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