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