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, 23, 4, 5, 6, 7, 8*	⊢
	: , : , :
3	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
4	instantiation	44, 31, 18	⊢
	: , : , :
5	instantiation	9, 27	⊢
	:
6	instantiation	10, 40	⊢
	:
7	instantiation	11, 12	⊢
	: , :
8	instantiation	13, 14, 15, 16*	⊢
	: , :
9	theorem		⊢
	proveit.numbers.negation.real_closure
10	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
11	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
12	instantiation	17, 26, 18, 19	⊢
	: , :
13	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
14	instantiation	44, 20, 21	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
16	instantiation	22, 23	⊢
	:
17	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
18	instantiation	24, 26, 27, 28	⊢
	: , : , :
19	instantiation	25, 26, 27, 28	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
21	instantiation	44, 29, 30	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
23	instantiation	44, 31, 32	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
27	instantiation	44, 36, 33	⊢
	: , : , :
28	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
30	instantiation	44, 34, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	44, 36, 37	⊢
	: , : , :
33	instantiation	44, 41, 38	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
35	instantiation	44, 39, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	44, 41, 42	⊢
	: , : , :
38	instantiation	44, 45, 43	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	44, 45, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements