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	47	⊢
2	reference	43	⊢
3	instantiation	47, 45, 4	⊢
	: , : , :
4	instantiation	5, 6	⊢
	:
5	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
6	instantiation	7, 22, 8, 9	⊢
	: , :
7	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
8	instantiation	10, 22, 11	⊢
	: , :
9	instantiation	12, 13	⊢
	: , :
10	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
11	instantiation	14, 15, 16	⊢
	: , :
12	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
13	instantiation	17, 49, 18, 19	⊢
	: , :
14	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
15	instantiation	20, 21, 22, 23	⊢
	: , :
16	instantiation	24, 25, 26	⊢
	: , :
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	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
21	instantiation	47, 28, 27	⊢
	: , : , :
22	instantiation	47, 28, 29	⊢
	: , : , :
23	instantiation	30, 37	⊢
	:
24	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
25	instantiation	31, 32, 33	⊢
	:
26	instantiation	34, 41	⊢
	:
27	instantiation	47, 36, 35	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
29	instantiation	47, 36, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
32	instantiation	38, 40, 41, 42	⊢
	: , : , :
33	instantiation	39, 40, 41, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.negation.real_closure
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
41	instantiation	47, 43, 44	⊢
	: , : , :
42	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	47, 45, 46	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
46	instantiation	47, 48, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat1