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	reference	40	⊢
3	reference	47	⊢
4	reference	42	⊢
5	instantiation	6, 7, 8	⊢
	: , :
6	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
7	instantiation	9, 40, 46, 10, 11, 12*, 13*	⊢
	: , : , :
8	instantiation	14, 46, 47, 48	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
10	instantiation	15, 42, 47	⊢
	: , :
11	instantiation	16, 46, 42, 47, 17, 18	⊢
	: , : , :
12	instantiation	19, 20, 21	⊢
	: , : , :
13	instantiation	22, 23, 24	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
15	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
16	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
17	instantiation	25, 46, 47, 48	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
19	theorem		⊢
	proveit.logic.equality.sub_right_side_into
20	instantiation	26, 34	⊢
	:
21	instantiation	27, 34, 28	⊢
	: , :
22	axiom		⊢
	proveit.logic.equality.equals_transitivity
23	instantiation	29, 30, 31, 55, 32, 33, 37, 36, 34	⊢
	: , : , : , : , : , :
24	instantiation	35, 36, 37, 38	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
26	theorem		⊢
	proveit.numbers.addition.elim_zero_right
27	theorem		⊢
	proveit.numbers.addition.commutation
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
29	theorem		⊢
	proveit.numbers.addition.disassociation
30	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
32	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
33	instantiation	39	⊢
	: , :
34	instantiation	53, 41, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
36	instantiation	53, 41, 47	⊢
	: , : , :
37	instantiation	53, 41, 42	⊢
	: , : , :
38	instantiation	43	⊢
	:
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	instantiation	44, 47	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	instantiation	45, 46, 47, 48	⊢
	: , : , :
43	axiom		⊢
	proveit.logic.equality.equals_reflexivity
44	theorem		⊢
	proveit.numbers.negation.real_closure
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
47	instantiation	53, 49, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	53, 51, 52	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	instantiation	53, 54, 55	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements