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