutation
85	instantiation	110, 92, 91	⊢
	: , : , :
86	instantiation	110, 92, 93	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
88	instantiation	110, 98, 94	⊢
	: , : , :
89	instantiation	110, 98, 95	⊢
	: , : , :
90	instantiation	110, 98, 96	⊢
	: , : , :
91	instantiation	110, 98, 97	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
93	instantiation	110, 98, 99	⊢
	: , : , :
94	instantiation	110, 104, 100	⊢
	: , : , :
95	instantiation	110, 104, 101	⊢
	: , : , :
96	instantiation	110, 104, 102	⊢
	: , : , :
97	instantiation	110, 104, 103	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
99	instantiation	110, 104, 105	⊢
	: , : , :
100	instantiation	110, 111, 106	⊢
	: , : , :
101	instantiation	110, 111, 107	⊢
	: , : , :
102	instantiation	110, 111, 108	⊢
	: , : , :
103	instantiation	110, 111, 109	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
105	instantiation	110, 111, 112	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
107	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
109	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
110	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
111	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
112	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements