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	,  ⊢
	: , :
1	theorem		⊢
	proveit.numbers.number_sets.real_numbers.not_int_if_not_int_in_interval
2	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
3	instantiation	28, 5, 6, 7, 8	⊢
	: , : , :
4	assumption		⊢
5	instantiation	52, 92, 85	⊢
	: , :
6	instantiation	52, 92, 93	⊢
	: , :
7	instantiation	9, 85, 93, 19	⊢
	: , : , :
8	instantiation	32, 10, 11	⊢
	: , :
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oo__is__real
10	instantiation	14, 12, 13	⊢
	: , : , :
11	instantiation	14, 15, 16	⊢
	: , : , :
12	instantiation	17, 85, 93, 19	⊢
	: , : , :
13	instantiation	20, 66	⊢
	:
14	theorem		⊢
	proveit.logic.equality.sub_left_side_into
15	instantiation	18, 85, 93, 19	⊢
	: , : , :
16	instantiation	20, 67	⊢
	:
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_lower_bound
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_upper_bound
19	instantiation	21, 22	⊢
	:
20	theorem		⊢
	proveit.numbers.addition.elim_zero_left
21	instantiation	23, 145, 24, 25, 26	⊢
	: , : , : , :
22	assumption		⊢
23	theorem		⊢
	proveit.logic.sets.enumeration.true_for_each_then_true_for_all
24	instantiation	123	⊢
	: , :
25	instantiation	28, 85, 93, 86, 27	⊢
	: , : , :
26	instantiation	28, 85, 93, 89, 29	⊢
	: , : , :
27	instantiation	32, 30, 31	⊢
	: , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOO
29	instantiation	32, 33, 34	⊢
	: , :
30	instantiation	39, 85, 92, 35, 36, 37*, 38*	⊢
	: , : , :
31	instantiation	82, 92, 93, 94	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
33	instantiation	39, 103, 40, 41, 42*, 43*	⊢
	: , : , :
34	instantiation	47, 44, 56	⊢
	: , : , :
35	instantiation	52, 86, 93	⊢
	: , :
36	instantiation	53, 92, 86, 93, 45, 46	⊢
	: , : , :
37	instantiation	47, 48, 49	⊢
	: , : , :
38	instantiation	106, 50, 51	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
40	instantiation	52, 89, 113	⊢
	: , :
41	instantiation	53, 103, 89, 113, 54, 84	⊢
	: , : , :
42	instantiation	55, 79, 67, 56	⊢
	: , : , :
43	instantiation	106, 57, 58	⊢
	: , : , :
44	instantiation	59, 89, 113, 60, 61	⊢
	: , : , :
45	instantiation	70, 92, 93, 94	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
47	theorem		⊢
	proveit.logic.equality.sub_right_side_into
48	instantiation	62, 66	⊢
	:
49	instantiation	63, 66, 64	⊢
	: , :
50	instantiation	73, 74, 145, 122, 75, 65, 68, 67, 66	⊢
	: , : , : , : , : , :
51	instantiation	78, 67, 68, 69	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
53	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
54	instantiation	70, 103, 113, 104	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
56	instantiation	71, 114, 142, 72*	⊢
	: , : , : , :
57	instantiation	73, 74, 145, 122, 75, 76, 80, 79, 77	⊢
	: , : , : , : , : , :
58	instantiation	78, 79, 80, 81	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.ordering.less_add_right
60	instantiation	82, 103, 113, 104	⊢
	: , : , :
61	instantiation	83, 84	⊢
	: , :
62	theorem		⊢
	proveit.numbers.addition.elim_zero_right
63	theorem		⊢
	proveit.numbers.addition.commutation
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
65	instantiation	123	⊢
	: , :
66	instantiation	143, 130, 85	⊢
	: , : , :
67	instantiation	143, 130, 93	⊢
	: , : , :
68	instantiation	143, 130, 86	⊢
	: , : , :
69	instantiation	90	⊢
	:
70	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
71	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
72	instantiation	106, 87, 88	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.addition.disassociation
74	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
75	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
76	instantiation	123	⊢
	: , :
77	instantiation	143, 130, 103	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
79	instantiation	143, 130, 113	⊢
	: , : , :
80	instantiation	143, 130, 89	⊢
	: , : , :
81	instantiation	90	⊢
	:
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
83	theorem		⊢
	proveit.numbers.ordering.relax_less
84	instantiation	91, 129	⊢
	:
85	instantiation	112, 93	⊢
	:
86	instantiation	102, 92, 93, 94	⊢
	: , : , :
87	instantiation	115, 145, 95, 96, 97, 98	⊢
	: , : , : , :
88	instantiation	99, 100, 101	⊢
	:
89	instantiation	102, 103, 113, 104	⊢
	: , : , :
90	axiom		⊢
	proveit.logic.equality.equals_reflexivity
91	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
93	instantiation	143, 136, 105	⊢
	: , : , :
94	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
95	instantiation	123	⊢
	: , :
96	instantiation	123	⊢
	: , :
97	instantiation	106, 107, 108	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
99	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
100	instantiation	143, 130, 109	⊢
	: , : , :
101	instantiation	110, 111	⊢
	:
102	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
103	instantiation	112, 113	⊢
	:
104	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
105	instantiation	143, 141, 114	⊢
	: , : , :
106	axiom		⊢
	proveit.logic.equality.equals_transitivity
107	instantiation	115, 145, 116, 117, 118, 119	⊢
	: , : , : , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
109	instantiation	143, 136, 120	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
111	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
112	theorem		⊢
	proveit.numbers.negation.real_closure
113	instantiation	143, 136, 121	⊢
	: , : , :
114	instantiation	143, 144, 122	⊢
	: , : , :
115	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
116	instantiation	123	⊢
	: , :
117	instantiation	123	⊢
	: , :
118	instantiation	124, 126	⊢
	:
119	instantiation	125, 126	⊢
	:
120	instantiation	143, 141, 127	⊢
	: , : , :
121	instantiation	143, 128, 129	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
123	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
124	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
125	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
126	instantiation	143, 130, 131	⊢
	: , : , :
127	instantiation	143, 144, 132	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
129	instantiation	133, 134, 135	⊢
	: , :
130	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
131	instantiation	143, 136, 137	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
133	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
134	instantiation	143, 139, 138	⊢
	: , : , :
135	instantiation	143, 139, 140	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
137	instantiation	143, 141, 142	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
139	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
140	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
141	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
142	instantiation	143, 144, 145	⊢
	: , : , :
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