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.exp_factored_real
2	instantiation	8, 20, 9	⊢
	:
3	reference	32	⊢
4	reference	30	⊢
5	instantiation	10, 32, 11	⊢
	: , :
6	instantiation	12, 13	⊢
	: , :
7	instantiation	14, 15	⊢
	:
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
9	instantiation	16, 24, 30, 25	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
11	instantiation	17, 30	⊢
	:
12	theorem		⊢
	proveit.logic.equality.equals_reversal
13	instantiation	18, 19, 29	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
15	instantiation	40, 31, 20	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
17	theorem		⊢
	proveit.numbers.negation.real_closure
18	axiom		⊢
	proveit.logic.equality.equals_transitivity
19	instantiation	21, 22	⊢
	: , : , :
20	instantiation	23, 24, 30, 25	⊢
	: , : , :
21	axiom		⊢
	proveit.logic.equality.substitution
22	instantiation	26, 27, 28, 29	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
25	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
26	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
27	instantiation	40, 31, 30	⊢
	: , : , :
28	instantiation	40, 31, 32	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
30	instantiation	40, 34, 33	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	40, 34, 35	⊢
	: , : , :
33	instantiation	40, 37, 36	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	40, 37, 38	⊢
	: , : , :
36	instantiation	40, 41, 39	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
38	instantiation	40, 41, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
40	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements