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	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 8, 44, 10, 12, 11, 13	⊢
	: , : , : , : , : , : , :
5	instantiation	7, 44, 47, 8, 9, 10, 11, 12, 13	⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
7	theorem		⊢
	proveit.numbers.multiplication.association
8	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
9	instantiation	14	⊢
	: , :
10	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
11	instantiation	45, 23, 15	⊢
	: , : , :
12	instantiation	45, 23, 34	⊢
	: , : , :
13	instantiation	45, 23, 16	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
15	instantiation	45, 17, 18	⊢
	: , : , :
16	instantiation	45, 19, 20	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
20	instantiation	21, 22	⊢
	:
21	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
22	instantiation	45, 23, 24	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
24	instantiation	25, 26, 29, 27	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
26	instantiation	28, 29	⊢
	:
27	instantiation	30, 31	⊢
	:
28	theorem		⊢
	proveit.numbers.negation.real_closure
29	instantiation	32, 33, 34, 35	⊢
	: , :
30	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
31	assumption		⊢
32	theorem		⊢
	proveit.numbers.division.div_real_closure
33	instantiation	45, 37, 36	⊢
	: , : , :
34	instantiation	45, 37, 38	⊢
	: , : , :
35	instantiation	39, 40	⊢
	:
36	instantiation	45, 42, 41	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	45, 42, 43	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
41	instantiation	45, 46, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
43	instantiation	45, 46, 47	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
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.nat2