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, 5, 6	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.booleans.disjunction.singular_constructive_dilemma
2	reference	9	⊢
3	instantiation	7, 9	⊢
	:
4	instantiation	8, 9	⊢
	:
5	deduction	10	⊢
6	instantiation	11, 12, 13	⊢
	: , :
7	theorem		⊢
	proveit.logic.booleans.negation.closure
8	theorem		⊢
	proveit.logic.booleans.unfold_is_bool
9	instantiation	14	⊢
	: , :
10	instantiation	15, 32, 16	⊢
	: , :
11	theorem		⊢
	proveit.logic.equality.rhs_via_equality
12	deduction	17	⊢
13	instantiation	18, 19	⊢
	: , : , :
14	axiom		⊢
	proveit.logic.equality.equality_in_bool
15	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_left
16	instantiation	20, 21	⊢
	: , :
17	instantiation	22, 23, 24	,  ⊢
	: , :
18	axiom		⊢
	proveit.logic.equality.substitution
19	instantiation	25	⊢
	: , :
20	theorem		⊢
	proveit.logic.sets.membership.double_negated_membership
21	instantiation	171, 172, 26	⊢
	: , : , :
22	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_right
23	instantiation	27, 31	⊢
	: , :
24	instantiation	28, 29, 30, 31	,  ⊢
	: , :
25	axiom		⊢
	proveit.logic.equality.not_equals_def
26	instantiation	42, 102, 32	⊢
	: , : , :
27	theorem		⊢
	proveit.logic.equality.unfold_not_equals
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.not_int_if_not_int_in_interval
29	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
30	instantiation	56, 33, 34, 35, 36	⊢
	: , : , :
31	assumption		⊢
32	assumption		⊢
33	instantiation	80, 120, 113	⊢
	: , :
34	instantiation	80, 120, 121	⊢
	: , :
35	instantiation	37, 113, 121, 47	⊢
	: , : , :
36	instantiation	60, 38, 39	⊢
	: , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oo__is__real
38	instantiation	42, 40, 41	⊢
	: , : , :
39	instantiation	42, 43, 44	⊢
	: , : , :
40	instantiation	45, 113, 121, 47	⊢
	: , : , :
41	instantiation	48, 94	⊢
	:
42	theorem		⊢
	proveit.logic.equality.sub_left_side_into
43	instantiation	46, 113, 121, 47	⊢
	: , : , :
44	instantiation	48, 95	⊢
	:
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_lower_bound
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_upper_bound
47	instantiation	49, 50	⊢
	:
48	theorem		⊢
	proveit.numbers.addition.elim_zero_left
49	instantiation	51, 173, 52, 53, 54	⊢
	: , : , : , :
50	assumption		⊢
51	theorem		⊢
	proveit.logic.sets.enumeration.true_for_each_then_true_for_all
52	instantiation	151	⊢
	: , :
53	instantiation	56, 113, 121, 114, 55	⊢
	: , : , :
54	instantiation	56, 113, 121, 117, 57	⊢
	: , : , :
55	instantiation	60, 58, 59	⊢
	: , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOO
57	instantiation	60, 61, 62	⊢
	: , :
58	instantiation	67, 113, 120, 63, 64, 65*, 66*	⊢
	: , : , :
59	instantiation	110, 120, 121, 122	⊢
	: , : , :
60	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
61	instantiation	67, 131, 68, 69, 70*, 71*	⊢
	: , : , :
62	instantiation	75, 72, 84	⊢
	: , : , :
63	instantiation	80, 114, 121	⊢
	: , :
64	instantiation	81, 120, 114, 121, 73, 74	⊢
	: , : , :
65	instantiation	75, 76, 77	⊢
	: , : , :
66	instantiation	134, 78, 79	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
68	instantiation	80, 117, 141	⊢
	: , :
69	instantiation	81, 131, 117, 141, 82, 112	⊢
	: , : , :
70	instantiation	83, 107, 95, 84	⊢
	: , : , :
71	instantiation	134, 85, 86	⊢
	: , : , :
72	instantiation	87, 117, 141, 88, 89	⊢
	: , : , :
73	instantiation	98, 120, 121, 122	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
75	theorem		⊢
	proveit.logic.equality.sub_right_side_into
76	instantiation	90, 94	⊢
	:
77	instantiation	91, 94, 92	⊢
	: , :
78	instantiation	101, 102, 173, 150, 103, 93, 96, 95, 94	⊢
	: , : , : , : , : , :
79	instantiation	106, 95, 96, 97	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
81	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
82	instantiation	98, 131, 141, 132	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
84	instantiation	99, 142, 170, 100*	⊢
	: , : , : , :
85	instantiation	101, 102, 173, 150, 103, 104, 108, 107, 105	⊢
	: , : , : , : , : , :
86	instantiation	106, 107, 108, 109	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.ordering.less_add_right
