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