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.strong_bound_via_left_term_bound
2	reference	59	⊢
3	reference	57	⊢
4	instantiation	84, 72, 8	⊢
	: , : , :
5	instantiation	9, 57, 10, 11, 12	⊢
	: , : , :
6	reference	44	⊢
7	instantiation	23, 13, 14	⊢
	: , : , :
8	instantiation	21, 15, 63	⊢
	: , :
9	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
10	instantiation	84, 72, 15	⊢
	: , : , :
11	theorem		⊢
	proveit.physics.quantum.QPE._e_value_ge_two
12	instantiation	16, 75	⊢
	:
13	instantiation	17, 18	⊢
	: , : , :
14	instantiation	23, 19, 20	⊢
	: , : , :
15	instantiation	21, 48, 22	⊢
	: , :
16	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
17	axiom		⊢
	proveit.logic.equality.substitution
18	instantiation	23, 24, 25	⊢
	: , : , :
19	instantiation	30, 33, 79, 86, 35, 26, 36, 50, 54	⊢
	: , : , : , : , : , :
20	instantiation	27, 50, 36, 28	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.add_rational_closure_bin
22	instantiation	84, 80, 29	⊢
	: , : , :
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	30, 33, 79, 86, 35, 31, 36, 54, 53	⊢
	: , : , : , : , : , :
25	instantiation	32, 86, 79, 33, 34, 35, 36, 54, 53, 37*	⊢
	: , : , : , : , : , :
26	instantiation	41	⊢
	: , :
27	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
28	instantiation	38	⊢
	:
29	instantiation	84, 39, 40	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.disassociation
31	instantiation	41	⊢
	: , :
32	theorem		⊢
	proveit.numbers.addition.association
33	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
34	instantiation	41	⊢
	: , :
35	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36	instantiation	84, 58, 42	⊢
	: , : , :
37	instantiation	43, 44, 45	⊢
	: , : , :
38	axiom		⊢
	proveit.logic.equality.equals_reflexivity
39	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
40	instantiation	46, 47	⊢
	:
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
42	instantiation	84, 72, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.equality.sub_right_side_into
44	instantiation	49, 50, 53, 51	⊢
	: , : , :
45	instantiation	52, 53, 54	⊢
	: , :
46	theorem		⊢
	proveit.numbers.negation.int_neg_closure
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
48	instantiation	84, 55, 56	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
50	instantiation	84, 58, 65	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
52	theorem		⊢
	proveit.numbers.addition.commutation
53	instantiation	84, 58, 57	⊢
	: , : , :
54	instantiation	84, 58, 59	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
56	instantiation	60, 61, 62	⊢
	: , :
57	instantiation	84, 72, 63	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
59	instantiation	64, 65	⊢
	:
60	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
61	instantiation	84, 66, 67	⊢
	: , : , :
62	instantiation	68, 69, 70	⊢
	: , :
63	instantiation	84, 80, 71	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.negation.real_closure
65	instantiation	84, 72, 73	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
67	instantiation	84, 74, 75	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
69	instantiation	84, 82, 76	⊢
	: , : , :
70	instantiation	77, 78	⊢
	:
71	instantiation	84, 85, 79	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
73	instantiation	84, 80, 81	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
75	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
76	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
77	theorem		⊢
	proveit.numbers.negation.int_closure
78	instantiation	84, 82, 83	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
80	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
81	instantiation	84, 85, 86	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
83	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
84	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
85	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
86	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements