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