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	⊢
	: , : , : , :
1	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
2	reference	24	⊢
3	instantiation	31, 6, 7, 8	⊢
	: , : , : , :
4	instantiation	9, 24	⊢
	: , :
5	instantiation	27, 10	⊢
	: , :
6	instantiation	57, 11, 12	⊢
	: , : , :
7	instantiation	68	⊢
	:
8	instantiation	27, 13	⊢
	: , :
9	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
10	instantiation	14, 101, 15, 16, 17	⊢
	: , : , : , : , : , :
11	instantiation	18, 19	⊢
	: , : , :
12	instantiation	20, 21, 22	⊢
	: , : , :
13	instantiation	23, 24	⊢
	: , :
14	theorem		⊢
	proveit.core_expr_types.tuples.shift_equivalence
15	instantiation	60, 25, 26	⊢
	:
16	instantiation	27, 28	⊢
	: , :
17	instantiation	68	⊢
	:
18	theorem		⊢
	proveit.core_expr_types.tuples.range_len
19	instantiation	104, 35, 29	⊢
	: , : , :
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	30, 81	⊢
	: , : , :
22	instantiation	31, 32, 33, 34	⊢
	: , : , : , :
23	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
24	instantiation	104, 35, 91	⊢
	: , : , :
25	instantiation	74, 36, 76	⊢
	: , :
26	instantiation	77, 37	⊢
	: , :
27	theorem		⊢
	proveit.logic.equality.equals_reversal
28	instantiation	38, 73, 72, 39	⊢
	: , : , :
29	instantiation	40, 50, 46, 41, 47, 42, 43, 106, 44	⊢
	: , : , : , : , :
30	axiom		⊢
	proveit.logic.equality.substitution
31	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
32	instantiation	45, 46, 50, 47, 51, 48, 54, 52, 73, 72	⊢
	: , : , : , : , : , :
33	instantiation	49, 50, 106, 51, 54, 52, 72	⊢
	: , : , : , :
34	instantiation	53, 72, 54, 55	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
36	instantiation	104, 88, 56	⊢
	: , : , :
37	instantiation	90, 56	⊢
	:
38	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
39	instantiation	57, 58, 59	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
41	instantiation	65	⊢
	: , :
42	instantiation	60, 61, 62	⊢
	:
43	instantiation	84, 63, 64	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
45	theorem		⊢
	proveit.numbers.addition.disassociation
46	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
47	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
48	instantiation	65	⊢
	: , :
49	theorem		⊢
	proveit.numbers.addition.elim_zero_any
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
51	instantiation	65	⊢
	: , :
52	instantiation	104, 86, 66	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
54	instantiation	104, 86, 67	⊢
	: , : , :
55	instantiation	68	⊢
	:
56	instantiation	69, 91, 103	⊢
	: , :
57	theorem		⊢
	proveit.logic.equality.sub_right_side_into
58	instantiation	70, 72	⊢
	:
59	instantiation	71, 72, 73	⊢
	: , :
60	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
61	instantiation	74, 75, 76	⊢
	: , :
62	instantiation	77, 78	⊢
	: , :
63	instantiation	94, 79	⊢
	: , :
64	instantiation	80, 81	⊢
	: , :
65	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
66	instantiation	104, 82, 83	⊢
	: , : , :
67	instantiation	84, 85, 91	⊢
	: , : , :
68	axiom		⊢
	proveit.logic.equality.equals_reflexivity
69	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
70	theorem		⊢
	proveit.numbers.addition.elim_zero_right
71	theorem		⊢
	proveit.numbers.addition.commutation
72	instantiation	104, 86, 87	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
74	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
75	instantiation	104, 88, 91	⊢
	: , : , :
76	instantiation	104, 89, 99	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
78	instantiation	90, 91	⊢
	:
79	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
80	theorem		⊢
	proveit.logic.sets.enumeration.fold_singleton
81	theorem		⊢
	proveit.numbers.negation.negated_zero
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
83	instantiation	104, 92, 93	⊢
	: , : , :
84	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
85	instantiation	94, 95	⊢
	: , :
86	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
87	instantiation	104, 96, 97	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
89	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
90	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
91	assumption		⊢
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
93	instantiation	104, 98, 99	⊢
	: , : , :
94	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
96	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
97	instantiation	104, 100, 101	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
99	instantiation	102, 103	⊢
	:
100	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
101	instantiation	104, 105, 106	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.negation.int_neg_closure
103	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
104	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
105	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
106	theorem		⊢
	proveit.numbers.numerals.decimals.nat1