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