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