88	instantiation	110, 131, 141, 132	⊢
	: , : , :
89	instantiation	111, 112	⊢
	: , :
90	theorem		⊢
	proveit.numbers.addition.elim_zero_right
91	theorem		⊢
	proveit.numbers.addition.commutation
92	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
93	instantiation	151	⊢
	: , :
94	instantiation	171, 158, 113	⊢
	: , : , :
95	instantiation	171, 158, 121	⊢
	: , : , :
96	instantiation	171, 158, 114	⊢
	: , : , :
97	instantiation	118	⊢
	:
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
99	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
100	instantiation	134, 115, 116	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.addition.disassociation
102	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
103	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
104	instantiation	151	⊢
	: , :
105	instantiation	171, 158, 131	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
107	instantiation	171, 158, 141	⊢
	: , : , :
108	instantiation	171, 158, 117	⊢
	: , : , :
109	instantiation	118	⊢
	:
110	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
111	theorem		⊢
	proveit.numbers.ordering.relax_less
112	instantiation	119, 157	⊢
	:
113	instantiation	140, 121	⊢
	:
114	instantiation	130, 120, 121, 122	⊢
	: , : , :
115	instantiation	143, 173, 123, 124, 125, 126	⊢
	: , : , : , :
116	instantiation	127, 128, 129	⊢
	:
117	instantiation	130, 131, 141, 132	⊢
	: , : , :
118	axiom		⊢
	proveit.logic.equality.equals_reflexivity
119	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
120	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
121	instantiation	171, 164, 133	⊢
	: , : , :
122	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
123	instantiation	151	⊢
	: , :
124	instantiation	151	⊢
	: , :
125	instantiation	134, 135, 136	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
127	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
128	instantiation	171, 158, 137	⊢
	: , : , :
129	instantiation	138, 139	⊢
	:
130	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
131	instantiation	140, 141	⊢
	:
132	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
133	instantiation	171, 169, 142	⊢
	: , : , :
134	axiom		⊢
	proveit.logic.equality.equals_transitivity
135	instantiation	143, 173, 144, 145, 146, 147	⊢
	: , : , : , :
136	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
137	instantiation	171, 164, 148	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
139	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
140	theorem		⊢
	proveit.numbers.negation.real_closure
141	instantiation	171, 164, 149	⊢
	: , : , :
142	instantiation	171, 172, 150	⊢
	: , : , :
143	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
144	instantiation	151	⊢
	: , :
145	instantiation	151	⊢
	: , :
146	instantiation	152, 154	⊢
	:
147	instantiation	153, 154	⊢
	:
148	instantiation	171, 169, 155	⊢
	: , : , :
149	instantiation	171, 156, 157	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
151	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
152	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
153	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
154	instantiation	171, 158, 159	⊢
	: , : , :
155	instantiation	171, 172, 160	⊢
	: , : , :
156	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
157	instantiation	161, 162, 163	⊢
	: , :
158	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
159	instantiation	171, 164, 165	⊢
	: , : , :
160	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
161	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
162	instantiation	171, 167, 166	⊢
	: , : , :
163	instantiation	171, 167, 168	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
165	instantiation	171, 169, 170	⊢
	: , : , :
166	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
167	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
168	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
169	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
170	instantiation	171, 172, 173	⊢
	: , : , :
171	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
172	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
173	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements