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	45	⊢
3	instantiation	7	⊢
	: , : , :
4	instantiation	8, 9	⊢
	: , :
5	instantiation	13, 42, 45, 10	⊢
	: , :
6	instantiation	13, 42, 11, 12	⊢
	: , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
8	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
9	instantiation	13, 14, 42, 15	⊢
	: , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
12	instantiation	16, 33, 17, 35, 18, 19*, 20*	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
15	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
16	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
18	instantiation	21, 22	⊢
	:
19	instantiation	25, 23, 24	⊢
	: , : , :
20	instantiation	25, 26, 27	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
23	instantiation	28, 31	⊢
	:
24	instantiation	30, 31, 29	⊢
	: , :
25	theorem		⊢
	proveit.logic.equality.sub_right_side_into
26	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
27	instantiation	30, 31, 32	⊢
	: , :
28	theorem		⊢
	proveit.numbers.addition.elim_zero_right
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
30	theorem		⊢
	proveit.numbers.addition.commutation
31	instantiation	43, 34, 33	⊢
	: , : , :
32	instantiation	43, 34, 35	⊢
	: , : , :
33	instantiation	43, 37, 36	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	instantiation	43, 37, 38	⊢
	: , : , :
36	instantiation	43, 40, 39	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	43, 40, 41	⊢
	: , : , :
39	instantiation	43, 44, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	43, 44, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
*equality replacement requirements