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.weak_bound_via_factor_bound
2	reference	122	⊢
3	reference	75	⊢
4	reference	27	⊢
5	reference	77	⊢
6	instantiation	120, 11, 10	⊢
	: , : , :
7	instantiation	120, 11, 12	⊢
	: , : , :
8	instantiation	13, 14, 15, 16*	,  ⊢
	:
9	instantiation	63, 17, 18	⊢
	: , : , :
10	instantiation	120, 19, 122	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
12	instantiation	120, 19, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.trigonometry.sine_linear_bound_nonneg
14	instantiation	21, 22, 23	,  ⊢
	:
15	instantiation	24, 42, 43, 44	,  ⊢
	: , : , :
16	instantiation	63, 25, 26	⊢
	: , : , :
17	instantiation	45, 122, 75, 27, 76, 77, 79, 39, 80	⊢
	: , : , : , : , : , :
18	instantiation	63, 28, 29	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
20	instantiation	120, 30, 62	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_real_is_real_nonneg
22	instantiation	31, 42, 43, 44	,  ⊢
	: , : , :
23	instantiation	32, 33	,  ⊢
	: , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
25	instantiation	53, 34	⊢
	: , : , :
26	instantiation	63, 35, 36	⊢
	: , : , :
27	instantiation	85	⊢
	: , :
28	instantiation	73, 119, 79, 39, 80	⊢
	: , : , : , : , : , : , :
29	instantiation	74, 75, 122, 77, 37, 38, 79, 39, 80, 40*	⊢
	: , : , : , : , : , :
30	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
32	theorem		⊢
	proveit.numbers.ordering.relax_less
33	instantiation	41, 42, 43, 44	,  ⊢
	: , : , :
34	instantiation	45, 119, 122, 75, 46, 77, 79, 78, 80	⊢
	: , : , : , : , : , :
35	instantiation	63, 47, 48	⊢
	: , : , :
36	instantiation	49, 58	⊢
	:
37	instantiation	85	⊢
	: , :
38	instantiation	85	⊢
	: , :
39	instantiation	120, 98, 50	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
43	instantiation	107, 86, 109, 110	⊢
	: , :
44	instantiation	51, 106, 52	,  ⊢
	:
45	theorem		⊢
	proveit.numbers.multiplication.disassociation
46	instantiation	85	⊢
	: , :
47	instantiation	53, 54	⊢
	: , : , :
48	instantiation	55, 56, 57, 58, 59*	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.division.frac_one_denom
50	instantiation	60, 61, 62	⊢
	: , : , :
51	theorem		⊢
	proveit.physics.quantum.QPE._scaled_abs_delta_b_floor_diff_interval
52	assumption		⊢
53	axiom		⊢
	proveit.logic.equality.substitution
54	instantiation	63, 64, 65	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.division.frac_cancel_left
56	instantiation	120, 67, 66	⊢
	: , : , :
57	instantiation	120, 67, 68	⊢
	: , : , :
58	instantiation	120, 98, 69	⊢
	: , : , :
59	instantiation	70, 78	⊢
	:
60	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
61	instantiation	71, 72	⊢
	: , :
62	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
63	axiom		⊢
	proveit.logic.equality.equals_transitivity
64	instantiation	73, 75, 119, 77, 79, 78, 80	⊢
	: , : , : , : , : , : , :
65	instantiation	74, 119, 122, 75, 76, 77, 78, 79, 80	⊢
	: , : , : , : , : , :
66	instantiation	120, 81, 91	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
68	instantiation	120, 82, 83	⊢
	: , : , :
69	instantiation	84, 109, 87	⊢
	: , :
70	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
71	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
73	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
74	theorem		⊢
	proveit.numbers.multiplication.association
75	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
76	instantiation	85	⊢
	: , :
77	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
78	instantiation	120, 98, 86	⊢
	: , : , :
79	instantiation	120, 98, 109	⊢
	: , : , :
80	instantiation	120, 98, 87	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
83	instantiation	120, 88, 89	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
85	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
86	instantiation	120, 90, 91	⊢
	: , : , :
87	instantiation	120, 92, 93	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
89	instantiation	120, 94, 95	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
91	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
93	instantiation	96, 97	⊢
	:
94	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
95	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
96	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
97	instantiation	120, 98, 99	⊢
	: , : , :
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