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	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	4, 34	⊢
	:
3	instantiation	5, 6, 7	⊢
	: , : , :
4	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
5	axiom		⊢
	proveit.logic.equality.equals_transitivity
6	instantiation	8, 9, 10, 11, 12, 13, 20, 16, 14	⊢
	: , : , : , : , : , :
7	instantiation	15, 20, 16, 17	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.disassociation
9	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	instantiation	18	⊢
	: , :
13	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14	instantiation	19, 20	⊢
	:
15	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
16	instantiation	37, 28, 21	⊢
	: , : , :
17	instantiation	22	⊢
	:
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19	theorem		⊢
	proveit.numbers.negation.complex_closure
20	instantiation	23, 24, 25, 26	⊢
	: , :
21	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
22	axiom		⊢
	proveit.logic.equality.equals_reflexivity
23	theorem		⊢
	proveit.numbers.division.div_complex_closure
24	instantiation	37, 28, 27	⊢
	: , : , :
25	instantiation	37, 28, 29	⊢
	: , : , :
26	instantiation	30, 39	⊢
	:
27	instantiation	37, 32, 31	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
29	instantiation	37, 32, 33	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
31	instantiation	37, 35, 34	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
33	instantiation	37, 35, 36	⊢
	: , : , :
34	assumption		⊢
35	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
36	instantiation	37, 38, 39	⊢
	: , : , :
37	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
38	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
39	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
*equality replacement requirements