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, 8, 9	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.association
2	reference	47	⊢
3	reference	35	⊢
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	instantiation	10	⊢
	: , :
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	reference	12	⊢
8	instantiation	11, 12, 13	⊢
	: , :
9	instantiation	45, 15, 14	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
12	instantiation	45, 15, 33	⊢
	: , : , :
13	instantiation	45, 15, 16	⊢
	: , : , :
14	instantiation	19, 17, 18	⊢
	: , :
15	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
16	instantiation	19, 20, 21	⊢
	: , :
17	instantiation	45, 41, 22	⊢
	: , : , :
18	instantiation	23, 39, 33, 24	⊢
	: , :
19	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
20	instantiation	45, 41, 25	⊢
	: , : , :
21	instantiation	26, 39	⊢
	:
22	instantiation	45, 43, 27	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.division.div_real_closure
24	instantiation	28, 29	⊢
	: , :
25	instantiation	45, 43, 30	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.negation.real_closure
27	instantiation	45, 46, 31	⊢
	: , : , :
28	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
29	instantiation	32, 38, 33, 34	⊢
	: , :
30	instantiation	45, 46, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
32	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
33	instantiation	36, 38, 39, 40	⊢
	: , : , :
34	instantiation	37, 38, 39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
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