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