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.numbers.multiplication.mult_rational_pos_closure_bin
2	instantiation	89, 4, 80	⊢
	: , : , :
3	instantiation	5, 20, 6	⊢
	:
4	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
5	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.pos_rational_is_rational_pos
6	instantiation	7, 8	⊢
	: , :
7	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
8	instantiation	9, 64, 62, 10, 11, 49*, 12*	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
10	instantiation	89, 77, 13	⊢
	: , : , :
11	instantiation	14, 62, 15, 16, 17	⊢
	: , : , :
12	instantiation	28, 18, 19	⊢
	: , : , :
13	instantiation	26, 20, 68	⊢
	: , :
14	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
15	instantiation	89, 77, 20	⊢
	: , : , :
16	theorem		⊢
	proveit.physics.quantum.QPE._e_value_ge_two
17	instantiation	21, 80	⊢
	:
18	instantiation	22, 23	⊢
	: , : , :
19	instantiation	28, 24, 25	⊢
	: , : , :
20	instantiation	26, 53, 27	⊢
	: , :
21	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
22	axiom		⊢
	proveit.logic.equality.substitution
23	instantiation	28, 29, 30	⊢
	: , : , :
24	instantiation	35, 38, 84, 91, 40, 31, 41, 55, 59	⊢
	: , : , : , : , : , :
25	instantiation	32, 55, 41, 33	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.add_rational_closure_bin
27	instantiation	89, 85, 34	⊢
	: , : , :
28	axiom		⊢
	proveit.logic.equality.equals_transitivity
29	instantiation	35, 38, 84, 91, 40, 36, 41, 59, 58	⊢
	: , : , : , : , : , :
30	instantiation	37, 91, 84, 38, 39, 40, 41, 59, 58, 42*	⊢
	: , : , : , : , : , :
31	instantiation	46	⊢
	: , :
32	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
33	instantiation	43	⊢
	:
34	instantiation	89, 44, 45	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.addition.disassociation
36	instantiation	46	⊢
	: , :
37	theorem		⊢
	proveit.numbers.addition.association
38	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
39	instantiation	46	⊢
	: , :
40	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
41	instantiation	89, 63, 47	⊢
	: , : , :
42	instantiation	48, 49, 50	⊢
	: , : , :
43	axiom		⊢
	proveit.logic.equality.equals_reflexivity
44	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
45	instantiation	51, 52	⊢
	:
46	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47	instantiation	89, 77, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.equality.sub_right_side_into
49	instantiation	54, 55, 58, 56	⊢
	: , : , :
50	instantiation	57, 58, 59	⊢
	: , :
51	theorem		⊢
	proveit.numbers.negation.int_neg_closure
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
53	instantiation	89, 60, 61	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
55	instantiation	89, 63, 70	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
57	theorem		⊢
	proveit.numbers.addition.commutation
58	instantiation	89, 63, 62	⊢
	: , : , :
59	instantiation	89, 63, 64	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
61	instantiation	65, 66, 67	⊢
	: , :
62	instantiation	89, 77, 68	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
64	instantiation	69, 70	⊢
	:
65	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
66	instantiation	89, 71, 72	⊢
	: , : , :
67	instantiation	73, 74, 75	⊢
	: , :
68	instantiation	89, 85, 76	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.negation.real_closure
70	instantiation	89, 77, 78	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
72	instantiation	89, 79, 80	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
74	instantiation	89, 87, 81	⊢
	: , : , :
75	instantiation	82, 83	⊢
	:
76	instantiation	89, 90, 84	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
78	instantiation	89, 85, 86	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
80	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
81	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
82	theorem		⊢
	proveit.numbers.negation.int_closure
83	instantiation	89, 87, 88	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
85	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
86	instantiation	89, 90, 91	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
88	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
89	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
90	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
91	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements