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