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, 5, 6, 7, 8, 9, 10, 11	,  ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.association
2	reference	43	⊢
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	instantiation	12	⊢
	: , : , : , :
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
8	reference	15	⊢
9	instantiation	44, 24, 13	⊢
	: , : , :
10	instantiation	14, 15, 16	,  ⊢
	: , :
11	instantiation	44, 24, 17	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
13	instantiation	44, 18, 19	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
15	instantiation	44, 24, 20	⊢
	: , : , :
16	instantiation	21, 22	,  ⊢
	:
17	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
20	instantiation	44, 27, 23	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.negation.complex_closure
22	instantiation	44, 24, 25	,  ⊢
	: , : , :
23	instantiation	44, 30, 26	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
25	instantiation	44, 27, 28	,  ⊢
	: , : , :
26	instantiation	44, 42, 29	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
28	instantiation	44, 30, 31	,  ⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
31	instantiation	44, 32, 33	,  ⊢
	: , : , :
32	instantiation	34, 35, 36	⊢
	: , :
33	assumption		⊢
34	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
35	instantiation	37, 38, 39	⊢
	: , :
36	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
37	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
38	instantiation	40, 41	⊢
	:
39	instantiation	44, 42, 43	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.negation.int_closure
41	instantiation	44, 45, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
46	assumption		⊢