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	15	⊢
2	instantiation	4, 5, 6, 7	, ,  ⊢
	: , : , :
3	reference	70	⊢
4	theorem		⊢
	proveit.logic.sets.unification.membership_folding
5	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
6	instantiation	103	⊢
	: , :
7	instantiation	26, 8, 9	, ,  ⊢
	: , :
8	instantiation	10, 128, 11, 121, 12	, ,  ⊢
	: , : , :
9	instantiation	13, 14	, ,  ⊢
	: , :
10	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
11	instantiation	139, 19	⊢
	:
12	instantiation	15, 16, 17	, ,  ⊢
	: , :
13	theorem		⊢
	proveit.logic.sets.membership.unfold_not_in_set
14	instantiation	18, 19, 137, 121, 20	, ,  ⊢
	: , : , :
15	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
16	instantiation	99, 128, 137, 125	⊢
	: , : , :
17	instantiation	21, 102, 116, 22, 23, 24*, 25*	, ,  ⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.integers.int_not_in_interval
19	instantiation	135, 122, 134	⊢
	: , :
20	instantiation	26, 27, 28	, ,  ⊢
	: , :
21	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
22	instantiation	48, 49, 30	, ,  ⊢
	: , : , :
23	instantiation	29, 30	, ,  ⊢
	:
24	instantiation	64, 31, 32	⊢
	: , : , :
25	instantiation	54, 33	,  ⊢
	: , :
26	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_left
27	instantiation	34, 109, 35	,  ⊢
	: , : , :
28	instantiation	36, 112, 37, 38	⊢
	: , :
29	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
30	instantiation	39, 40	, ,  ⊢
	:
31	instantiation	89, 138, 145, 94, 91, 95, 107, 97, 98	⊢
	: , : , : , : , : , :
32	instantiation	41, 107, 97, 42	⊢
	: , : , :
33	instantiation	76, 43, 44, 45	,  ⊢
	: , : , : , :
34	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
35	instantiation	46, 47	⊢
	:
36	theorem		⊢
	proveit.numbers.ordering.not_less_from_less_eq
37	instantiation	48, 49, 142	⊢
	: , : , :
38	instantiation	50, 128, 137, 125	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.negation.nat_pos_closure
40	instantiation	51, 52, 53	, ,  ⊢
	:
41	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
42	instantiation	86	⊢
	:
43	instantiation	87, 105, 107	⊢
	: , :
44	instantiation	86	⊢
	:
45	instantiation	54, 55	,  ⊢
	: , :
46	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
47	instantiation	56, 57, 58	⊢
	: , :
48	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
49	instantiation	59, 60	⊢
	: , :
50	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
51	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_is_int_neg
52	instantiation	135, 122, 121	,  ⊢
	: , :
53	instantiation	61, 112, 113, 104, 62, 63*	, ,  ⊢
	: , : , :
54	theorem		⊢
	proveit.logic.equality.equals_reversal
55	instantiation	64, 65, 66	,  ⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
57	instantiation	67, 122, 68	⊢
	:
58	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
59	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
61	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
62	instantiation	69, 70, 71	,  ⊢
	: , : , :
63	instantiation	72, 97, 73	⊢
	: , :
64	axiom		⊢
	proveit.logic.equality.equals_transitivity
65	instantiation	74, 75	,  ⊢
	: , : , :
66	instantiation	76, 77, 78, 79	,  ⊢
	: , : , : , :
67	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
68	instantiation	80, 81, 82	⊢
	: , : , :
69	theorem		⊢
	proveit.logic.equality.sub_right_side_into
70	instantiation	83, 130	⊢
	: , :
71	instantiation	84, 125, 85*	,  ⊢
	:
72	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
73	instantiation	86	⊢
	:
74	axiom		⊢
	proveit.logic.equality.substitution
75	instantiation	87, 105, 97	,  ⊢
	: , :
76	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
77	instantiation	89, 94, 145, 138, 95, 90, 96, 92, 88	,  ⊢
	: , : , : , : , : , :
78	instantiation	89, 145, 94, 90, 91, 95, 96, 92, 97, 98	,  ⊢
	: , : , : , : , : , :
79	instantiation	93, 138, 94, 95, 96, 97, 98	,  ⊢
	: , : , : , : , : , : , : , :
80	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
81	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
82	instantiation	99, 134, 132, 127	⊢
	: , : , :
83	theorem		⊢
	proveit.logic.booleans.conjunction.right_from_and
84	theorem		⊢
	proveit.physics.quantum.QPE._modabs_in_full_domain_simp
85	instantiation	100, 101	⊢
	:
86	axiom		⊢
	proveit.logic.equality.equals_reflexivity
87	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
88	instantiation	143, 114, 102	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.addition.disassociation
90	instantiation	103	⊢
	: , :
91	instantiation	103	⊢
	: , :
92	instantiation	143, 114, 104	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
94	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
95	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
96	instantiation	106, 105	⊢
	:
97	instantiation	143, 114, 112	⊢
	: , : , :
98	instantiation	106, 107	⊢
	:
99	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
100	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
101	instantiation	108, 109	⊢
	: , :
102	instantiation	110, 112, 111	⊢
	: , :
103	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
104	instantiation	115, 112	⊢
	:
105	instantiation	143, 114, 113	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.negation.complex_closure
107	instantiation	143, 114, 116	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.ordering.relax_less
109	assumption		⊢
110	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
111	instantiation	115, 116	⊢
	:
112	instantiation	143, 119, 117	⊢
	: , : , :
113	instantiation	143, 119, 118	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
115	theorem		⊢
	proveit.numbers.negation.real_closure
116	instantiation	143, 119, 120	⊢
	: , : , :
117	instantiation	143, 123, 121	⊢
	: , : , :
118	instantiation	143, 123, 122	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
120	instantiation	143, 123, 134	⊢
	: , : , :
121	instantiation	143, 124, 125	⊢
	: , : , :
122	instantiation	143, 126, 127	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
124	instantiation	131, 128, 137	⊢
	: , :
125	instantiation	129, 130	⊢
	: , :
126	instantiation	131, 134, 132	⊢
	: , :
127	assumption		⊢
128	instantiation	135, 133, 134	⊢
	: , :
129	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
130	assumption		⊢
131	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
132	instantiation	135, 137, 136	⊢
	: , :
133	instantiation	139, 137	⊢
	:
134	instantiation	143, 144, 138	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
136	instantiation	139, 140	⊢
	:
137	instantiation	143, 141, 142	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
139	theorem		⊢
	proveit.numbers.negation.int_closure
140	instantiation	143, 144, 145	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
142	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
143	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
144	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
145	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements