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, 32, 5, 6	⊢
	: , : , :
3	instantiation	45, 7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.fold
5	instantiation	9	⊢
	: , : , :
6	instantiation	10, 11, 53, 12, 13, 14, 15, 16, 18	⊢
	: , : , : , : , :
7	instantiation	29, 17, 18	⊢
	: , : , :
8	instantiation	19, 53, 24, 20, 31, 21	⊢
	: , : , : , :
9	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
10	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_any
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13	instantiation	28	⊢
	: , :
14	instantiation	22	⊢
	: , :
15	instantiation	22	⊢
	: , :
16	instantiation	22	⊢
	: , :
17	instantiation	23, 53, 24, 25, 26	⊢
	: , : , :
18	assumption		⊢
19	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
20	instantiation	28	⊢
	: , :
21	instantiation	27, 41	⊢
	: , :
22	axiom		⊢
	proveit.logic.equality.equality_in_bool
23	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
24	instantiation	28	⊢
	: , :
25	instantiation	29, 30, 31	⊢
	: , : , :
26	instantiation	34, 62, 32, 33	⊢
	: , :
27	theorem		⊢
	proveit.logic.equality.equals_reversal
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29	theorem		⊢
	proveit.logic.equality.sub_left_side_into
30	instantiation	34, 62, 53, 35	⊢
	: , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
33	instantiation	36, 55, 37, 38, 39, 40*, 41*	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
35	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
36	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
38	instantiation	60, 56, 42	⊢
	: , : , :
39	instantiation	43, 44	⊢
	:
40	instantiation	45, 46, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
42	instantiation	60, 58, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
45	theorem		⊢
	proveit.logic.equality.sub_right_side_into
46	instantiation	49, 51	⊢
	:
47	instantiation	50, 51, 52	⊢
	: , :
48	instantiation	60, 61, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.addition.elim_zero_right
50	theorem		⊢
	proveit.numbers.addition.commutation
51	instantiation	60, 54, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
55	instantiation	60, 56, 57	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
57	instantiation	60, 58, 59	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
59	instantiation	60, 61, 62	⊢
	: , : , :
60	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements