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