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	100	⊢
	: , :
4	instantiation	23, 5, 6	, ,  ⊢
	: , :
5	instantiation	7, 125, 8, 118, 9	, ,  ⊢
	: , : , :
6	instantiation	10, 11	, ,  ⊢
	: , :
7	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
8	instantiation	136, 16	⊢
	:
9	instantiation	12, 13, 14	, ,  ⊢
	: , :
10	theorem		⊢
	proveit.logic.sets.membership.unfold_not_in_set
11	instantiation	15, 16, 134, 118, 17	, ,  ⊢
	: , : , :
12	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
13	instantiation	96, 125, 134, 122	⊢
	: , : , :
14	instantiation	18, 99, 113, 19, 20, 21*, 22*	, ,  ⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.integers.int_not_in_interval
16	instantiation	132, 119, 131	⊢
	: , :
17	instantiation	23, 24, 25	, ,  ⊢
	: , :
18	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
19	instantiation	45, 46, 27	, ,  ⊢
	: , : , :
20	instantiation	26, 27	, ,  ⊢
	:
21	instantiation	61, 28, 29	⊢
	: , : , :
22	instantiation	51, 30	,  ⊢
	: , :
23	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_left
24	instantiation	31, 106, 32	,  ⊢
	: , : , :
25	instantiation	33, 109, 34, 35	⊢
	: , :
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
27	instantiation	36, 37	, ,  ⊢
	:
28	instantiation	86, 135, 142, 91, 88, 92, 104, 94, 95	⊢
	: , : , : , : , : , :
29	instantiation	38, 104, 94, 39	⊢
	: , : , :
30	instantiation	73, 40, 41, 42	,  ⊢
	: , : , : , :
31	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
32	instantiation	43, 44	⊢
	:
33	theorem		⊢
	proveit.numbers.ordering.not_less_from_less_eq
34	instantiation	45, 46, 139	⊢
	: , : , :
35	instantiation	47, 125, 134, 122	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.negation.nat_pos_closure
37	instantiation	48, 49, 50	, ,  ⊢
	:
38	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
39	instantiation	83	⊢
	:
40	instantiation	84, 102, 104	⊢
	: , :
41	instantiation	83	⊢
	:
42	instantiation	51, 52	,  ⊢
	: , :
43	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
44	instantiation	53, 54, 55	⊢
	: , :
45	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
46	instantiation	56, 57	⊢
	: , :
47	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
48	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_is_int_neg
49	instantiation	132, 119, 118	,  ⊢
	: , :
50	instantiation	58, 109, 110, 101, 59, 60*	, ,  ⊢
	: , : , :
51	theorem		⊢
	proveit.logic.equality.equals_reversal
52	instantiation	61, 62, 63	,  ⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
54	instantiation	64, 119, 65	⊢
	:
55	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
56	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
58	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
59	instantiation	66, 67, 68	,  ⊢
	: , : , :
60	instantiation	69, 94, 70	⊢
	: , :
61	axiom		⊢
	proveit.logic.equality.equals_transitivity
62	instantiation	71, 72	,  ⊢
	: , : , :
63	instantiation	73, 74, 75, 76	,  ⊢
	: , : , : , :
64	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
65	instantiation	77, 78, 79	⊢
	: , : , :
66	theorem		⊢
	proveit.logic.equality.sub_right_side_into
67	instantiation	80, 127	⊢
	: , :
68	instantiation	81, 122, 82*	,  ⊢
	:
69	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
70	instantiation	83	⊢
	:
71	axiom		⊢
	proveit.logic.equality.substitution
72	instantiation	84, 102, 94	,  ⊢
	: , :
73	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
74	instantiation	86, 91, 142, 135, 92, 87, 93, 89, 85	,  ⊢
	: , : , : , : , : , :
75	instantiation	86, 142, 91, 87, 88, 92, 93, 89, 94, 95	,  ⊢
	: , : , : , : , : , :
76	instantiation	90, 135, 91, 92, 93, 94, 95	,  ⊢
	: , : , : , : , : , : , : , :
77	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
78	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
79	instantiation	96, 131, 129, 124	⊢
	: , : , :
80	theorem		⊢
	proveit.logic.booleans.conjunction.right_from_and
81	theorem		⊢
	proveit.physics.quantum.QPE._modabs_in_full_domain_simp
82	instantiation	97, 98	⊢
	:
83	axiom		⊢
	proveit.logic.equality.equals_reflexivity
84	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
85	instantiation	140, 111, 99	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.addition.disassociation
87	instantiation	100	⊢
	: , :
88	instantiation	100	⊢
	: , :
89	instantiation	140, 111, 101	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
91	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
92	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
93	instantiation	103, 102	⊢
	:
94	instantiation	140, 111, 109	⊢
	: , : , :
95	instantiation	103, 104	⊢
	:
96	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
97	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
98	instantiation	105, 106	⊢
	: , :
99	instantiation	107, 109, 108	⊢
	: , :
100	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
101	instantiation	112, 109	⊢
	:
102	instantiation	140, 111, 110	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.negation.complex_closure
104	instantiation	140, 111, 113	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.ordering.relax_less
106	assumption		⊢
107	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
108	instantiation	112, 113	⊢
	:
109	instantiation	140, 116, 114	⊢
	: , : , :
110	instantiation	140, 116, 115	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
112	theorem		⊢
	proveit.numbers.negation.real_closure
113	instantiation	140, 116, 117	⊢
	: , : , :
114	instantiation	140, 120, 118	⊢
	: , : , :
115	instantiation	140, 120, 119	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
117	instantiation	140, 120, 131	⊢
	: , : , :
118	instantiation	140, 121, 122	⊢
	: , : , :
119	instantiation	140, 123, 124	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
121	instantiation	128, 125, 134	⊢
	: , :
122	instantiation	126, 127	⊢
	: , :
123	instantiation	128, 131, 129	⊢
	: , :
124	assumption		⊢
125	instantiation	132, 130, 131	⊢
	: , :
126	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
127	assumption		⊢
128	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
129	instantiation	132, 134, 133	⊢
	: , :
130	instantiation	136, 134	⊢
	:
131	instantiation	140, 141, 135	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
133	instantiation	136, 137	⊢
	:
134	instantiation	140, 138, 139	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
136	theorem		⊢
	proveit.numbers.negation.int_closure
137	instantiation	140, 141, 142	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
139	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
140	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
141	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
142	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements