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*	,  ⊢
	:
1	theorem		⊢
	proveit.trigonometry.sine_linear_bound_nonneg
2	instantiation	5, 6, 7	,  ⊢
	:
3	instantiation	8, 18, 19, 20	,  ⊢
	: , : , :
4	instantiation	35, 9, 10	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_real_is_real_nonneg
6	instantiation	11, 18, 19, 20	,  ⊢
	: , : , :
7	instantiation	12, 13	,  ⊢
	: , :
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
9	instantiation	28, 14	⊢
	: , : , :
10	instantiation	35, 15, 16	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
12	theorem		⊢
	proveit.numbers.ordering.relax_less
13	instantiation	17, 18, 19, 20	,  ⊢
	: , : , :
14	instantiation	21, 89, 92, 45, 22, 47, 49, 48, 50	⊢
	: , : , : , : , : , :
15	instantiation	35, 23, 24	⊢
	: , : , :
16	instantiation	25, 33	⊢
	:
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
19	instantiation	77, 56, 79, 80	⊢
	: , :
20	instantiation	26, 76, 27	,  ⊢
	:
21	theorem		⊢
	proveit.numbers.multiplication.disassociation
22	instantiation	55	⊢
	: , :
23	instantiation	28, 29	⊢
	: , : , :
24	instantiation	30, 31, 32, 33, 34*	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.division.frac_one_denom
26	theorem		⊢
	proveit.physics.quantum.QPE._scaled_abs_delta_b_floor_diff_interval
27	assumption		⊢
28	axiom		⊢
	proveit.logic.equality.substitution
29	instantiation	35, 36, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.division.frac_cancel_left
31	instantiation	90, 39, 38	⊢
	: , : , :
32	instantiation	90, 39, 40	⊢
	: , : , :
33	instantiation	90, 68, 41	⊢
	: , : , :
34	instantiation	42, 48	⊢
	:
35	axiom		⊢
	proveit.logic.equality.equals_transitivity
36	instantiation	43, 45, 89, 47, 49, 48, 50	⊢
	: , : , : , : , : , : , :
37	instantiation	44, 89, 92, 45, 46, 47, 48, 49, 50	⊢
	: , : , : , : , : , :
38	instantiation	90, 51, 61	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
40	instantiation	90, 52, 53	⊢
	: , : , :
41	instantiation	54, 79, 57	⊢
	: , :
42	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
43	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
44	theorem		⊢
	proveit.numbers.multiplication.association
45	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
46	instantiation	55	⊢
	: , :
47	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
48	instantiation	90, 68, 56	⊢
	: , : , :
49	instantiation	90, 68, 79	⊢
	: , : , :
50	instantiation	90, 68, 57	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
53	instantiation	90, 58, 59	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
55	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
56	instantiation	90, 60, 61	⊢
	: , : , :
57	instantiation	90, 62, 63	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
59	instantiation	90, 64, 65	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
63	instantiation	66, 67	⊢
	:
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
66	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
67	instantiation	90, 68, 69	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
69	instantiation	70, 71, 74, 72	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
71	instantiation	73, 74	⊢
	:
72	instantiation	75, 76	⊢
	:
73	theorem		⊢
	proveit.numbers.negation.real_closure
74	instantiation	77, 78, 79, 80	⊢
	: , :
75	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
76	assumption		⊢
77	theorem		⊢
	proveit.numbers.division.div_real_closure
78	instantiation	90, 82, 81	⊢
	: , : , :
79	instantiation	90, 82, 83	⊢
	: , : , :
80	instantiation	84, 85	⊢
	:
81	instantiation	90, 87, 86	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
83	instantiation	90, 87, 88	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
85	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
86	instantiation	90, 91, 89	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
88	instantiation	90, 91, 92	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
90	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
91	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
92	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements