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	reference	9	⊢
2	instantiation	16, 4	⊢
	: , : , :
3	instantiation	9, 5, 6	,  ⊢
	: , : , :
4	instantiation	9, 7, 8	⊢
	: , : , :
5	instantiation	9, 10, 11	,  ⊢
	: , : , :
6	instantiation	12, 21	,  ⊢
	:
7	instantiation	16, 13	⊢
	: , : , :
8	instantiation	14, 39, 15*	⊢
	:
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	16, 17	⊢
	: , : , :
11	instantiation	18, 19, 20, 21, 22*	,  ⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.division.frac_one_denom
13	instantiation	23, 24	⊢
	:
14	theorem		⊢
	proveit.numbers.absolute_value.abs_even
15	instantiation	25, 26, 27, 70, 71, 74, 28*, 29*	⊢
	: , :
16	axiom		⊢
	proveit.logic.equality.substitution
17	instantiation	30, 104, 107, 67, 31, 68, 70, 71, 32	⊢
	: , : , : , : , : , :
18	theorem		⊢
	proveit.numbers.division.frac_cancel_left
19	instantiation	105, 34, 33	⊢
	: , : , :
20	instantiation	105, 34, 35	⊢
	: , : , :
21	instantiation	105, 79, 36	,  ⊢
	: , : , :
22	instantiation	37, 70	⊢
	:
23	theorem		⊢
	proveit.numbers.addition.elim_zero_left
24	instantiation	38, 39	⊢
	:
25	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
26	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
27	instantiation	40	⊢
	: , : , :
28	instantiation	42, 41	⊢
	:
29	instantiation	42, 43	⊢
	:
30	theorem		⊢
	proveit.numbers.multiplication.association
31	instantiation	78	⊢
	: , :
32	instantiation	105, 79, 44	⊢
	: , : , :
33	instantiation	105, 46, 45	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
35	instantiation	105, 46, 47	⊢
	: , : , :
36	instantiation	48, 49, 50, 51	,  ⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
38	theorem		⊢
	proveit.numbers.negation.complex_closure
39	instantiation	52, 53, 54	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
41	instantiation	55, 107	⊢
	:
42	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
43	instantiation	56, 57	⊢
	: , :
44	instantiation	105, 58, 59	⊢
	: , : , :
45	instantiation	105, 61, 60	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
47	instantiation	105, 61, 62	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
50	instantiation	92, 82, 94, 95	⊢
	: , :
51	instantiation	63, 91, 64	,  ⊢
	:
52	theorem		⊢
	proveit.logic.equality.sub_right_side_into
53	instantiation	105, 79, 65	⊢
	: , : , :
54	instantiation	66, 67, 107, 104, 68, 69, 70, 71, 74	⊢
	: , : , : , : , : , :
55	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
56	theorem		⊢
	proveit.numbers.ordering.relax_less
57	instantiation	72, 87	⊢
	:
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
59	instantiation	73, 74	⊢
	:
60	instantiation	105, 75, 100	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
62	instantiation	105, 75, 76	⊢
	: , : , :
63	theorem		⊢
	proveit.physics.quantum.QPE._scaled_abs_delta_b_floor_diff_interval
64	assumption		⊢
65	instantiation	81, 77, 80	⊢
	: , :
66	theorem		⊢
	proveit.numbers.multiplication.disassociation
67	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
68	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
69	instantiation	78	⊢
	: , :
70	instantiation	105, 79, 94	⊢
	: , : , :
71	instantiation	105, 79, 82	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
73	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
74	instantiation	105, 79, 80	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
76	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
77	instantiation	81, 94, 82	⊢
	: , :
78	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
79	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
80	instantiation	83, 84, 89, 85	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
82	instantiation	105, 86, 87	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
84	instantiation	88, 89	⊢
	:
85	instantiation	90, 91	⊢
	:
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.negation.real_closure
89	instantiation	92, 93, 94, 95	⊢
	: , :
90	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
91	assumption		⊢
92	theorem		⊢
	proveit.numbers.division.div_real_closure
93	instantiation	105, 97, 96	⊢
	: , : , :
94	instantiation	105, 97, 98	⊢
	: , : , :
95	instantiation	99, 100	⊢
	:
96	instantiation	105, 102, 101	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
98	instantiation	105, 102, 103	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
100	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
101	instantiation	105, 106, 104	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
103	instantiation	105, 106, 107	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
105	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
106	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
107	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements