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