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	deduction	1	,  ⊢
1	instantiation	16, 2, 72	, ,  ⊢
	: , :
2	instantiation	3, 4, 5, 6	, ,  ⊢
	: , : , :
3	theorem		⊢
	proveit.logic.sets.unification.membership_folding
4	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
5	instantiation	62	⊢
	: , :
6	instantiation	20, 7, 8	, ,  ⊢
	: , :
7	instantiation	9, 10	, ,  ⊢
	: , :
8	instantiation	11, 19, 108, 84, 12	, ,  ⊢
	: , : , :
9	theorem		⊢
	proveit.logic.sets.membership.unfold_not_in_set
10	instantiation	13, 97, 14, 84, 15	, ,  ⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
12	instantiation	16, 17, 18	, ,  ⊢
	: , :
13	theorem		⊢
	proveit.numbers.number_sets.integers.int_not_in_interval
14	instantiation	110, 19	⊢
	:
15	instantiation	20, 21, 22	, ,  ⊢
	: , :
16	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
17	instantiation	23, 75, 48, 24, 25, 26*, 27*	, ,  ⊢
	: , : , :
18	instantiation	28, 97, 108, 92	⊢
	: , : , :
19	instantiation	106, 90, 105	⊢
	: , :
20	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_right
21	instantiation	29, 30, 65, 31	⊢
	: , :
22	instantiation	93, 32, 88	,  ⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
24	instantiation	33, 65, 34	,  ⊢
	: , :
25	instantiation	35, 36	, ,  ⊢
	:
26	instantiation	37, 38, 64	⊢
	: , :
27	instantiation	39, 40, 41	,  ⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
29	theorem		⊢
	proveit.numbers.ordering.not_less_from_less_eq
30	instantiation	114, 82, 42	⊢
	: , : , :
31	instantiation	100, 97, 108, 92	⊢
	: , : , :
32	instantiation	43, 44	⊢
	:
33	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
34	instantiation	45, 75	⊢
	:
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
36	instantiation	85, 46, 47	, ,  ⊢
	:
37	theorem		⊢
	proveit.numbers.addition.commutation
38	instantiation	114, 74, 48	⊢
	: , : , :
39	axiom		⊢
	proveit.logic.equality.equals_transitivity
40	instantiation	49, 50, 116, 109, 51, 52, 55, 53, 64	,  ⊢
	: , : , : , : , : , :
41	instantiation	54, 64, 55, 56	,  ⊢
	: , : , :
42	instantiation	114, 89, 97	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
44	instantiation	77, 57	⊢
	:
45	theorem		⊢
	proveit.numbers.negation.real_closure
46	instantiation	106, 84, 58	,  ⊢
	: , :
47	instantiation	59, 60	,  ⊢
	: , :
48	instantiation	114, 82, 61	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.addition.disassociation
50	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
51	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
52	instantiation	62	⊢
	: , :
53	instantiation	63, 64	⊢
	:
54	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
55	instantiation	114, 74, 65	⊢
	: , : , :
56	instantiation	66	⊢
	:
57	instantiation	67, 78, 68	⊢
	: , :
58	instantiation	114, 69, 70	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
60	instantiation	71, 72, 73	,  ⊢
	: , : , :
61	instantiation	114, 89, 105	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
63	theorem		⊢
	proveit.numbers.negation.complex_closure
64	instantiation	114, 74, 75	⊢
	: , : , :
65	instantiation	114, 82, 76	⊢
	: , : , :
66	axiom		⊢
	proveit.logic.equality.equals_reflexivity
67	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
68	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
69	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
70	instantiation	77, 78	⊢
	:
71	theorem		⊢
	proveit.logic.equality.sub_right_side_into
72	instantiation	79, 99	⊢
	: , :
73	instantiation	80, 92, 81*	,  ⊢
	:
74	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
75	instantiation	114, 82, 83	⊢
	: , : , :
76	instantiation	114, 89, 84	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.negation.int_neg_closure
78	instantiation	85, 90, 86	⊢
	:
79	theorem		⊢
	proveit.logic.booleans.conjunction.right_from_and
80	theorem		⊢
	proveit.physics.quantum.QPE._modabs_in_full_domain_simp
81	instantiation	87, 88	⊢
	:
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
83	instantiation	114, 89, 90	⊢
	: , : , :
84	instantiation	114, 91, 92	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
86	instantiation	93, 94, 95	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
88	assumption		⊢
89	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
90	instantiation	114, 96, 101	⊢
	: , : , :
91	instantiation	102, 97, 108	⊢
	: , :
92	instantiation	98, 99	⊢
	: , :
93	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
94	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
95	instantiation	100, 105, 103, 101	⊢
	: , : , :
96	instantiation	102, 105, 103	⊢
	: , :
97	instantiation	106, 104, 105	⊢
	: , :
98	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
99	assumption		⊢
100	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
101	assumption		⊢
102	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
103	instantiation	106, 108, 107	⊢
	: , :
104	instantiation	110, 108	⊢
	:
105	instantiation	114, 115, 109	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
107	instantiation	110, 111	⊢
	:
108	instantiation	114, 112, 113	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
110	theorem		⊢
	proveit.numbers.negation.int_closure
111	instantiation	114, 115, 116	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
113	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
114	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
115	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
116	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements