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