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, 6, 7, 8, 9*	,  ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_factor_bound
2	reference	141	⊢
3	reference	86	⊢
4	reference	15	⊢
5	reference	88	⊢
6	reference	25	⊢
7	instantiation	139, 36, 10	⊢
	: , : , :
8	instantiation	11, 12, 13	,  ⊢
	: , : , :
9	instantiation	14, 141, 86, 15, 88, 90, 16	⊢
	: , : , : , :
10	instantiation	139, 48, 35	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
12	instantiation	17, 18	,  ⊢
	:
13	instantiation	19, 20, 21, 22*	,  ⊢
	:
14	theorem		⊢
	proveit.numbers.multiplication.mult_zero_any
15	instantiation	98	⊢
	: , :
16	instantiation	139, 117, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
18	instantiation	24, 25, 26	,  ⊢
	: , :
19	theorem		⊢
	proveit.trigonometry.sine_linear_bound_nonneg
20	instantiation	27, 28, 29	,  ⊢
	:
21	instantiation	30, 52, 53, 54	,  ⊢
	: , : , :
22	instantiation	74, 31, 32	⊢
	: , : , :
23	instantiation	33, 34, 35	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
25	instantiation	139, 36, 37	⊢
	: , : , :
26	instantiation	38, 39	,  ⊢
	:
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_real_is_real_nonneg
28	instantiation	40, 52, 53, 54	,  ⊢
	: , : , :
29	instantiation	41, 42	,  ⊢
	: , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
31	instantiation	63, 43	⊢
	: , : , :
32	instantiation	74, 44, 45	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
34	instantiation	46, 47	⊢
	: , :
35	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
37	instantiation	139, 48, 134	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
39	instantiation	49, 114, 50	,  ⊢
	:
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
41	theorem		⊢
	proveit.numbers.ordering.relax_less
42	instantiation	51, 52, 53, 54	,  ⊢
	: , : , :
43	instantiation	55, 138, 141, 86, 56, 88, 90, 89, 91	⊢
	: , : , : , : , : , :
44	instantiation	74, 57, 58	⊢
	: , : , :
45	instantiation	59, 68	⊢
	:
46	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
50	instantiation	60, 61	,  ⊢
	: , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
53	instantiation	126, 99, 128, 129	⊢
	: , :
54	instantiation	62, 125, 73	,  ⊢
	:
55	theorem		⊢
	proveit.numbers.multiplication.disassociation
56	instantiation	98	⊢
	: , :
57	instantiation	63, 64	⊢
	: , : , :
58	instantiation	65, 66, 67, 68, 69*	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.division.frac_one_denom
60	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
61	instantiation	70, 71, 72, 73	,  ⊢
	: , :
62	theorem		⊢
	proveit.physics.quantum.QPE._scaled_abs_delta_b_floor_diff_interval
63	axiom		⊢
	proveit.logic.equality.substitution
64	instantiation	74, 75, 76	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.division.frac_cancel_left
66	instantiation	139, 78, 77	⊢
	: , : , :
67	instantiation	139, 78, 79	⊢
	: , : , :
68	instantiation	139, 117, 80	⊢
	: , : , :
69	instantiation	81, 89	⊢
	:
70	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt
71	instantiation	82, 86, 138, 88	⊢
	: , : , : , : , :
72	instantiation	139, 83, 125	⊢
	: , : , :
73	assumption		⊢
74	axiom		⊢
	proveit.logic.equality.equals_transitivity
75	instantiation	84, 86, 138, 88, 90, 89, 91	⊢
	: , : , : , : , : , : , :
76	instantiation	85, 138, 141, 86, 87, 88, 89, 90, 91	⊢
	: , : , : , : , : , :
77	instantiation	139, 92, 106	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
79	instantiation	139, 93, 94	⊢
	: , : , :
80	instantiation	95, 128, 100	⊢
	: , :
81	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
82	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
83	instantiation	96, 97, 112	⊢
	: , :
84	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
85	theorem		⊢
	proveit.numbers.multiplication.association
86	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
87	instantiation	98	⊢
	: , :
88	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
89	instantiation	139, 117, 99	⊢
	: , : , :
90	instantiation	139, 117, 128	⊢
	: , : , :
91	instantiation	139, 117, 100	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
94	instantiation	139, 101, 102	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
96	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
97	instantiation	103, 104, 135	⊢
	: , :
98	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
99	instantiation	139, 105, 106	⊢
	: , : , :
100	instantiation	139, 107, 108	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
102	instantiation	139, 109, 110	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
104	instantiation	111, 112	⊢
	:
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
108	instantiation	113, 114	⊢
	:
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
110	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
111	theorem		⊢
	proveit.numbers.negation.int_closure
112	instantiation	139, 115, 116	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
114	instantiation	139, 117, 118	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
116	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
117	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
118	instantiation	119, 120, 123, 121	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
120	instantiation	122, 123	⊢
	:
121	instantiation	124, 125	⊢
	:
122	theorem		⊢
	proveit.numbers.negation.real_closure
123	instantiation	126, 127, 128, 129	⊢
	: , :
124	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
125	assumption		⊢
126	theorem		⊢
	proveit.numbers.division.div_real_closure
127	instantiation	139, 131, 130	⊢
	: , : , :
128	instantiation	139, 131, 132	⊢
	: , : , :
129	instantiation	133, 134	⊢
	:
130	instantiation	139, 136, 135	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
132	instantiation	139, 136, 137	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
134	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
135	instantiation	139, 140, 138	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
137	instantiation	139, 140, 141	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
139	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
140	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
141	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements