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*	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_equiv
2	reference	91	⊢
3	reference	34	⊢
4	instantiation	45, 5, 6	⊢
	: , : , :
5	instantiation	7, 91, 8, 18, 9, 10, 11	⊢
	: , : , : , :
6	instantiation	21, 12	⊢
	:
7	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
8	instantiation	48	⊢
	: , : , :
9	instantiation	15, 13*	⊢
	: , :
10	instantiation	15, 14*	⊢
	: , :
11	instantiation	15, 16*	⊢
	: , :
12	instantiation	17, 91, 18, 19	⊢
	: , :
13	instantiation	45, 20, 24	⊢
	: , : , :
14	instantiation	21, 22	⊢
	:
15	axiom		⊢
	proveit.logic.equality.not_equals_def
16	instantiation	45, 23, 24	⊢
	: , : , :
17	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
18	instantiation	48	⊢
	: , : , :
19	axiom		⊢
	proveit.logic.booleans.true_axiom
20	instantiation	54, 25	⊢
	: , : , :
21	axiom		⊢
	proveit.logic.booleans.eq_true_intro
22	instantiation	36, 26	⊢
	: , :
23	instantiation	54, 27	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.booleans.negation.not_f
25	instantiation	31, 28	⊢
	:
26	instantiation	29, 92, 30	⊢
	: , : , : , : , :
27	instantiation	31, 32	⊢
	:
28	instantiation	36, 42	⊢
	: , :
29	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
30	instantiation	33, 91, 34, 35	⊢
	: , : , :
31	axiom		⊢
	proveit.logic.booleans.negation.negation_elim
32	instantiation	36, 43	⊢
	: , :
33	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_unfold
34	instantiation	48	⊢
	: , : , :
35	instantiation	37, 38, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.logic.equality.unfold_not_equals
37	theorem		⊢
	proveit.logic.equality.sub_left_side_into
38	instantiation	40, 91, 41, 42, 43, 44	⊢
	: , : , :
39	instantiation	45, 46, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
41	instantiation	48	⊢
	: , : , :
42	instantiation	49, 50	⊢
	: , :
43	instantiation	59, 95, 91, 51	⊢
	: , :
44	instantiation	59, 95, 52, 53	⊢
	: , :
45	axiom		⊢
	proveit.logic.equality.equals_transitivity
46	instantiation	54, 55	⊢
	: , : , :
47	instantiation	56, 92, 57, 58	⊢
	: , : , : , : , : , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
49	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
50	instantiation	59, 92, 95, 60	⊢
	: , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
53	instantiation	61, 82, 62, 63, 64*, 65*	⊢
	: , : , :
54	axiom		⊢
	proveit.logic.equality.substitution
55	instantiation	70, 66, 67	⊢
	: , : , :
56	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
57	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
58	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
59	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
60	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
61	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
63	instantiation	68, 69	⊢
	:
64	instantiation	70, 71, 72	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
66	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
67	instantiation	76, 73, 74	⊢
	: , :
68	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
69	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
70	theorem		⊢
	proveit.logic.equality.sub_right_side_into
71	instantiation	75, 77	⊢
	:
72	instantiation	76, 77, 78	⊢
	: , :
73	instantiation	93, 81, 79	⊢
	: , : , :
74	instantiation	93, 81, 80	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.addition.elim_zero_right
76	theorem		⊢
	proveit.numbers.addition.commutation
77	instantiation	93, 81, 82	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
79	instantiation	93, 85, 83	⊢
	: , : , :
80	instantiation	93, 85, 84	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
82	instantiation	93, 85, 86	⊢
	: , : , :
83	instantiation	93, 89, 87	⊢
	: , : , :
84	instantiation	93, 89, 88	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
86	instantiation	93, 89, 90	⊢
	: , : , :
87	instantiation	93, 94, 91	⊢
	: , : , :
88	instantiation	93, 94, 92	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
90	instantiation	93, 94, 95	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
92	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
93	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
94	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
95	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements