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.equality.four_chain_transitivity
2	instantiation	5, 6, 7, 8, 9, 10, 11, 12*	⊢
	: , : , : , :
3	instantiation	59	⊢
	:
4	instantiation	13, 14	⊢
	: , :
5	theorem		⊢
	proveit.core_expr_types.tuples.general_len
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
7	instantiation	56	⊢
	: , :
8	instantiation	56	⊢
	: , :
9	instantiation	56	⊢
	: , :
10	instantiation	15, 87, 27	⊢
	: , : , :
11	instantiation	15, 16, 28	⊢
	: , : , :
12	instantiation	29, 17, 18	⊢
	: , : , :
13	theorem		⊢
	proveit.logic.equality.equals_reversal
14	instantiation	19, 20	⊢
	: , :
15	theorem		⊢
	proveit.logic.equality.sub_left_side_into
16	instantiation	21, 22, 23	⊢
	:
17	instantiation	24, 92, 25, 26, 27, 28	⊢
	: , : , : , :
18	instantiation	29, 30, 31	⊢
	: , : , :
19	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
20	instantiation	90, 32, 69	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
22	instantiation	33, 34, 35	⊢
	: , :
23	instantiation	36, 37	⊢
	: , :
24	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
25	instantiation	56	⊢
	: , :
26	instantiation	56	⊢
	: , :
27	instantiation	38, 63, 49	⊢
	: , : , :
28	instantiation	39, 87, 92, 43, 40, 45, 48, 64, 63, 41*	⊢
	: , : , : , : , : , :
29	axiom		⊢
	proveit.logic.equality.equals_transitivity
30	instantiation	42, 87, 92, 43, 44, 45, 63, 48, 46	⊢
	: , : , : , : , : , :
31	instantiation	47, 63, 48, 49	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
33	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
34	instantiation	90, 50, 69	⊢
	: , : , :
35	instantiation	90, 51, 81	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
37	instantiation	52, 69	⊢
	:
38	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
39	theorem		⊢
	proveit.numbers.addition.association
40	instantiation	56	⊢
	: , :
41	instantiation	53, 54, 55	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.addition.disassociation
43	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
44	instantiation	56	⊢
	: , :
45	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
46	instantiation	90, 78, 57	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
48	instantiation	90, 78, 58	⊢
	: , : , :
49	instantiation	59	⊢
	:
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
51	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
52	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
53	theorem		⊢
	proveit.logic.equality.sub_right_side_into
54	instantiation	60, 63, 72, 61	⊢
	: , : , :
55	instantiation	62, 63, 64	⊢
	: , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
57	instantiation	90, 65, 66	⊢
	: , : , :
58	instantiation	67, 68, 69	⊢
	: , : , :
59	axiom		⊢
	proveit.logic.equality.equals_reflexivity
60	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
61	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
62	theorem		⊢
	proveit.numbers.addition.commutation
63	instantiation	90, 78, 70	⊢
	: , : , :
64	instantiation	71, 72	⊢
	:
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
66	instantiation	90, 73, 74	⊢
	: , : , :
67	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
68	instantiation	75, 76	⊢
	: , :
69	assumption		⊢
70	instantiation	90, 83, 77	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.negation.complex_closure
72	instantiation	90, 78, 79	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
74	instantiation	90, 80, 81	⊢
	: , : , :
75	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
77	instantiation	90, 88, 82	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
79	instantiation	90, 83, 84	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
81	instantiation	85, 86	⊢
	:
82	instantiation	90, 91, 87	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
84	instantiation	90, 88, 89	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.negation.int_neg_closure
86	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
87	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
88	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
89	instantiation	90, 91, 92	⊢
	: , : , :
90	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
91	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
92	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements