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, 4, 5, 6	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
2	reference	40	⊢
3	instantiation	7	⊢
	: , : , :
4	instantiation	14, 8	⊢
	: , :
5	instantiation	9, 10, 11	⊢
	: , : , :
6	instantiation	14, 12	⊢
	: , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
8	instantiation	21, 52, 22, 13	⊢
	: , :
9	theorem		⊢
	proveit.logic.equality.sub_left_side_into
10	instantiation	14, 15	⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
12	instantiation	21, 40, 22, 16	⊢
	: , :
13	instantiation	28, 41, 29, 17, 18, 19*, 20*	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
15	instantiation	21, 57, 22, 23	⊢
	: , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.less_3_4
17	instantiation	55, 50, 24	⊢
	: , : , :
18	instantiation	35, 25	⊢
	:
19	instantiation	37, 26, 27	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
21	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
23	instantiation	28, 48, 29, 30, 31*, 32*	⊢
	: , : , :
24	instantiation	55, 53, 33	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
26	instantiation	42, 34	⊢
	:
27	instantiation	43, 34, 45	⊢
	: , :
28	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
30	instantiation	35, 36	⊢
	:
31	instantiation	37, 38, 39	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
33	instantiation	55, 56, 40	⊢
	: , : , :
34	instantiation	55, 47, 41	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
37	theorem		⊢
	proveit.logic.equality.sub_right_side_into
38	instantiation	42, 44	⊢
	:
39	instantiation	43, 44, 45	⊢
	: , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
41	instantiation	55, 50, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.addition.elim_zero_right
43	theorem		⊢
	proveit.numbers.addition.commutation
44	instantiation	55, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
46	instantiation	55, 53, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
48	instantiation	55, 50, 51	⊢
	: , : , :
49	instantiation	55, 56, 52	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
51	instantiation	55, 53, 54	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
54	instantiation	55, 56, 57	⊢
	: , : , :
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements