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.subtraction.membership_folding
2	instantiation	4, 26, 5, 6	⊢
	: , : , :
3	instantiation	23, 7, 16	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.fold
5	instantiation	8	⊢
	: , : , :
6	instantiation	9, 10, 47, 11, 12, 13, 14, 15, 16	⊢
	: , : , : , : , :
7	instantiation	17, 47, 18, 19, 20	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
9	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_any
10	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	instantiation	22	⊢
	: , :
13	instantiation	21	⊢
	: , :
14	instantiation	21	⊢
	: , :
15	instantiation	21	⊢
	: , :
16	assumption		⊢
17	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
18	instantiation	22	⊢
	: , :
19	instantiation	23, 24, 25	⊢
	: , : , :
20	instantiation	28, 56, 26, 27	⊢
	: , :
21	axiom		⊢
	proveit.logic.equality.equality_in_bool
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
23	theorem		⊢
	proveit.logic.equality.sub_left_side_into
24	instantiation	28, 56, 47, 29	⊢
	: , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
27	instantiation	30, 49, 31, 32, 33, 34*, 35*	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
29	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
30	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
32	instantiation	54, 50, 36	⊢
	: , : , :
33	instantiation	37, 38	⊢
	:
34	instantiation	39, 40, 41	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
36	instantiation	54, 52, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
39	theorem		⊢
	proveit.logic.equality.sub_right_side_into
40	instantiation	43, 45	⊢
	:
41	instantiation	44, 45, 46	⊢
	: , :
42	instantiation	54, 55, 47	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.addition.elim_zero_right
44	theorem		⊢
	proveit.numbers.addition.commutation
45	instantiation	54, 48, 49	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	instantiation	54, 50, 51	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
51	instantiation	54, 52, 53	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
53	instantiation	54, 55, 56	⊢
	: , : , :
54	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements