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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	4, 5, 6, 43, 7	⊢
	: , : , :
3	instantiation	8, 21, 9, 59, 22, 10, 24, 25, 26, 11	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
5	instantiation	12, 38	⊢
	:
6	instantiation	13, 15, 43, 16	⊢
	: , : , :
7	instantiation	14, 15, 43, 16	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.association
9	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
10	instantiation	17	⊢
	: , : , :
11	instantiation	29, 25	⊢
	:
12	theorem		⊢
	proveit.numbers.negation.real_closure
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
14	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
16	instantiation	18, 35, 19*	⊢
	:
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
18	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
19	instantiation	20, 21, 62, 59, 22, 23, 24, 25, 26	⊢
	: , : , : , : , : , :
20	theorem		⊢
	proveit.numbers.addition.disassociation
21	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
22	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23	instantiation	27	⊢
	: , :
24	instantiation	60, 28, 37	⊢
	: , : , :
25	instantiation	60, 28, 38	⊢
	: , : , :
26	instantiation	29, 30	⊢
	:
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
29	theorem		⊢
	proveit.numbers.negation.complex_closure
30	instantiation	46, 31, 32	⊢
	: , : , :
31	instantiation	54, 33	⊢
	: , :
32	instantiation	34, 35	⊢
	:
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.int_within_complex
34	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
35	instantiation	36, 37, 38	⊢
	: , :
36	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
37	instantiation	39, 40, 41	⊢
	: , :
38	instantiation	42, 43, 44, 45	⊢
	: , :
39	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
40	instantiation	46, 47, 48	⊢
	: , : , :
41	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
42	theorem		⊢
	proveit.numbers.division.div_real_closure
43	instantiation	60, 50, 49	⊢
	: , : , :
44	instantiation	60, 50, 51	⊢
	: , : , :
45	instantiation	52, 53	⊢
	:
46	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
47	instantiation	54, 55	⊢
	: , :
48	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
49	instantiation	60, 57, 56	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
51	instantiation	60, 57, 58	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
53	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
54	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
56	instantiation	60, 61, 59	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
58	instantiation	60, 61, 62	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
60	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements