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