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	⊢
	: , : , :
1	reference	45	⊢
2	reference	41	⊢
3	instantiation	45, 43, 4	⊢
	: , : , :
4	instantiation	5, 6	⊢
	:
5	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
6	instantiation	7, 27, 8, 9	⊢
	: , :
7	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
8	instantiation	10, 27, 11	⊢
	: , :
9	instantiation	12, 13	⊢
	: , :
10	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
11	instantiation	14, 15, 25, 16	⊢
	: , :
12	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
13	instantiation	17, 47, 18, 19	⊢
	: , :
14	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
15	instantiation	45, 29, 20	⊢
	: , : , :
16	instantiation	21, 22	⊢
	:
17	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
18	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
19	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
20	instantiation	45, 34, 23	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
22	instantiation	45, 24, 25	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
25	instantiation	26, 27, 28	⊢
	: , :
26	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
27	instantiation	45, 29, 30	⊢
	: , : , :
28	instantiation	31, 32, 33	⊢
	:
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
30	instantiation	45, 34, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
32	instantiation	36, 38, 39, 40	⊢
	: , : , :
33	instantiation	37, 38, 39, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
39	instantiation	45, 41, 42	⊢
	: , : , :
40	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
42	instantiation	45, 43, 44	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
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