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	reference	60	⊢
2	instantiation	5, 6, 7, 8, 9, 10, 11, 12*	⊢
	: , : , : , :
3	instantiation	75, 13, 99	⊢
	: , :
4	instantiation	14, 15	⊢
	: , :
5	theorem		⊢
	proveit.core_expr_types.tuples.general_len
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
7	instantiation	101	⊢
	: , : , :
8	instantiation	101	⊢
	: , : , :
9	instantiation	101	⊢
	: , : , :
10	instantiation	16, 129, 31	⊢
	: , : , :
11	instantiation	17, 87, 18, 86, 19, 129	⊢
	: , :
12	instantiation	44, 20, 21	⊢
	: , : , :
13	instantiation	127, 112, 22	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.equality.equals_reversal
15	instantiation	23, 24, 25	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.equality.sub_left_side_into
17	theorem		⊢
	proveit.numbers.addition.add_nat_closure
18	instantiation	101	⊢
	: , : , :
19	instantiation	26, 27	⊢
	:
20	instantiation	28, 87, 29, 30, 31, 32	⊢
	: , : , : , :
21	instantiation	44, 33, 34	⊢
	: , : , :
22	instantiation	127, 117, 35	⊢
	: , : , :
23	theorem		⊢
	proveit.logic.equality.sub_right_side_into
24	instantiation	36, 37	⊢
	: , : , :
25	instantiation	44, 38, 39	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.negation.nat_closure
27	instantiation	40, 41, 42	⊢
	:
28	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
29	instantiation	101	⊢
	: , : , :
30	instantiation	101	⊢
	: , : , :
31	instantiation	43, 103, 92	⊢
	: , : , :
32	instantiation	44, 45, 46	⊢
	: , : , :
33	instantiation	47, 129, 86, 88, 103, 99	⊢
	: , : , : , : , : , : , :
34	instantiation	71, 86, 82, 129, 88, 72, 103, 99, 73*	⊢
	: , : , : , : , : , :
35	instantiation	127, 123, 48	⊢
	: , : , :
36	theorem		⊢
	proveit.core_expr_types.tuples.range_len
37	instantiation	127, 93, 49	⊢
	: , : , :
38	instantiation	58, 109	⊢
	: , : , :
39	instantiation	60, 50, 51, 52	⊢
	: , : , : , :
40	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
41	instantiation	53, 114, 124	⊢
	: , :
42	instantiation	54, 97, 113, 111, 55, 56*, 57*	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
44	axiom		⊢
	proveit.logic.equality.equals_transitivity
45	instantiation	58, 59	⊢
	: , : , :
46	instantiation	60, 61, 62, 63	⊢
	: , : , : , :
47	theorem		⊢
	proveit.numbers.addition.leftward_commutation
48	instantiation	127, 128, 82	⊢
	: , : , :
49	instantiation	64, 82, 86, 65, 88, 66, 67, 129, 68	⊢
	: , : , : , : , :
50	instantiation	81, 86, 82, 88, 70, 69, 99, 103, 84	⊢
	: , : , : , : , : , :
51	instantiation	85, 82, 129, 70, 99, 103	⊢
	: , : , : , :
52	instantiation	71, 129, 82, 86, 72, 88, 99, 103, 73*	⊢
	: , : , : , : , : , :
53	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
54	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
55	instantiation	74, 126	⊢
	:
56	instantiation	75, 103, 79	⊢
	: , :
57	instantiation	76, 99, 77	⊢
	: , :
58	axiom		⊢
	proveit.logic.equality.substitution
59	instantiation	78, 79, 103, 80*	⊢
	: , :
60	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
61	instantiation	81, 129, 82, 83, 84, 99, 90, 103	⊢
	: , : , : , : , : , :
62	instantiation	85, 86, 87, 88, 89, 99, 90, 103	⊢
	: , : , : , :
63	instantiation	91, 103, 99, 92	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
65	instantiation	100	⊢
	: , :
66	instantiation	127, 93, 94	⊢
	: , : , :
67	instantiation	115, 95, 96	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
69	instantiation	100	⊢
	: , :
70	instantiation	100	⊢
	: , :
71	theorem		⊢
	proveit.numbers.addition.association
72	instantiation	100	⊢
	: , :
73	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
74	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
75	theorem		⊢
	proveit.numbers.addition.commutation
76	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
77	instantiation	104	⊢
	:
78	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
79	instantiation	127, 112, 97	⊢
	: , : , :
80	instantiation	98, 99	⊢
	:
81	theorem		⊢
	proveit.numbers.addition.disassociation
82	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
83	instantiation	100	⊢
	: , :
84	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
85	theorem		⊢
	proveit.numbers.addition.elim_zero_any
86	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
87	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
88	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
89	instantiation	101	⊢
	: , : , :
90	instantiation	102, 103	⊢
	:
91	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
92	instantiation	104	⊢
	:
93	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
94	instantiation	105, 126, 106	⊢
	: , :
95	instantiation	121, 107	⊢
	: , :
96	instantiation	108, 109	⊢
	: , :
97	instantiation	127, 117, 110	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.negation.double_negation
99	instantiation	127, 112, 111	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
101	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
102	theorem		⊢
	proveit.numbers.negation.complex_closure
103	instantiation	127, 112, 113	⊢
	: , : , :
104	axiom		⊢
	proveit.logic.equality.equals_reflexivity
105	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
106	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
107	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
108	theorem		⊢
	proveit.logic.sets.enumeration.fold_singleton
109	theorem		⊢
	proveit.numbers.negation.negated_zero
110	instantiation	127, 123, 114	⊢
	: , : , :
111	instantiation	115, 116, 126	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
113	instantiation	127, 117, 118	⊢
	: , : , :
114	instantiation	119, 120	⊢
	:
115	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
116	instantiation	121, 122	⊢
	: , :
117	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
118	instantiation	127, 123, 124	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.negation.int_closure
120	instantiation	127, 125, 126	⊢
	: , : , :
121	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
123	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
124	instantiation	127, 128, 129	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
126	assumption		⊢
127	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
128	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
129	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements