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, 55, 15, 16, 5	⊢
	: , : , : , : , :
3	instantiation	6, 7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
5	instantiation	9, 55, 15, 10, 11	⊢
	: , : , :
6	axiom		⊢
	proveit.logic.equality.equals_transitivity
7	instantiation	13, 64, 55, 12	⊢
	: , : , : , : , : , : , :
8	instantiation	13, 55, 14, 15, 16, 17	⊢
	: , : , : , : , : , : , :
9	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
10	instantiation	19, 18	⊢
	: , :
11	instantiation	19, 20	⊢
	: , :
12	instantiation	21	⊢
	: , :
13	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
14	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
15	instantiation	21	⊢
	: , :
16	instantiation	21	⊢
	: , :
17	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
18	instantiation	23, 64, 24, 22	⊢
	: , :
19	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
20	instantiation	23, 67, 24, 25	⊢
	: , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
22	instantiation	30, 54, 31, 26, 27, 28*, 29*	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
24	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
25	instantiation	30, 57, 31, 32, 33, 34*, 35*	⊢
	: , : , :
26	instantiation	65, 59, 36	⊢
	: , : , :
27	instantiation	41, 37	⊢
	:
28	instantiation	43, 38, 39	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
30	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
32	instantiation	65, 59, 40	⊢
	: , : , :
33	instantiation	41, 42	⊢
	:
34	instantiation	43, 44, 45	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
36	instantiation	65, 62, 46	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
38	instantiation	49, 47	⊢
	:
39	instantiation	50, 47, 52	⊢
	: , :
40	instantiation	65, 62, 48	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
43	theorem		⊢
	proveit.logic.equality.sub_right_side_into
44	instantiation	49, 51	⊢
	:
45	instantiation	50, 51, 52	⊢
	: , :
46	instantiation	65, 66, 53	⊢
	: , : , :
47	instantiation	65, 56, 54	⊢
	: , : , :
48	instantiation	65, 66, 55	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.addition.elim_zero_right
50	theorem		⊢
	proveit.numbers.addition.commutation
51	instantiation	65, 56, 57	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
54	instantiation	65, 59, 58	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
57	instantiation	65, 59, 60	⊢
	: , : , :
58	instantiation	65, 62, 61	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
60	instantiation	65, 62, 63	⊢
	: , : , :
61	instantiation	65, 66, 64	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
63	instantiation	65, 66, 67	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
65	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
66	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
*equality replacement requirements