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.addition.leftward_commutation
2	reference	48	⊢
3	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
4	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
5	instantiation	46, 10, 8	⊢
	: , : , :
6	instantiation	46, 10, 9	⊢
	: , : , :
7	instantiation	46, 10, 11	⊢
	: , : , :
8	instantiation	46, 42, 12	⊢
	: , : , :
9	instantiation	46, 13, 14	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
11	instantiation	15, 40	⊢
	:
12	instantiation	46, 44, 16	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
14	instantiation	17, 18, 26, 19	⊢
	: , :
15	theorem		⊢
	proveit.numbers.negation.real_closure
16	instantiation	46, 47, 20	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
18	instantiation	46, 30, 21	⊢
	: , : , :
19	instantiation	22, 23	⊢
	:
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
21	instantiation	46, 35, 24	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
23	instantiation	46, 25, 26	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
26	instantiation	27, 28, 29	⊢
	: , :
27	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
28	instantiation	46, 30, 31	⊢
	: , : , :
29	instantiation	32, 33, 34	⊢
	:
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
31	instantiation	46, 35, 36	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
33	instantiation	37, 39, 40, 41	⊢
	: , : , :
34	instantiation	38, 39, 40, 41	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
40	instantiation	46, 42, 43	⊢
	: , : , :
41	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	46, 44, 45	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
45	instantiation	46, 47, 48	⊢
	: , : , :
46	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat1