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.physics.quantum.QPE._alpha_sqrd_upper_bound
2	instantiation	4, 23, 49, 7, 5	,  ⊢
	: , : , :
3	instantiation	6, 7, 8, 16	,  ⊢
	: , :
4	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
5	instantiation	9, 10, 11	,  ⊢
	: , :
6	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
7	instantiation	55, 12, 25	,  ⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
9	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
10	instantiation	43, 23, 24, 25	,  ⊢
	: , : , :
11	instantiation	13, 14	,  ⊢
	: , :
12	instantiation	42, 23, 24	⊢
	: , :
13	theorem		⊢
	proveit.numbers.ordering.relax_less
14	instantiation	15, 16, 17	,  ⊢
	: , : , :
15	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
16	instantiation	18, 19, 20	,  ⊢
	: , : , :
17	instantiation	21, 52	⊢
	:
18	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
19	instantiation	22, 23, 24, 25	,  ⊢
	: , : , :
20	instantiation	26, 27	⊢
	:
21	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
22	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
23	instantiation	48, 28, 44	⊢
	: , :
24	instantiation	53, 29	⊢
	:
25	assumption		⊢
26	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
27	instantiation	30, 31	⊢
	:
28	instantiation	53, 49	⊢
	:
29	instantiation	48, 36, 44	⊢
	: , :
30	theorem		⊢
	proveit.numbers.negation.int_neg_closure
31	instantiation	32, 33, 34	⊢
	: , :
32	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
33	instantiation	35, 36, 37	⊢
	:
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
35	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
36	instantiation	55, 38, 46	⊢
	: , : , :
37	instantiation	39, 40, 41	⊢
	: , : , :
38	instantiation	42, 44, 45	⊢
	: , :
39	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
40	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
41	instantiation	43, 44, 45, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
43	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
44	instantiation	55, 56, 47	⊢
	: , : , :
45	instantiation	48, 49, 50	⊢
	: , :
46	assumption		⊢
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
48	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
49	instantiation	55, 51, 52	⊢
	: , : , :
50	instantiation	53, 54	⊢
	:
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
52	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
53	theorem		⊢
	proveit.numbers.negation.int_closure
54	instantiation	55, 56, 57	⊢
	: , : , :
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat2