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.numbers.number_sets.real_numbers.in_IntervalOO
2	reference	26	⊢
3	reference	86	⊢
4	instantiation	6, 26, 17, 15	,  ⊢
	: , : , :
5	instantiation	7, 8, 9	,  ⊢
	: , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
7	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
8	instantiation	10, 26, 17, 15	,  ⊢
	: , : , :
9	instantiation	11, 12, 13	,  ⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
11	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
12	instantiation	14, 26, 17, 15	,  ⊢
	: , : , :
13	instantiation	16, 17, 18, 55, 19, 20*, 21*	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
15	instantiation	22, 23, 24	,  ⊢
	:
16	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
17	instantiation	101, 86, 125, 103	⊢
	: , :
18	instantiation	60, 61, 26	⊢
	: , :
19	instantiation	25, 61, 26, 86, 27, 28	⊢
	: , : , :
20	instantiation	29, 30, 31, 32	⊢
	: , : , : , :
21	instantiation	91, 33, 34	⊢
	: , : , :
22	theorem		⊢
	proveit.physics.quantum.QPE._scaled_abs_delta_b_floor_diff_interval
23	assumption		⊢
24	assumption		⊢
25	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
27	instantiation	35, 100	⊢
	:
28	instantiation	36, 75	⊢
	:
29	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
30	instantiation	91, 37, 38	⊢
	: , : , :
31	instantiation	39	⊢
	:
32	instantiation	40, 54	⊢
	: , :
33	instantiation	69, 54	⊢
	: , : , :
34	instantiation	40, 41, 42*	⊢
	: , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
37	instantiation	91, 43, 44	⊢
	: , : , :
38	instantiation	45, 46	⊢
	:
39	axiom		⊢
	proveit.logic.equality.equals_reflexivity
40	theorem		⊢
	proveit.logic.equality.equals_reversal
41	instantiation	47, 48, 136, 129, 49, 50, 73, 72	⊢
	: , : , : , : , : , :
42	instantiation	91, 51, 52	⊢
	: , : , :
43	instantiation	69, 53	⊢
	: , : , :
44	instantiation	69, 54	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.addition.elim_zero_left
46	instantiation	134, 124, 55	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
48	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
49	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
50	instantiation	116	⊢
	: , :
51	instantiation	69, 56	⊢
	: , : , :
52	instantiation	117, 72	⊢
	:
53	instantiation	57, 73	⊢
	:
54	instantiation	58, 72, 119, 103, 59*	⊢
	: , :
55	instantiation	60, 61, 86	⊢
	: , :
56	instantiation	62, 123, 133, 63*	⊢
	: , : , : , :
57	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
58	theorem		⊢
	proveit.numbers.division.div_as_mult
59	instantiation	91, 64, 65	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
61	instantiation	134, 130, 66	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
63	instantiation	91, 67, 68	⊢
	: , : , :
64	instantiation	69, 70	⊢
	: , : , :
65	instantiation	71, 72, 73	⊢
	: , :
66	instantiation	134, 74, 75	⊢
	: , : , :
67	instantiation	106, 136, 76, 77, 78, 79	⊢
	: , : , : , :
68	instantiation	80, 81, 82	⊢
	:
69	axiom		⊢
	proveit.logic.equality.substitution
70	instantiation	83, 84, 104, 85*	⊢
	: , :
71	theorem		⊢
	proveit.numbers.multiplication.commutation
72	instantiation	134, 124, 86	⊢
	: , : , :
73	instantiation	134, 124, 87	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
75	instantiation	88, 89, 90	⊢
	: , :
76	instantiation	116	⊢
	: , :
77	instantiation	116	⊢
	: , :
78	instantiation	91, 92, 93	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
80	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
81	instantiation	134, 124, 94	⊢
	: , : , :
82	instantiation	115, 95	⊢
	:
83	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
84	instantiation	134, 96, 97	⊢
	: , : , :
85	instantiation	98, 119	⊢
	:
86	instantiation	134, 99, 100	⊢
	: , : , :
87	instantiation	101, 102, 125, 103	⊢
	: , :
88	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
89	instantiation	134, 105, 104	⊢
	: , : , :
90	instantiation	134, 105, 128	⊢
	: , : , :
91	axiom		⊢
	proveit.logic.equality.equals_transitivity
92	instantiation	106, 136, 107, 108, 109, 110	⊢
	: , : , : , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
94	instantiation	134, 130, 111	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
96	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
97	instantiation	134, 112, 113	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
100	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
101	theorem		⊢
	proveit.numbers.division.div_real_closure
102	instantiation	134, 130, 114	⊢
	: , : , :
103	instantiation	115, 128	⊢
	:
104	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
105	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
106	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
107	instantiation	116	⊢
	: , :
108	instantiation	116	⊢
	: , :
109	instantiation	117, 119	⊢
	:
110	instantiation	118, 119	⊢
	:
111	instantiation	134, 132, 120	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
113	instantiation	134, 121, 122	⊢
	: , : , :
114	instantiation	134, 132, 123	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
116	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
117	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
118	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
119	instantiation	134, 124, 125	⊢
	: , : , :
120	instantiation	134, 135, 126	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
122	instantiation	134, 127, 128	⊢
	: , : , :
123	instantiation	134, 135, 129	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
125	instantiation	134, 130, 131	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
127	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
128	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
129	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
130	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
131	instantiation	134, 132, 133	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
133	instantiation	134, 135, 136	⊢
	: , : , :
134	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
135	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
136	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements