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	, ,  ⊢
	: , :
1	reference	20	⊢
2	instantiation	4, 122, 5, 115, 6	, ,  ⊢
	: , : , :
3	instantiation	7, 8	, ,  ⊢
	: , :
4	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
5	instantiation	133, 13	⊢
	:
6	instantiation	9, 10, 11	, ,  ⊢
	: , :
7	theorem		⊢
	proveit.logic.sets.membership.unfold_not_in_set
8	instantiation	12, 13, 131, 115, 14	, ,  ⊢
	: , : , :
9	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
10	instantiation	93, 122, 131, 119	⊢
	: , : , :
11	instantiation	15, 96, 110, 16, 17, 18*, 19*	, ,  ⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.integers.int_not_in_interval
13	instantiation	129, 116, 128	⊢
	: , :
14	instantiation	20, 21, 22	, ,  ⊢
	: , :
15	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
16	instantiation	42, 43, 24	, ,  ⊢
	: , : , :
17	instantiation	23, 24	, ,  ⊢
	:
18	instantiation	58, 25, 26	⊢
	: , : , :
19	instantiation	48, 27	,  ⊢
	: , :
20	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_left
21	instantiation	28, 103, 29	,  ⊢
	: , : , :
22	instantiation	30, 106, 31, 32	⊢
	: , :
23	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
24	instantiation	33, 34	, ,  ⊢
	:
25	instantiation	83, 132, 139, 88, 85, 89, 101, 91, 92	⊢
	: , : , : , : , : , :
26	instantiation	35, 101, 91, 36	⊢
	: , : , :
27	instantiation	70, 37, 38, 39	,  ⊢
	: , : , : , :
28	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
29	instantiation	40, 41	⊢
	:
30	theorem		⊢
	proveit.numbers.ordering.not_less_from_less_eq
31	instantiation	42, 43, 136	⊢
	: , : , :
32	instantiation	44, 122, 131, 119	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.negation.nat_pos_closure
34	instantiation	45, 46, 47	, ,  ⊢
	:
35	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
36	instantiation	80	⊢
	:
37	instantiation	81, 99, 101	⊢
	: , :
38	instantiation	80	⊢
	:
39	instantiation	48, 49	,  ⊢
	: , :
40	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
41	instantiation	50, 51, 52	⊢
	: , :
42	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
43	instantiation	53, 54	⊢
	: , :
44	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
45	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_is_int_neg
46	instantiation	129, 116, 115	,  ⊢
	: , :
47	instantiation	55, 106, 107, 98, 56, 57*	, ,  ⊢
	: , : , :
48	theorem		⊢
	proveit.logic.equality.equals_reversal
49	instantiation	58, 59, 60	,  ⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
51	instantiation	61, 116, 62	⊢
	:
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
53	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
55	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
56	instantiation	63, 64, 65	,  ⊢
	: , : , :
57	instantiation	66, 91, 67	⊢
	: , :
58	axiom		⊢
	proveit.logic.equality.equals_transitivity
59	instantiation	68, 69	,  ⊢
	: , : , :
60	instantiation	70, 71, 72, 73	,  ⊢
	: , : , : , :
61	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
62	instantiation	74, 75, 76	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.equality.sub_right_side_into
64	instantiation	77, 124	⊢
	: , :
65	instantiation	78, 119, 79*	,  ⊢
	:
66	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
67	instantiation	80	⊢
	:
68	axiom		⊢
	proveit.logic.equality.substitution
69	instantiation	81, 99, 91	,  ⊢
	: , :
70	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
71	instantiation	83, 88, 139, 132, 89, 84, 90, 86, 82	,  ⊢
	: , : , : , : , : , :
72	instantiation	83, 139, 88, 84, 85, 89, 90, 86, 91, 92	,  ⊢
	: , : , : , : , : , :
73	instantiation	87, 132, 88, 89, 90, 91, 92	,  ⊢
	: , : , : , : , : , : , : , :
74	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
75	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
76	instantiation	93, 128, 126, 121	⊢
	: , : , :
77	theorem		⊢
	proveit.logic.booleans.conjunction.right_from_and
78	theorem		⊢
	proveit.physics.quantum.QPE._modabs_in_full_domain_simp
79	instantiation	94, 95	⊢
	:
80	axiom		⊢
	proveit.logic.equality.equals_reflexivity
81	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
82	instantiation	137, 108, 96	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.addition.disassociation
84	instantiation	97	⊢
	: , :
85	instantiation	97	⊢
	: , :
86	instantiation	137, 108, 98	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
88	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
89	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
90	instantiation	100, 99	⊢
	:
91	instantiation	137, 108, 106	⊢
	: , : , :
92	instantiation	100, 101	⊢
	:
93	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
94	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
95	instantiation	102, 103	⊢
	: , :
96	instantiation	104, 106, 105	⊢
	: , :
97	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
98	instantiation	109, 106	⊢
	:
99	instantiation	137, 108, 107	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.negation.complex_closure
101	instantiation	137, 108, 110	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.ordering.relax_less
103	assumption		⊢
104	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
105	instantiation	109, 110	⊢
	:
106	instantiation	137, 113, 111	⊢
	: , : , :
107	instantiation	137, 113, 112	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
109	theorem		⊢
	proveit.numbers.negation.real_closure
110	instantiation	137, 113, 114	⊢
	: , : , :
111	instantiation	137, 117, 115	⊢
	: , : , :
112	instantiation	137, 117, 116	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
114	instantiation	137, 117, 128	⊢
	: , : , :
115	instantiation	137, 118, 119	⊢
	: , : , :
116	instantiation	137, 120, 121	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
118	instantiation	125, 122, 131	⊢
	: , :
119	instantiation	123, 124	⊢
	: , :
120	instantiation	125, 128, 126	⊢
	: , :
121	assumption		⊢
122	instantiation	129, 127, 128	⊢
	: , :
123	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
124	assumption		⊢
125	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
126	instantiation	129, 131, 130	⊢
	: , :
127	instantiation	133, 131	⊢
	:
128	instantiation	137, 138, 132	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
130	instantiation	133, 134	⊢
	:
131	instantiation	137, 135, 136	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
133	theorem		⊢
	proveit.numbers.negation.int_closure
134	instantiation	137, 138, 139	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
136	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
137	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
138	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
139	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements