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.integers.in_interval
2	instantiation	82, 66, 81	⊢
	: , :
3	reference	84	⊢
4	reference	60	⊢
5	instantiation	6, 7, 8	, ,  ⊢
	: , :
6	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
7	instantiation	9, 51, 27, 10, 11, 12*, 13*	, ,  ⊢
	: , : , :
8	instantiation	14, 73, 84, 68	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
10	instantiation	15, 43, 16	,  ⊢
	: , :
11	instantiation	17, 18	, ,  ⊢
	:
12	instantiation	19, 20, 42	⊢
	: , :
13	instantiation	21, 22, 23	,  ⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
15	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
16	instantiation	24, 51	⊢
	:
17	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
18	instantiation	61, 25, 26	, ,  ⊢
	:
19	theorem		⊢
	proveit.numbers.addition.commutation
20	instantiation	90, 50, 27	⊢
	: , : , :
21	axiom		⊢
	proveit.logic.equality.equals_transitivity
22	instantiation	28, 29, 92, 85, 30, 31, 34, 32, 42	,  ⊢
	: , : , : , : , : , :
23	instantiation	33, 42, 34, 35	,  ⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.negation.real_closure
25	instantiation	82, 60, 36	,  ⊢
	: , :
26	instantiation	37, 38	,  ⊢
	: , :
27	instantiation	90, 58, 39	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.disassociation
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
31	instantiation	40	⊢
	: , :
32	instantiation	41, 42	⊢
	:
33	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
34	instantiation	90, 50, 43	⊢
	: , : , :
35	instantiation	44	⊢
	:
36	instantiation	90, 45, 46	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
38	instantiation	47, 48, 49	,  ⊢
	: , : , :
39	instantiation	90, 65, 81	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
41	theorem		⊢
	proveit.numbers.negation.complex_closure
42	instantiation	90, 50, 51	⊢
	: , : , :
43	instantiation	90, 58, 52	⊢
	: , : , :
44	axiom		⊢
	proveit.logic.equality.equals_reflexivity
45	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
46	instantiation	53, 54	⊢
	:
47	theorem		⊢
	proveit.logic.equality.sub_right_side_into
48	instantiation	55, 75	⊢
	: , :
49	instantiation	56, 68, 57*	,  ⊢
	:
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
51	instantiation	90, 58, 59	⊢
	: , : , :
52	instantiation	90, 65, 60	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.negation.int_neg_closure
54	instantiation	61, 66, 62	⊢
	:
55	theorem		⊢
	proveit.logic.booleans.conjunction.right_from_and
56	theorem		⊢
	proveit.physics.quantum.QPE._modabs_in_full_domain_simp
57	instantiation	63, 64	⊢
	:
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
59	instantiation	90, 65, 66	⊢
	: , : , :
60	instantiation	90, 67, 68	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
62	instantiation	69, 70, 71	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
64	assumption		⊢
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
66	instantiation	90, 72, 77	⊢
	: , : , :
67	instantiation	78, 73, 84	⊢
	: , :
68	instantiation	74, 75	⊢
	: , :
69	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
70	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
71	instantiation	76, 81, 79, 77	⊢
	: , : , :
72	instantiation	78, 81, 79	⊢
	: , :
73	instantiation	82, 80, 81	⊢
	: , :
74	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
75	assumption		⊢
76	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
77	assumption		⊢
78	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
79	instantiation	82, 84, 83	⊢
	: , :
80	instantiation	86, 84	⊢
	:
81	instantiation	90, 91, 85	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
83	instantiation	86, 87	⊢
	:
84	instantiation	90, 88, 89	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
86	theorem		⊢
	proveit.numbers.negation.int_closure
87	instantiation	90, 91, 92	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
89	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
90	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
91	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
92	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements