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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.inclusion.refined_nonmembership
2	instantiation	4, 5, 47, 6, 8	⊢
	: , : , : , :
3	instantiation	7, 47, 8, 9, 10, 11	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.subset_eq_of_superset
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
8	instantiation	12	⊢
	: , : , :
9	instantiation	13, 14	⊢
	: , :
10	instantiation	19, 47, 15, 16	⊢
	: , :
11	instantiation	19, 47, 17, 18	⊢
	: , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
13	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
14	instantiation	19, 38, 47, 20	⊢
	: , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
16	instantiation	21, 40, 22, 23, 24, 25*, 26*	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
18	theorem		⊢
	proveit.numbers.numerals.decimals.less_3_4
19	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
20	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
21	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
23	instantiation	45, 41, 27	⊢
	: , : , :
24	instantiation	28, 29	⊢
	:
25	instantiation	30, 31, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
27	instantiation	45, 43, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
30	theorem		⊢
	proveit.logic.equality.sub_right_side_into
31	instantiation	34, 36	⊢
	:
32	instantiation	35, 36, 37	⊢
	: , :
33	instantiation	45, 46, 38	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.addition.elim_zero_right
35	theorem		⊢
	proveit.numbers.addition.commutation
36	instantiation	45, 39, 40	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
40	instantiation	45, 41, 42	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
42	instantiation	45, 43, 44	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
44	instantiation	45, 46, 47	⊢
	: , : , :
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