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