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