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	30	⊢
3	instantiation	42, 6, 95, 7	⊢
	: , : , : , :
4	instantiation	8, 30	⊢
	: , :
5	instantiation	9, 109, 10, 11, 12, 13*	⊢
	: , : , : , : , : , :
6	instantiation	14, 15, 16	⊢
	: , : , :
7	instantiation	21, 17	⊢
	: , :
8	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
9	theorem		⊢
	proveit.core_expr_types.tuples.shift_equivalence
10	instantiation	18, 19, 40	⊢
	: , :
11	instantiation	21, 20	⊢
	: , :
12	instantiation	21, 22	⊢
	: , :
13	instantiation	49, 23, 24	,  ⊢
	: , : , :
14	theorem		⊢
	proveit.logic.equality.sub_right_side_into
15	instantiation	25, 26	⊢
	: , : , :
16	instantiation	49, 27, 28	⊢
	: , : , :
17	instantiation	29, 30	⊢
	: , :
18	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
19	instantiation	116, 46, 31	⊢
	: , : , :
20	instantiation	49, 32, 33	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.equality.equals_reversal
22	instantiation	49, 34, 35	⊢
	: , : , :
23	instantiation	67, 68, 69, 113, 70, 36, 37, 92, 94	,  ⊢
	: , : , : , : , : , :
24	instantiation	65, 94, 37, 95	,  ⊢
	: , : , :
25	theorem		⊢
	proveit.core_expr_types.tuples.range_len
26	instantiation	38, 62, 39, 68, 40, 113	⊢
	: , :
27	instantiation	52, 41	⊢
	: , : , :
28	instantiation	42, 43, 44, 45	⊢
	: , : , : , :
29	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
30	instantiation	116, 46, 118	⊢
	: , : , :
31	instantiation	47, 113, 68, 70, 48	⊢
	: , : , : , : , :
32	instantiation	52, 58	⊢
	: , : , :
33	instantiation	49, 50, 51	⊢
	: , : , :
34	instantiation	52, 58	⊢
	: , : , :
35	instantiation	53, 94	⊢
	:
36	instantiation	80	⊢
	: , :
37	instantiation	116, 99, 54	,  ⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.addition.add_nat_closure
39	instantiation	78	⊢
	: , : , :
40	instantiation	55, 56	⊢
	:
41	instantiation	57, 92, 91, 58*	⊢
	: , :
42	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
43	instantiation	67, 113, 69, 59, 60, 94, 64, 91	⊢
	: , : , : , : , : , :
44	instantiation	61, 68, 62, 70, 63, 94, 64, 91	⊢
	: , : , : , :
45	instantiation	65, 91, 94, 66	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
47	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
48	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
49	axiom		⊢
	proveit.logic.equality.equals_transitivity
50	instantiation	67, 68, 69, 113, 70, 71, 92, 91, 94	⊢
	: , : , : , : , : , :
51	instantiation	72, 94, 91, 95	⊢
	: , : , :
52	axiom		⊢
	proveit.logic.equality.substitution
53	theorem		⊢
	proveit.numbers.addition.elim_zero_left
54	instantiation	116, 103, 73	,  ⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.negation.nat_closure
56	instantiation	74, 75, 76	⊢
	:
57	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
58	instantiation	77, 94	⊢
	:
59	instantiation	80	⊢
	: , :
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
61	theorem		⊢
	proveit.numbers.addition.elim_zero_any
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
63	instantiation	78	⊢
	: , : , :
64	instantiation	79, 91	⊢
	:
65	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
66	instantiation	101	⊢
	:
67	theorem		⊢
	proveit.numbers.addition.disassociation
68	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
70	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
71	instantiation	80	⊢
	: , :
72	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_31
73	instantiation	116, 108, 81	,  ⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
75	instantiation	82, 109, 107	⊢
	: , :
76	instantiation	83, 98, 97, 100, 84, 85*, 86*	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.negation.double_negation
78	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
79	theorem		⊢
	proveit.numbers.negation.complex_closure
80	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
81	instantiation	116, 87, 88	,  ⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
83	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
84	instantiation	89, 118	⊢
	:
85	instantiation	90, 91, 92	⊢
	: , :
86	instantiation	93, 94, 95	⊢
	: , :
87	instantiation	96, 107, 115	⊢
	: , :
88	assumption		⊢
89	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
90	theorem		⊢
	proveit.numbers.addition.commutation
91	instantiation	116, 99, 97	⊢
	: , : , :
92	instantiation	116, 99, 98	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
94	instantiation	116, 99, 100	⊢
	: , : , :
95	instantiation	101	⊢
	:
96	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
97	instantiation	116, 103, 102	⊢
	: , : , :
98	instantiation	116, 103, 104	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
100	instantiation	105, 106, 118	⊢
	: , : , :
101	axiom		⊢
	proveit.logic.equality.equals_reflexivity
102	instantiation	116, 108, 107	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
104	instantiation	116, 108, 109	⊢
	: , : , :
105	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
106	instantiation	110, 111	⊢
	: , :
107	instantiation	116, 112, 113	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
109	instantiation	114, 115	⊢
	:
110	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
111	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
112	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
113	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
114	theorem		⊢
	proveit.numbers.negation.int_closure
115	instantiation	116, 117, 118	⊢
	: , : , :
116	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
117	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
118	assumption		⊢
*equality replacement requirements