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	⊢
	: , :
1	reference	28	⊢
2	instantiation	3, 25, 4, 5, 6	⊢
	: , : , : , :
3	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
4	instantiation	32, 7, 8, 9	⊢
	: , : , : , :
5	instantiation	10, 25	⊢
	: , :
6	instantiation	28, 11	⊢
	: , :
7	instantiation	58, 12, 13	⊢
	: , : , :
8	instantiation	69	⊢
	:
9	instantiation	28, 14	⊢
	: , :
10	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
11	instantiation	15, 102, 16, 17, 18	⊢
	: , : , : , : , : , :
12	instantiation	19, 20	⊢
	: , : , :
13	instantiation	21, 22, 23	⊢
	: , : , :
14	instantiation	24, 25	⊢
	: , :
15	theorem		⊢
	proveit.core_expr_types.tuples.shift_equivalence
16	instantiation	61, 26, 27	⊢
	:
17	instantiation	28, 29	⊢
	: , :
18	instantiation	69	⊢
	:
19	theorem		⊢
	proveit.core_expr_types.tuples.range_len
20	instantiation	105, 36, 30	⊢
	: , : , :
21	axiom		⊢
	proveit.logic.equality.equals_transitivity
22	instantiation	31, 82	⊢
	: , : , :
23	instantiation	32, 33, 34, 35	⊢
	: , : , : , :
24	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
25	instantiation	105, 36, 92	⊢
	: , : , :
26	instantiation	75, 37, 77	⊢
	: , :
27	instantiation	78, 38	⊢
	: , :
28	theorem		⊢
	proveit.logic.equality.equals_reversal
29	instantiation	39, 74, 73, 40	⊢
	: , : , :
30	instantiation	41, 51, 47, 42, 48, 43, 44, 107, 45	⊢
	: , : , : , : , :
31	axiom		⊢
	proveit.logic.equality.substitution
32	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
33	instantiation	46, 47, 51, 48, 52, 49, 55, 53, 74, 73	⊢
	: , : , : , : , : , :
34	instantiation	50, 51, 107, 52, 55, 53, 73	⊢
	: , : , : , :
35	instantiation	54, 73, 55, 56	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
37	instantiation	105, 89, 57	⊢
	: , : , :
38	instantiation	91, 57	⊢
	:
39	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
40	instantiation	58, 59, 60	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
42	instantiation	66	⊢
	: , :
43	instantiation	61, 62, 63	⊢
	:
44	instantiation	85, 64, 65	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
46	theorem		⊢
	proveit.numbers.addition.disassociation
47	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
48	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
49	instantiation	66	⊢
	: , :
50	theorem		⊢
	proveit.numbers.addition.elim_zero_any
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
52	instantiation	66	⊢
	: , :
53	instantiation	105, 87, 67	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
55	instantiation	105, 87, 68	⊢
	: , : , :
56	instantiation	69	⊢
	:
57	instantiation	70, 92, 104	⊢
	: , :
58	theorem		⊢
	proveit.logic.equality.sub_right_side_into
59	instantiation	71, 73	⊢
	:
60	instantiation	72, 73, 74	⊢
	: , :
61	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
62	instantiation	75, 76, 77	⊢
	: , :
63	instantiation	78, 79	⊢
	: , :
64	instantiation	95, 80	⊢
	: , :
65	instantiation	81, 82	⊢
	: , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
67	instantiation	105, 83, 84	⊢
	: , : , :
68	instantiation	85, 86, 92	⊢
	: , : , :
69	axiom		⊢
	proveit.logic.equality.equals_reflexivity
70	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
71	theorem		⊢
	proveit.numbers.addition.elim_zero_right
72	theorem		⊢
	proveit.numbers.addition.commutation
73	instantiation	105, 87, 88	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
75	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
76	instantiation	105, 89, 92	⊢
	: , : , :
77	instantiation	105, 90, 100	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
79	instantiation	91, 92	⊢
	:
80	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
81	theorem		⊢
	proveit.logic.sets.enumeration.fold_singleton
82	theorem		⊢
	proveit.numbers.negation.negated_zero
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
84	instantiation	105, 93, 94	⊢
	: , : , :
85	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
86	instantiation	95, 96	⊢
	: , :
87	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
88	instantiation	105, 97, 98	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
90	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
91	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
92	assumption		⊢
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
94	instantiation	105, 99, 100	⊢
	: , : , :
95	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
96	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
98	instantiation	105, 101, 102	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
100	instantiation	103, 104	⊢
	:
101	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
102	instantiation	105, 106, 107	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.negation.int_neg_closure
104	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
105	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
106	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
107	theorem		⊢
	proveit.numbers.numerals.decimals.nat1