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