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	2, 3, 4	,  ⊢
	: , :
2	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_right
3	instantiation	5, 9	⊢
	: , :
4	instantiation	6, 7, 8, 9	,  ⊢
	: , :
5	theorem		⊢
	proveit.logic.equality.unfold_not_equals
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.not_int_if_not_int_in_interval
7	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
8	instantiation	33, 10, 11, 12, 13	⊢
	: , : , :
9	assumption		⊢
10	instantiation	57, 97, 90	⊢
	: , :
11	instantiation	57, 97, 98	⊢
	: , :
12	instantiation	14, 90, 98, 24	⊢
	: , : , :
13	instantiation	37, 15, 16	⊢
	: , :
14	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oo__is__real
15	instantiation	19, 17, 18	⊢
	: , : , :
16	instantiation	19, 20, 21	⊢
	: , : , :
17	instantiation	22, 90, 98, 24	⊢
	: , : , :
18	instantiation	25, 71	⊢
	:
19	theorem		⊢
	proveit.logic.equality.sub_left_side_into
20	instantiation	23, 90, 98, 24	⊢
	: , : , :
21	instantiation	25, 72	⊢
	:
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_lower_bound
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_upper_bound
24	instantiation	26, 27	⊢
	:
25	theorem		⊢
	proveit.numbers.addition.elim_zero_left
26	instantiation	28, 150, 29, 30, 31	⊢
	: , : , : , :
27	assumption		⊢
28	theorem		⊢
	proveit.logic.sets.enumeration.true_for_each_then_true_for_all
29	instantiation	128	⊢
	: , :
30	instantiation	33, 90, 98, 91, 32	⊢
	: , : , :
31	instantiation	33, 90, 98, 94, 34	⊢
	: , : , :
32	instantiation	37, 35, 36	⊢
	: , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOO
34	instantiation	37, 38, 39	⊢
	: , :
35	instantiation	44, 90, 97, 40, 41, 42*, 43*	⊢
	: , : , :
36	instantiation	87, 97, 98, 99	⊢
	: , : , :
37	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
38	instantiation	44, 108, 45, 46, 47*, 48*	⊢
	: , : , :
39	instantiation	52, 49, 61	⊢
	: , : , :
40	instantiation	57, 91, 98	⊢
	: , :
41	instantiation	58, 97, 91, 98, 50, 51	⊢
	: , : , :
42	instantiation	52, 53, 54	⊢
	: , : , :
43	instantiation	111, 55, 56	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
45	instantiation	57, 94, 118	⊢
	: , :
46	instantiation	58, 108, 94, 118, 59, 89	⊢
	: , : , :
47	instantiation	60, 84, 72, 61	⊢
	: , : , :
48	instantiation	111, 62, 63	⊢
	: , : , :
49	instantiation	64, 94, 118, 65, 66	⊢
	: , : , :
50	instantiation	75, 97, 98, 99	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
52	theorem		⊢
	proveit.logic.equality.sub_right_side_into
53	instantiation	67, 71	⊢
	:
54	instantiation	68, 71, 69	⊢
	: , :
55	instantiation	78, 79, 150, 127, 80, 70, 73, 72, 71	⊢
	: , : , : , : , : , :
56	instantiation	83, 72, 73, 74	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
58	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
59	instantiation	75, 108, 118, 109	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
61	instantiation	76, 119, 147, 77*	⊢
	: , : , : , :
62	instantiation	78, 79, 150, 127, 80, 81, 85, 84, 82	⊢
	: , : , : , : , : , :
63	instantiation	83, 84, 85, 86	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.ordering.less_add_right
65	instantiation	87, 108, 118, 109	⊢
	: , : , :
66	instantiation	88, 89	⊢
	: , :
67	theorem		⊢
	proveit.numbers.addition.elim_zero_right
68	theorem		⊢
	proveit.numbers.addition.commutation
69	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
70	instantiation	128	⊢
	: , :
71	instantiation	148, 135, 90	⊢
	: , : , :
72	instantiation	148, 135, 98	⊢
	: , : , :
73	instantiation	148, 135, 91	⊢
	: , : , :
74	instantiation	95	⊢
	:
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
76	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
77	instantiation	111, 92, 93	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.addition.disassociation
79	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
80	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
81	instantiation	128	⊢
	: , :
82	instantiation	148, 135, 108	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
84	instantiation	148, 135, 118	⊢
	: , : , :
85	instantiation	148, 135, 94	⊢
	: , : , :
86	instantiation	95	⊢
	:
87	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
88	theorem		⊢
	proveit.numbers.ordering.relax_less
89	instantiation	96, 134	⊢
	:
90	instantiation	117, 98	⊢
	:
91	instantiation	107, 97, 98, 99	⊢
	: , : , :
92	instantiation	120, 150, 100, 101, 102, 103	⊢
	: , : , : , :
93	instantiation	104, 105, 106	⊢
	:
94	instantiation	107, 108, 118, 109	⊢
	: , : , :
95	axiom		⊢
	proveit.logic.equality.equals_reflexivity
96	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
98	instantiation	148, 141, 110	⊢
	: , : , :
99	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
100	instantiation	128	⊢
	: , :
101	instantiation	128	⊢
	: , :
102	instantiation	111, 112, 113	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
104	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
105	instantiation	148, 135, 114	⊢
	: , : , :
106	instantiation	115, 116	⊢
	:
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
108	instantiation	117, 118	⊢
	:
109	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
110	instantiation	148, 146, 119	⊢
	: , : , :
111	axiom		⊢
	proveit.logic.equality.equals_transitivity
112	instantiation	120, 150, 121, 122, 123, 124	⊢
	: , : , : , :
113	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
114	instantiation	148, 141, 125	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
116	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
117	theorem		⊢
	proveit.numbers.negation.real_closure
118	instantiation	148, 141, 126	⊢
	: , : , :
119	instantiation	148, 149, 127	⊢
	: , : , :
120	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
121	instantiation	128	⊢
	: , :
122	instantiation	128	⊢
	: , :
123	instantiation	129, 131	⊢
	:
124	instantiation	130, 131	⊢
	:
125	instantiation	148, 146, 132	⊢
	: , : , :
126	instantiation	148, 133, 134	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
128	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
129	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
130	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
131	instantiation	148, 135, 136	⊢
	: , : , :
132	instantiation	148, 149, 137	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
134	instantiation	138, 139, 140	⊢
	: , :
135	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
136	instantiation	148, 141, 142	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
138	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
139	instantiation	148, 144, 143	⊢
	: , : , :
140	instantiation	148, 144, 145	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
142	instantiation	148, 146, 147	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
144	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
145	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
146	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
147	instantiation	148, 149, 150	⊢
	: , : , :
148	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
149	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
150	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements