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	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOO
2	instantiation	101, 94, 6	⊢
	: , : , :
3	reference	33	⊢
4	reference	50	⊢
5	instantiation	7, 8, 9	⊢
	: , :
6	instantiation	101, 99, 10	⊢
	: , : , :
7	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
8	instantiation	11, 61, 12, 13, 14*, 15*	⊢
	: , : , :
9	instantiation	16, 17, 25	⊢
	: , : , :
10	instantiation	18, 52	⊢
	:
11	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
12	instantiation	19, 50, 71	⊢
	: , :
13	instantiation	20, 61, 50, 71, 21, 22	⊢
	: , : , :
14	instantiation	23, 42, 24, 25	⊢
	: , : , :
15	instantiation	64, 26, 27	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.equality.sub_right_side_into
17	instantiation	28, 50, 71, 29, 32	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.negation.int_closure
19	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
20	theorem		⊢
	proveit.numbers.ordering.less_add_right
21	instantiation	30, 61, 71, 62	⊢
	: , : , :
22	instantiation	31, 32	⊢
	: , :
23	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
24	instantiation	101, 88, 33	⊢
	: , : , :
25	instantiation	34, 52, 100, 35*	⊢
	: , : , : , :
26	instantiation	36, 37, 103, 63, 38, 39, 43, 42, 40	⊢
	: , : , : , : , : , :
27	instantiation	41, 42, 43, 44	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
29	instantiation	45, 61, 71, 62	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
31	theorem		⊢
	proveit.numbers.ordering.relax_less
32	instantiation	46, 87	⊢
	:
33	instantiation	101, 94, 47	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
35	instantiation	64, 48, 49	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.disassociation
37	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
38	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
39	instantiation	81	⊢
	: , :
40	instantiation	101, 88, 61	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
42	instantiation	101, 88, 71	⊢
	: , : , :
43	instantiation	101, 88, 50	⊢
	: , : , :
44	instantiation	51	⊢
	:
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
47	instantiation	101, 99, 52	⊢
	: , : , :
48	instantiation	74, 103, 53, 54, 55, 56	⊢
	: , : , : , :
49	instantiation	57, 58, 59	⊢
	:
50	instantiation	60, 61, 71, 62	⊢
	: , : , :
51	axiom		⊢
	proveit.logic.equality.equals_reflexivity
52	instantiation	101, 102, 63	⊢
	: , : , :
53	instantiation	81	⊢
	: , :
54	instantiation	81	⊢
	: , :
55	instantiation	64, 65, 66	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
57	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
58	instantiation	101, 88, 67	⊢
	: , : , :
59	instantiation	68, 69	⊢
	:
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
61	instantiation	70, 71	⊢
	:
62	instantiation	72, 73	⊢
	:
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
64	axiom		⊢
	proveit.logic.equality.equals_transitivity
65	instantiation	74, 103, 75, 76, 77, 78	⊢
	: , : , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
67	instantiation	101, 94, 79	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
69	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
70	theorem		⊢
	proveit.numbers.negation.real_closure
71	instantiation	101, 94, 80	⊢
	: , : , :
72	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_in_interval
73	assumption		⊢
74	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
75	instantiation	81	⊢
	: , :
76	instantiation	81	⊢
	: , :
77	instantiation	82, 84	⊢
	:
78	instantiation	83, 84	⊢
	:
79	instantiation	101, 99, 85	⊢
	: , : , :
80	instantiation	101, 86, 87	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
82	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
83	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
84	instantiation	101, 88, 89	⊢
	: , : , :
85	instantiation	101, 102, 90	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
87	instantiation	91, 92, 93	⊢
	: , :
88	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
89	instantiation	101, 94, 95	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
91	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
92	instantiation	101, 97, 96	⊢
	: , : , :
93	instantiation	101, 97, 98	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
95	instantiation	101, 99, 100	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
97	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
98	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
99	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
100	instantiation	101, 102, 103	⊢
	: , : , :
101	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
102	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
103	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements