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