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.unfold_subset_eq
2	instantiation	3, 4	⊢
	: , :
3	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
4	instantiation	5, 6, 7	⊢
	: , : , :
5	theorem		⊢
	proveit.logic.equality.sub_left_side_into
6	instantiation	8, 77, 73, 14, 9	⊢
	: , : , : , : , :
7	instantiation	10, 77, 73, 11, 14, 12	⊢
	: , : , : , : , : , : , :
8	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
9	instantiation	13, 77, 14, 15, 16, 17	⊢
	: , : , :
10	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
14	instantiation	18	⊢
	: , : , :
15	instantiation	21, 19	⊢
	: , :
16	instantiation	21, 20	⊢
	: , :
17	instantiation	21, 22	⊢
	: , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
19	instantiation	25, 73, 26, 23	⊢
	: , :
20	instantiation	25, 74, 26, 24	⊢
	: , :
21	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
22	instantiation	25, 77, 26, 27	⊢
	: , :
23	instantiation	35, 61, 36, 28, 29, 30*, 31*	⊢
	: , : , :
24	instantiation	35, 62, 36, 64, 32, 33*, 34*	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
27	instantiation	35, 64, 36, 62, 37, 38*, 46*	⊢
	: , : , :
28	instantiation	75, 67, 39	⊢
	: , : , :
29	instantiation	48, 40	⊢
	:
30	instantiation	50, 41, 42	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
32	instantiation	48, 43	⊢
	:
33	instantiation	50, 44, 45	⊢
	: , : , :
34	instantiation	50, 46, 47	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
37	instantiation	48, 49	⊢
	:
38	instantiation	50, 51, 52	⊢
	: , : , :
39	instantiation	75, 71, 53	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
41	instantiation	56, 54	⊢
	:
42	instantiation	57, 54, 59	⊢
	: , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
44	instantiation	56, 55	⊢
	:
45	instantiation	57, 55, 59	⊢
	: , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
47	instantiation	57, 55, 58	⊢
	: , :
48	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
49	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
50	theorem		⊢
	proveit.logic.equality.sub_right_side_into
51	instantiation	56, 58	⊢
	:
52	instantiation	57, 58, 59	⊢
	: , :
53	instantiation	75, 76, 60	⊢
	: , : , :
54	instantiation	75, 63, 61	⊢
	: , : , :
55	instantiation	75, 63, 62	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.elim_zero_right
57	theorem		⊢
	proveit.numbers.addition.commutation
58	instantiation	75, 63, 64	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
61	instantiation	75, 67, 65	⊢
	: , : , :
62	instantiation	75, 67, 66	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
64	instantiation	75, 67, 68	⊢
	: , : , :
65	instantiation	75, 71, 69	⊢
	: , : , :
66	instantiation	75, 71, 70	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
68	instantiation	75, 71, 72	⊢
	: , : , :
69	instantiation	75, 76, 73	⊢
	: , : , :
70	instantiation	75, 76, 74	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
72	instantiation	75, 76, 77	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
74	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
75	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
*equality replacement requirements