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_IntervalOC
2	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
3	instantiation	70, 45, 72, 73	⊢
	: , :
4	instantiation	6, 45, 17	⊢
	: , :
5	instantiation	7, 8, 9	,  ⊢
	: , :
6	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
7	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
8	instantiation	44, 10	,  ⊢
	:
9	instantiation	11, 12, 13	⊢
	: , : , :
10	instantiation	14, 52, 15	,  ⊢
	: , :
11	theorem		⊢
	proveit.logic.equality.sub_right_side_into
12	instantiation	16, 45, 17, 65, 18, 19, 20*	⊢
	: , : , :
13	instantiation	21, 22, 36, 23, 73, 24*	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
15	instantiation	25, 26	,  ⊢
	:
16	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
17	instantiation	89, 27, 28	⊢
	: , : , :
18	instantiation	29, 30, 31	⊢
	: , :
19	instantiation	42, 32	⊢
	: , :
20	instantiation	33, 36, 34	⊢
	: , :
21	theorem		⊢
	proveit.numbers.division.mult_frac_left
22	instantiation	89, 48, 71	⊢
	: , : , :
23	instantiation	89, 48, 72	⊢
	: , : , :
24	instantiation	35, 36	⊢
	:
25	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
26	instantiation	37, 40, 38	,  ⊢
	:
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
28	instantiation	39, 40	⊢
	:
29	theorem		⊢
	proveit.numbers.absolute_value.weak_upper_bound
30	instantiation	41, 58, 65, 59	⊢
	: , : , :
31	instantiation	42, 43	⊢
	: , :
32	instantiation	44, 52	⊢
	:
33	theorem		⊢
	proveit.numbers.multiplication.commutation
34	instantiation	89, 48, 65	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
36	instantiation	89, 48, 45	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
38	instantiation	46, 47	,  ⊢
	: , :
39	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
40	instantiation	89, 48, 49	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
42	theorem		⊢
	proveit.numbers.ordering.relax_less
43	instantiation	50, 58, 65, 59	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
45	instantiation	89, 51, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
47	instantiation	53, 54, 55, 56	,  ⊢
	: , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	instantiation	57, 58, 65, 59	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
53	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt
54	instantiation	60, 61, 88, 62	⊢
	: , : , : , : , :
55	instantiation	89, 63, 67	⊢
	: , : , :
56	assumption		⊢
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
58	instantiation	64, 65	⊢
	:
59	instantiation	66, 67	⊢
	:
60	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
61	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
62	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
63	instantiation	68, 69, 82	⊢
	: , :
64	theorem		⊢
	proveit.numbers.negation.real_closure
65	instantiation	70, 71, 72, 73	⊢
	: , :
66	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
67	assumption		⊢
68	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
69	instantiation	74, 75, 83	⊢
	: , :
70	theorem		⊢
	proveit.numbers.division.div_real_closure
71	instantiation	89, 77, 76	⊢
	: , : , :
72	instantiation	89, 77, 78	⊢
	: , : , :
73	instantiation	79, 80	⊢
	:
74	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
75	instantiation	81, 82	⊢
	:
76	instantiation	89, 84, 83	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
78	instantiation	89, 84, 85	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
80	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
81	theorem		⊢
	proveit.numbers.negation.int_closure
82	instantiation	89, 86, 87	⊢
	: , : , :
83	instantiation	89, 90, 88	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
85	instantiation	89, 90, 91	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
87	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
88	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
89	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
90	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
91	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements