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	reference	15	⊢
2	instantiation	4, 5	, ,  ⊢
	: , :
3	instantiation	6, 14, 103, 79, 7	, ,  ⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.membership.unfold_not_in_set
5	instantiation	8, 92, 9, 79, 10	, ,  ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
7	instantiation	11, 12, 13	, ,  ⊢
	: , :
8	theorem		⊢
	proveit.numbers.number_sets.integers.int_not_in_interval
9	instantiation	105, 14	⊢
	:
10	instantiation	15, 16, 17	, ,  ⊢
	: , :
11	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
12	instantiation	18, 70, 43, 19, 20, 21*, 22*	, ,  ⊢
	: , : , :
13	instantiation	23, 92, 103, 87	⊢
	: , : , :
14	instantiation	101, 85, 100	⊢
	: , :
15	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_right
16	instantiation	24, 25, 60, 26	⊢
	: , :
17	instantiation	88, 27, 83	,  ⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
19	instantiation	28, 60, 29	,  ⊢
	: , :
20	instantiation	30, 31	, ,  ⊢
	:
21	instantiation	32, 33, 59	⊢
	: , :
22	instantiation	34, 35, 36	,  ⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
24	theorem		⊢
	proveit.numbers.ordering.not_less_from_less_eq
25	instantiation	109, 77, 37	⊢
	: , : , :
26	instantiation	95, 92, 103, 87	⊢
	: , : , :
27	instantiation	38, 39	⊢
	:
28	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
29	instantiation	40, 70	⊢
	:
30	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
31	instantiation	80, 41, 42	, ,  ⊢
	:
32	theorem		⊢
	proveit.numbers.addition.commutation
33	instantiation	109, 69, 43	⊢
	: , : , :
34	axiom		⊢
	proveit.logic.equality.equals_transitivity
35	instantiation	44, 45, 111, 104, 46, 47, 50, 48, 59	,  ⊢
	: , : , : , : , : , :
36	instantiation	49, 59, 50, 51	,  ⊢
	: , : , :
37	instantiation	109, 84, 92	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
39	instantiation	72, 52	⊢
	:
40	theorem		⊢
	proveit.numbers.negation.real_closure
41	instantiation	101, 79, 53	,  ⊢
	: , :
42	instantiation	54, 55	,  ⊢
	: , :
43	instantiation	109, 77, 56	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.addition.disassociation
45	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
46	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
47	instantiation	57	⊢
	: , :
48	instantiation	58, 59	⊢
	:
49	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
50	instantiation	109, 69, 60	⊢
	: , : , :
51	instantiation	61	⊢
	:
52	instantiation	62, 73, 63	⊢
	: , :
53	instantiation	109, 64, 65	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
55	instantiation	66, 67, 68	,  ⊢
	: , : , :
56	instantiation	109, 84, 100	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
58	theorem		⊢
	proveit.numbers.negation.complex_closure
59	instantiation	109, 69, 70	⊢
	: , : , :
60	instantiation	109, 77, 71	⊢
	: , : , :
61	axiom		⊢
	proveit.logic.equality.equals_reflexivity
62	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
63	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
64	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
65	instantiation	72, 73	⊢
	:
66	theorem		⊢
	proveit.logic.equality.sub_right_side_into
67	instantiation	74, 94	⊢
	: , :
68	instantiation	75, 87, 76*	,  ⊢
	:
69	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
70	instantiation	109, 77, 78	⊢
	: , : , :
71	instantiation	109, 84, 79	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.negation.int_neg_closure
73	instantiation	80, 85, 81	⊢
	:
74	theorem		⊢
	proveit.logic.booleans.conjunction.right_from_and
75	theorem		⊢
	proveit.physics.quantum.QPE._modabs_in_full_domain_simp
76	instantiation	82, 83	⊢
	:
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
78	instantiation	109, 84, 85	⊢
	: , : , :
79	instantiation	109, 86, 87	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
81	instantiation	88, 89, 90	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
83	assumption		⊢
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
85	instantiation	109, 91, 96	⊢
	: , : , :
86	instantiation	97, 92, 103	⊢
	: , :
87	instantiation	93, 94	⊢
	: , :
88	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
89	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
90	instantiation	95, 100, 98, 96	⊢
	: , : , :
91	instantiation	97, 100, 98	⊢
	: , :
92	instantiation	101, 99, 100	⊢
	: , :
93	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
94	assumption		⊢
95	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
96	assumption		⊢
97	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
98	instantiation	101, 103, 102	⊢
	: , :
99	instantiation	105, 103	⊢
	:
100	instantiation	109, 110, 104	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
102	instantiation	105, 106	⊢
	:
103	instantiation	109, 107, 108	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
105	theorem		⊢
	proveit.numbers.negation.int_closure
106	instantiation	109, 110, 111	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
108	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
109	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
110	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
111	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements