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	21, 7, 6	⊢
	: , :
3	instantiation	21, 7, 75	⊢
	: , :
4	reference	58	⊢
5	instantiation	8, 9, 10	⊢
	: , :
6	instantiation	116, 112, 11	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
8	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
9	instantiation	12, 66, 13, 14, 15*, 16*	⊢
	: , : , :
10	instantiation	17, 18, 19	⊢
	: , : , :
11	instantiation	116, 114, 20	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
13	instantiation	21, 58, 77	⊢
	: , :
14	instantiation	22, 66, 58, 77, 23, 24	⊢
	: , : , :
15	instantiation	32, 25, 26, 27	⊢
	: , : , : , :
16	instantiation	80, 28, 29	⊢
	: , : , :
17	theorem		⊢
	proveit.logic.equality.sub_right_side_into
18	instantiation	30, 58, 77, 31, 38	⊢
	: , : , :
19	instantiation	32, 40, 33, 34	⊢
	: , : , : , :
20	instantiation	35, 94	⊢
	:
21	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
22	theorem		⊢
	proveit.numbers.ordering.less_add_right
23	instantiation	36, 66, 77, 67	⊢
	: , : , :
24	instantiation	37, 38	⊢
	: , :
25	instantiation	39, 48, 64, 40	⊢
	: , : , :
26	instantiation	59	⊢
	:
27	instantiation	52, 41	⊢
	: , :
28	instantiation	42, 43, 118, 102, 44, 45, 49, 48, 46	⊢
	: , : , : , : , : , :
29	instantiation	47, 48, 49, 50	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
31	instantiation	51, 66, 77, 67	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
33	instantiation	59	⊢
	:
34	instantiation	52, 53	⊢
	: , :
35	theorem		⊢
	proveit.numbers.negation.int_closure
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
37	theorem		⊢
	proveit.numbers.ordering.relax_less
38	instantiation	54, 96	⊢
	:
39	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
40	instantiation	55, 94, 115, 56*	⊢
	: , : , : , :
41	instantiation	60, 57	⊢
	:
42	theorem		⊢
	proveit.numbers.addition.disassociation
43	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
44	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
45	instantiation	97	⊢
	: , :
46	instantiation	116, 106, 66	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
48	instantiation	116, 106, 77	⊢
	: , : , :
49	instantiation	116, 106, 58	⊢
	: , : , :
50	instantiation	59	⊢
	:
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
52	theorem		⊢
	proveit.logic.equality.equals_reversal
53	instantiation	60, 64	⊢
	:
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
55	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
56	instantiation	80, 61, 62	⊢
	: , : , :
57	instantiation	63, 64	⊢
	:
58	instantiation	65, 66, 77, 67	⊢
	: , : , :
59	axiom		⊢
	proveit.logic.equality.equals_reflexivity
60	theorem		⊢
	proveit.numbers.addition.elim_zero_left
61	instantiation	88, 118, 68, 69, 70, 71	⊢
	: , : , : , :
62	instantiation	72, 73, 74	⊢
	:
63	theorem		⊢
	proveit.numbers.negation.complex_closure
64	instantiation	116, 106, 75	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
66	instantiation	76, 77	⊢
	:
67	instantiation	78, 79	⊢
	:
68	instantiation	97	⊢
	: , :
69	instantiation	97	⊢
	: , :
70	instantiation	80, 81, 82	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
72	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
73	instantiation	116, 106, 83	⊢
	: , : , :
74	instantiation	84, 85	⊢
	:
75	instantiation	116, 112, 86	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.negation.real_closure
77	instantiation	116, 112, 87	⊢
	: , : , :
78	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_in_interval
79	assumption		⊢
80	axiom		⊢
	proveit.logic.equality.equals_transitivity
81	instantiation	88, 118, 89, 90, 91, 92	⊢
	: , : , : , :
82	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
83	instantiation	116, 112, 93	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
85	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
86	instantiation	116, 114, 94	⊢
	: , : , :
87	instantiation	116, 95, 96	⊢
	: , : , :
88	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
89	instantiation	97	⊢
	: , :
90	instantiation	97	⊢
	: , :
91	instantiation	98, 100	⊢
	:
92	instantiation	99, 100	⊢
	:
93	instantiation	116, 114, 101	⊢
	: , : , :
94	instantiation	116, 117, 102	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
96	instantiation	103, 104, 105	⊢
	: , :
97	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
98	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
99	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
100	instantiation	116, 106, 107	⊢
	: , : , :
101	instantiation	116, 117, 108	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
103	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
104	instantiation	116, 110, 109	⊢
	: , : , :
105	instantiation	116, 110, 111	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
107	instantiation	116, 112, 113	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
109	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
110	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
111	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
113	instantiation	116, 114, 115	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
115	instantiation	116, 117, 118	⊢
	: , : , :
116	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
117	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
118	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements