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	47	⊢
3	instantiation	7	⊢
	: , : , :
4	instantiation	9, 8	⊢
	: , :
5	instantiation	9, 10	⊢
	: , :
6	instantiation	14, 16, 11, 12	⊢
	: , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
8	instantiation	14, 44, 16, 13	⊢
	: , :
9	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
10	instantiation	14, 15, 16, 17	⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
12	theorem		⊢
	proveit.numbers.numerals.decimals.less_5_6
13	instantiation	18, 35, 19, 37, 20, 21*, 22*	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
15	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
17	theorem		⊢
	proveit.numbers.numerals.decimals.less_4_5
18	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
20	instantiation	23, 24	⊢
	:
21	instantiation	27, 25, 26	⊢
	: , : , :
22	instantiation	27, 28, 29	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
25	instantiation	30, 33	⊢
	:
26	instantiation	32, 33, 31	⊢
	: , :
27	theorem		⊢
	proveit.logic.equality.sub_right_side_into
28	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
29	instantiation	32, 33, 34	⊢
	: , :
30	theorem		⊢
	proveit.numbers.addition.elim_zero_right
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
32	theorem		⊢
	proveit.numbers.addition.commutation
33	instantiation	45, 36, 35	⊢
	: , : , :
34	instantiation	45, 36, 37	⊢
	: , : , :
35	instantiation	45, 39, 38	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	instantiation	45, 39, 40	⊢
	: , : , :
38	instantiation	45, 42, 41	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
40	instantiation	45, 42, 43	⊢
	: , : , :
41	instantiation	45, 46, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
43	instantiation	45, 46, 47	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
*equality replacement requirements