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*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
2	reference	23	⊢
3	instantiation	49, 8, 9	⊢
	: , : , :
4	reference	33	⊢
5	instantiation	10, 11, 12	⊢
	: , :
6	instantiation	20, 13	⊢
	: , :
7	instantiation	14, 15, 16	⊢
	: , :
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
9	instantiation	17, 18	⊢
	:
10	theorem		⊢
	proveit.numbers.absolute_value.weak_upper_bound
11	instantiation	19, 30, 33, 31	⊢
	: , : , :
12	instantiation	20, 21	⊢
	: , :
13	instantiation	22, 28	⊢
	:
14	theorem		⊢
	proveit.numbers.multiplication.commutation
15	instantiation	49, 24, 23	⊢
	: , : , :
16	instantiation	49, 24, 33	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
18	instantiation	49, 24, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
20	theorem		⊢
	proveit.numbers.ordering.relax_less
21	instantiation	26, 30, 33, 31	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
23	instantiation	49, 27, 28	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
25	instantiation	29, 30, 33, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
30	instantiation	32, 33	⊢
	:
31	instantiation	34, 35	⊢
	:
32	theorem		⊢
	proveit.numbers.negation.real_closure
33	instantiation	36, 37, 38, 39	⊢
	: , :
34	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
35	assumption		⊢
36	theorem		⊢
	proveit.numbers.division.div_real_closure
37	instantiation	49, 41, 40	⊢
	: , : , :
38	instantiation	49, 41, 42	⊢
	: , : , :
39	instantiation	43, 44	⊢
	:
40	instantiation	49, 46, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
42	instantiation	49, 46, 47	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
45	instantiation	49, 50, 48	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	49, 50, 51	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements