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	47	⊢
2	instantiation	5, 6, 7*	⊢
	: , : , : , :
3	reference	44	⊢
4	instantiation	32, 8	⊢
	: , :
5	theorem		⊢
	proveit.core_expr_types.tuples.extended_range_len
6	instantiation	9, 10	⊢
	: , : , :
7	instantiation	39, 11, 12	⊢
	: , : , :
8	instantiation	13, 14	⊢
	: , :
9	theorem		⊢
	proveit.core_expr_types.tuples.range_len_is_nat
10	instantiation	71, 15, 16	⊢
	: , : , :
11	instantiation	45, 46	⊢
	: , : , :
12	instantiation	47, 17, 18, 19	⊢
	: , : , : , :
13	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
14	instantiation	102, 20, 95	⊢
	: , : , :
15	instantiation	21, 22	⊢
	:
16	instantiation	47, 23, 24, 25	⊢
	: , : , : , :
17	instantiation	55, 99, 104, 56, 57, 68, 80, 86	⊢
	: , : , : , : , : , :
18	instantiation	58, 62, 59, 64, 26, 68, 80, 86	⊢
	: , : , : , :
19	instantiation	27, 86, 68, 28	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
21	theorem		⊢
	proveit.numbers.negation.nat_closure
22	instantiation	29, 30, 31	⊢
	:
23	instantiation	52, 53, 79, 54*	⊢
	: , :
24	instantiation	51	⊢
	:
25	instantiation	32, 33	⊢
	: , :
26	instantiation	69	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
28	instantiation	51	⊢
	:
29	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
30	instantiation	34, 81, 96	⊢
	: , :
31	instantiation	35, 66, 84, 75, 36, 37*, 38*	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.equality.equals_reversal
33	instantiation	39, 40, 41	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
35	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
36	instantiation	42, 95	⊢
	:
37	instantiation	78, 79, 53	⊢
	: , :
38	instantiation	43, 68, 44	⊢
	: , :
39	axiom		⊢
	proveit.logic.equality.equals_transitivity
40	instantiation	45, 46	⊢
	: , : , :
41	instantiation	47, 48, 49, 50	⊢
	: , : , : , :
42	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
43	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
44	instantiation	51	⊢
	:
45	axiom		⊢
	proveit.logic.equality.substitution
46	instantiation	52, 53, 86, 54*	⊢
	: , :
47	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
48	instantiation	55, 99, 104, 56, 57, 68, 80, 79	⊢
	: , : , : , : , : , :
49	instantiation	58, 62, 59, 64, 60, 68, 80, 79	⊢
	: , : , : , :
50	instantiation	61, 99, 104, 62, 63, 64, 68, 80, 79, 65*	⊢
	: , : , : , : , : , :
51	axiom		⊢
	proveit.logic.equality.equals_reflexivity
52	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
53	instantiation	102, 92, 66	⊢
	: , : , :
54	instantiation	67, 68	⊢
	:
55	theorem		⊢
	proveit.numbers.addition.disassociation
56	instantiation	70	⊢
	: , :
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
58	theorem		⊢
	proveit.numbers.addition.elim_zero_any
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
60	instantiation	69	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.addition.association
62	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
63	instantiation	70	⊢
	: , :
64	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
65	instantiation	71, 72, 73	⊢
	: , : , :
66	instantiation	102, 97, 74	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.negation.double_negation
68	instantiation	102, 92, 75	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
70	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
71	theorem		⊢
	proveit.logic.equality.sub_right_side_into
72	instantiation	76, 79, 86, 77	⊢
	: , : , :
73	instantiation	78, 79, 80	⊢
	: , :
74	instantiation	102, 100, 81	⊢
	: , : , :
75	instantiation	82, 83, 95	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
77	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
78	theorem		⊢
	proveit.numbers.addition.commutation
79	instantiation	102, 92, 84	⊢
	: , : , :
80	instantiation	85, 86	⊢
	:
81	instantiation	87, 88	⊢
	:
82	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
83	instantiation	89, 90	⊢
	: , :
84	instantiation	102, 97, 91	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.negation.complex_closure
86	instantiation	102, 92, 93	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.negation.int_closure
88	instantiation	102, 94, 95	⊢
	: , : , :
89	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
91	instantiation	102, 100, 96	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
93	instantiation	102, 97, 98	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
95	assumption		⊢
96	instantiation	102, 103, 99	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
98	instantiation	102, 100, 101	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
100	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
101	instantiation	102, 103, 104	⊢
	: , : , :
102	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
103	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
104	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements