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