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