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, 69, 66, 14, 35, 5	⊢
	: , : , : , : , :
3	instantiation	20, 6, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
5	instantiation	8, 69, 14, 9, 10, 11	⊢
	: , : , :
6	instantiation	20, 12, 13	⊢
	: , : , :
7	instantiation	33, 69, 66, 29, 14, 35, 31	⊢
	: , : , : , : , : , : , :
8	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
9	instantiation	16, 15	⊢
	: , :
10	instantiation	16, 17	⊢
	: , :
11	instantiation	26, 27, 18, 19	⊢
	: , :
12	instantiation	20, 21, 22	⊢
	: , : , :
13	instantiation	33, 66, 69, 29, 23, 24, 31	⊢
	: , : , : , : , : , : , :
14	instantiation	37	⊢
	: , : , :
15	instantiation	26, 66, 27, 25	⊢
	: , :
16	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
17	instantiation	26, 30, 27, 28	⊢
	: , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
19	theorem		⊢
	proveit.numbers.numerals.decimals.less_5_6
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	33, 29, 34, 30, 31, 32	⊢
	: , : , : , : , : , : , :
22	instantiation	33, 34, 66, 35, 36	⊢
	: , : , : , : , : , : , :
23	instantiation	44	⊢
	: , :
24	instantiation	37	⊢
	: , : , :
25	instantiation	38, 57, 39, 59, 40, 41*, 42*	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
28	theorem		⊢
	proveit.numbers.numerals.decimals.less_4_5
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
31	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32	instantiation	43	⊢
	: , : , : , :
33	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
35	instantiation	44	⊢
	: , :
36	instantiation	44	⊢
	: , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
38	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
40	instantiation	45, 46	⊢
	:
41	instantiation	49, 47, 48	⊢
	: , : , :
42	instantiation	49, 50, 51	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
45	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
47	instantiation	52, 55	⊢
	:
48	instantiation	54, 55, 53	⊢
	: , :
49	theorem		⊢
	proveit.logic.equality.sub_right_side_into
50	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
51	instantiation	54, 55, 56	⊢
	: , :
52	theorem		⊢
	proveit.numbers.addition.elim_zero_right
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
54	theorem		⊢
	proveit.numbers.addition.commutation
55	instantiation	67, 58, 57	⊢
	: , : , :
56	instantiation	67, 58, 59	⊢
	: , : , :
57	instantiation	67, 61, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
59	instantiation	67, 61, 62	⊢
	: , : , :
60	instantiation	67, 64, 63	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
62	instantiation	67, 64, 65	⊢
	: , : , :
63	instantiation	67, 68, 66	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
65	instantiation	67, 68, 69	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
*equality replacement requirements