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	generalization	1	⊢
1	instantiation	2, 3, 4, 5	,  ⊢
	: , : , :
2	theorem		⊢
	proveit.linear_algebra.matrices.exponentiation.U_closure
3	instantiation	7, 8, 6	,  ⊢
	: , :
4	instantiation	7, 8, 9	⊢
	: , :
5	axiom		⊢
	proveit.physics.quantum.QPE._unitary_U
6	instantiation	10, 11	,  ⊢
	:
7	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
9	instantiation	30, 12, 13	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.negation.nat_closure
11	instantiation	14, 15, 16	,  ⊢
	:
12	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
13	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
14	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
15	instantiation	30, 17, 19	,  ⊢
	: , : , :
16	instantiation	18, 21, 22, 19	,  ⊢
	: , : , :
17	instantiation	20, 21, 22	⊢
	: , :
18	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
19	assumption		⊢
20	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
21	instantiation	23, 24, 25	⊢
	: , :
22	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
23	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
24	instantiation	26, 27	⊢
	:
25	instantiation	30, 28, 29	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.negation.int_closure
27	instantiation	30, 31, 32	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
30	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
31	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
32	assumption		⊢