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