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*	⊢
	: , :
1	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
3	instantiation	9	⊢
	: , : , : , :
4	reference	24	⊢
5	reference	25	⊢
6	reference	60	⊢
7	reference	27	⊢
8	instantiation	10, 11, 12	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
10	axiom		⊢
	proveit.logic.equality.equals_transitivity
11	instantiation	13, 21, 14, 15, 16, 17, 18	⊢
	: , : , : , :
12	instantiation	19, 20, 21, 22, 23, 24, 25, 26, 27	⊢
	: , : , : , : , : , : , :
13	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
14	instantiation	32	⊢
	: , : , :
15	instantiation	32	⊢
	: , : , :
16	instantiation	30, 28	⊢
	:
17	instantiation	30, 29	⊢
	:
18	instantiation	30, 31	⊢
	:
19	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
20	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
22	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23	instantiation	32	⊢
	: , : , :
24	instantiation	62, 63, 33	⊢
	: , : , :
25	instantiation	62, 63, 34	⊢
	: , : , :
26	instantiation	62, 63, 35	⊢
	: , : , :
27	instantiation	62, 63, 36	⊢
	: , : , :
28	instantiation	37, 58	⊢
	:
29	instantiation	39, 38	⊢
	: , :
30	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
31	instantiation	39, 40	⊢
	: , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
33	instantiation	62, 41, 42	⊢
	: , : , :
34	instantiation	62, 43, 48	⊢
	: , : , :
35	instantiation	62, 43, 44	⊢
	: , : , :
36	instantiation	45, 46, 50	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
38	instantiation	47, 48	⊢
	:
39	theorem		⊢
	proveit.numbers.ordering.relax_less
40	instantiation	49, 50	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
42	instantiation	62, 51, 52	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
44	instantiation	53, 54	⊢
	:
45	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
46	instantiation	55, 56	⊢
	: , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
49	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
50	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	instantiation	62, 57, 58	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
54	instantiation	59, 60, 61	⊢
	:
55	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
60	instantiation	62, 63, 64	⊢
	: , : , :
61	assumption		⊢
62	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
64	instantiation	65, 66	⊢
	:
65	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
66	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
*equality replacement requirements