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