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	deduction	1	,  ⊢
1	instantiation	14, 2, 69	, ,  ⊢
	: , :
2	instantiation	3, 4, 5, 6	, ,  ⊢
	: , : , :
3	theorem		⊢
	proveit.logic.sets.unification.membership_folding
4	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
5	instantiation	102	⊢
	: , :
6	instantiation	25, 7, 8	, ,  ⊢
	: , :
7	instantiation	9, 127, 10, 120, 11	, ,  ⊢
	: , : , :
8	instantiation	12, 13	, ,  ⊢
	: , :
9	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
10	instantiation	138, 18	⊢
	:
11	instantiation	14, 15, 16	, ,  ⊢
	: , :
12	theorem		⊢
	proveit.logic.sets.membership.unfold_not_in_set
13	instantiation	17, 18, 136, 120, 19	, ,  ⊢
	: , : , :
14	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
15	instantiation	98, 127, 136, 124	⊢
	: , : , :
16	instantiation	20, 101, 115, 21, 22, 23*, 24*	, ,  ⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.integers.int_not_in_interval
18	instantiation	134, 121, 133	⊢
	: , :
19	instantiation	25, 26, 27	, ,  ⊢
	: , :
20	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
21	instantiation	47, 48, 29	, ,  ⊢
	: , : , :
22	instantiation	28, 29	, ,  ⊢
	:
23	instantiation	63, 30, 31	⊢
	: , : , :
24	instantiation	53, 32	,  ⊢
	: , :
25	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_left
26	instantiation	33, 108, 34	,  ⊢
	: , : , :
27	instantiation	35, 111, 36, 37	⊢
	: , :
28	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
29	instantiation	38, 39	, ,  ⊢
	:
30	instantiation	88, 137, 144, 93, 90, 94, 106, 96, 97	⊢
	: , : , : , : , : , :
31	instantiation	40, 106, 96, 41	⊢
	: , : , :
32	instantiation	75, 42, 43, 44	,  ⊢
	: , : , : , :
33	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
34	instantiation	45, 46	⊢
	:
35	theorem		⊢
	proveit.numbers.ordering.not_less_from_less_eq
36	instantiation	47, 48, 141	⊢
	: , : , :
37	instantiation	49, 127, 136, 124	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.negation.nat_pos_closure
39	instantiation	50, 51, 52	, ,  ⊢
	:
40	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
41	instantiation	85	⊢
	:
42	instantiation	86, 104, 106	⊢
	: , :
43	instantiation	85	⊢
	:
44	instantiation	53, 54	,  ⊢
	: , :
45	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
46	instantiation	55, 56, 57	⊢
	: , :
47	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
48	instantiation	58, 59	⊢
	: , :
49	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
50	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_is_int_neg
51	instantiation	134, 121, 120	,  ⊢
	: , :
52	instantiation	60, 111, 112, 103, 61, 62*	, ,  ⊢
	: , : , :
53	theorem		⊢
	proveit.logic.equality.equals_reversal
54	instantiation	63, 64, 65	,  ⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
56	instantiation	66, 121, 67	⊢
	:
57	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
58	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
60	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
61	instantiation	68, 69, 70	,  ⊢
	: , : , :
62	instantiation	71, 96, 72	⊢
	: , :
63	axiom		⊢
	proveit.logic.equality.equals_transitivity
64	instantiation	73, 74	,  ⊢
	: , : , :
65	instantiation	75, 76, 77, 78	,  ⊢
	: , : , : , :
66	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
67	instantiation	79, 80, 81	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.equality.sub_right_side_into
69	instantiation	82, 129	⊢
	: , :
70	instantiation	83, 124, 84*	,  ⊢
	:
71	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
72	instantiation	85	⊢
	:
73	axiom		⊢
	proveit.logic.equality.substitution
74	instantiation	86, 104, 96	,  ⊢
	: , :
75	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
76	instantiation	88, 93, 144, 137, 94, 89, 95, 91, 87	,  ⊢
	: , : , : , : , : , :
77	instantiation	88, 144, 93, 89, 90, 94, 95, 91, 96, 97	,  ⊢
	: , : , : , : , : , :
78	instantiation	92, 137, 93, 94, 95, 96, 97	,  ⊢
	: , : , : , : , : , : , : , :
79	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
80	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
81	instantiation	98, 133, 131, 126	⊢
	: , : , :
82	theorem		⊢
	proveit.logic.booleans.conjunction.right_from_and
83	theorem		⊢
	proveit.physics.quantum.QPE._modabs_in_full_domain_simp
84	instantiation	99, 100	⊢
	:
85	axiom		⊢
	proveit.logic.equality.equals_reflexivity
86	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
87	instantiation	142, 113, 101	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.addition.disassociation
89	instantiation	102	⊢
	: , :
90	instantiation	102	⊢
	: , :
91	instantiation	142, 113, 103	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
93	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
94	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
95	instantiation	105, 104	⊢
	:
96	instantiation	142, 113, 111	⊢
	: , : , :
97	instantiation	105, 106	⊢
	:
98	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
99	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
100	instantiation	107, 108	⊢
	: , :
101	instantiation	109, 111, 110	⊢
	: , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
103	instantiation	114, 111	⊢
	:
104	instantiation	142, 113, 112	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.negation.complex_closure
106	instantiation	142, 113, 115	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.ordering.relax_less
108	assumption		⊢
109	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
110	instantiation	114, 115	⊢
	:
111	instantiation	142, 118, 116	⊢
	: , : , :
112	instantiation	142, 118, 117	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
114	theorem		⊢
	proveit.numbers.negation.real_closure
115	instantiation	142, 118, 119	⊢
	: , : , :
116	instantiation	142, 122, 120	⊢
	: , : , :
117	instantiation	142, 122, 121	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
119	instantiation	142, 122, 133	⊢
	: , : , :
120	instantiation	142, 123, 124	⊢
	: , : , :
121	instantiation	142, 125, 126	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
123	instantiation	130, 127, 136	⊢
	: , :
124	instantiation	128, 129	⊢
	: , :
125	instantiation	130, 133, 131	⊢
	: , :
126	assumption		⊢
127	instantiation	134, 132, 133	⊢
	: , :
128	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
129	assumption		⊢
130	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
131	instantiation	134, 136, 135	⊢
	: , :
132	instantiation	138, 136	⊢
	:
133	instantiation	142, 143, 137	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
135	instantiation	138, 139	⊢
	:
136	instantiation	142, 140, 141	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
138	theorem		⊢
	proveit.numbers.negation.int_closure
139	instantiation	142, 143, 144	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
141	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
142	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
143	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
144	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements