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	modus ponens	1, 2	⊢
1	instantiation	3	⊢
	: , : , :
2	generalization	4	⊢
3	theorem		⊢
	proveit.numbers.summation.weak_summation_from_summands_bound
4	instantiation	5, 6, 7	,  ⊢
	:
5	theorem		⊢
	proveit.physics.quantum.QPE._alpha_sqrd_upper_bound
6	instantiation	8, 27, 53, 11, 9	,  ⊢
	: , : , :
7	instantiation	10, 11, 12, 20	,  ⊢
	: , :
8	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
9	instantiation	13, 14, 15	,  ⊢
	: , :
10	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
11	instantiation	59, 16, 29	,  ⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
13	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
14	instantiation	47, 27, 28, 29	,  ⊢
	: , : , :
15	instantiation	17, 18	,  ⊢
	: , :
16	instantiation	46, 27, 28	⊢
	: , :
17	theorem		⊢
	proveit.numbers.ordering.relax_less
18	instantiation	19, 20, 21	,  ⊢
	: , : , :
19	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
20	instantiation	22, 23, 24	,  ⊢
	: , : , :
21	instantiation	25, 56	⊢
	:
22	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
23	instantiation	26, 27, 28, 29	,  ⊢
	: , : , :
24	instantiation	30, 31	⊢
	:
25	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
26	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
27	instantiation	52, 32, 48	⊢
	: , :
28	instantiation	57, 33	⊢
	:
29	assumption		⊢
30	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
31	instantiation	34, 35	⊢
	:
32	instantiation	57, 53	⊢
	:
33	instantiation	52, 40, 48	⊢
	: , :
34	theorem		⊢
	proveit.numbers.negation.int_neg_closure
35	instantiation	36, 37, 38	⊢
	: , :
36	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
37	instantiation	39, 40, 41	⊢
	:
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
39	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
40	instantiation	59, 42, 50	⊢
	: , : , :
41	instantiation	43, 44, 45	⊢
	: , : , :
42	instantiation	46, 48, 49	⊢
	: , :
43	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
44	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
45	instantiation	47, 48, 49, 50	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
47	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
48	instantiation	59, 60, 51	⊢
	: , : , :
49	instantiation	52, 53, 54	⊢
	: , :
50	assumption		⊢
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
52	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
53	instantiation	59, 55, 56	⊢
	: , : , :
54	instantiation	57, 58	⊢
	:
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
56	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
57	theorem		⊢
	proveit.numbers.negation.int_closure
58	instantiation	59, 60, 61	⊢
	: , : , :
59	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat2