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