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, 12	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.association
2	reference	47	⊢
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	instantiation	13	⊢
	: , : , : , : , :
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	instantiation	45, 18, 14	⊢
	: , : , :
8	instantiation	45, 18, 15	⊢
	: , : , :
9	instantiation	45, 18, 16	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
11	instantiation	45, 18, 17	⊢
	: , : , :
12	instantiation	45, 18, 19	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
14	instantiation	20, 21, 42	⊢
	: , : , :
15	instantiation	45, 25, 22	⊢
	: , : , :
16	instantiation	45, 23, 24	⊢
	: , : , :
17	instantiation	45, 25, 26	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
19	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
20	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
21	instantiation	27, 28	⊢
	: , :
22	instantiation	45, 30, 29	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
26	instantiation	45, 30, 31	⊢
	: , : , :
27	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
29	instantiation	45, 46, 32	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
31	instantiation	45, 33, 34	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
33	instantiation	35, 36, 37	⊢
	: , :
34	assumption		⊢
35	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
36	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
37	instantiation	38, 39, 40	⊢
	: , :
38	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
39	instantiation	45, 41, 42	⊢
	: , : , :
40	instantiation	43, 44	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
42	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
43	theorem		⊢
	proveit.numbers.negation.int_closure
44	instantiation	45, 46, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1