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	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
2	instantiation	7, 109, 8	⊢
	: , : , :
3	reference	111	⊢
4	reference	27	⊢
5	instantiation	9, 106, 74, 83, 10, 11, 82*	⊢
	: , : , :
6	instantiation	12, 13, 14	⊢
	: , :
7	theorem		⊢
	proveit.logic.equality.sub_left_side_into
8	instantiation	15, 106, 74, 85, 16, 17*	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
10	instantiation	18, 19, 83, 20	⊢
	: , : , :
11	instantiation	21, 117	⊢
	:
12	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
13	instantiation	115, 94, 22	⊢
	: , : , :
14	instantiation	75	⊢
	:
15	theorem		⊢
	proveit.numbers.multiplication.left_mult_eq_real
16	instantiation	23, 24	⊢
	: , :
17	instantiation	51, 25, 26	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
20	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
21	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
22	instantiation	115, 110, 27	⊢
	: , : , :
23	theorem		⊢
	proveit.logic.equality.equals_reversal
24	instantiation	28, 95, 39, 29, 40, 30*, 31*	⊢
	: , : , :
25	instantiation	51, 32, 33	⊢
	: , : , :
26	instantiation	34, 35, 36, 37	⊢
	: , : , : , :
27	instantiation	38, 100	⊢
	:
28	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
29	instantiation	51, 39, 40	⊢
	: , : , :
30	instantiation	41, 73	⊢
	:
31	instantiation	79, 42, 43	⊢
	: , : , :
32	instantiation	44, 68, 69, 45, 46	⊢
	: , : , : , : , :
33	instantiation	79, 47, 48	⊢
	: , : , :
34	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
35	instantiation	89, 49	⊢
	: , : , :
36	instantiation	89, 50	⊢
	: , : , :
37	instantiation	98, 69	⊢
	:
38	theorem		⊢
	proveit.numbers.negation.int_closure
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
40	instantiation	51, 52, 53	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.addition.elim_zero_left
42	instantiation	54, 55, 56, 108, 57, 58, 61, 59, 73	⊢
	: , : , : , : , : , :
43	instantiation	60, 73, 61, 62	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
45	instantiation	115, 64, 63	⊢
	: , : , :
46	instantiation	115, 64, 65	⊢
	: , : , :
47	instantiation	89, 66	⊢
	: , : , :
48	instantiation	89, 67	⊢
	: , : , :
49	instantiation	91, 68	⊢
	:
50	instantiation	91, 69	⊢
	:
51	theorem		⊢
	proveit.logic.equality.sub_right_side_into
52	instantiation	70, 109	⊢
	:
53	assumption		⊢
54	theorem		⊢
	proveit.numbers.addition.disassociation
55	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
57	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
58	instantiation	71	⊢
	: , :
59	instantiation	72, 73	⊢
	:
60	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
61	instantiation	115, 105, 74	⊢
	: , : , :
62	instantiation	75	⊢
	:
63	instantiation	115, 77, 76	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
65	instantiation	115, 77, 78	⊢
	: , : , :
66	instantiation	79, 80, 81	⊢
	: , : , :
67	instantiation	89, 82	⊢
	: , : , :
68	instantiation	115, 105, 83	⊢
	: , : , :
69	instantiation	115, 105, 84	⊢
	: , : , :
70	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
71	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
72	theorem		⊢
	proveit.numbers.negation.complex_closure
73	instantiation	115, 105, 85	⊢
	: , : , :
74	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
75	axiom		⊢
	proveit.logic.equality.equals_reflexivity
76	instantiation	115, 87, 86	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
78	instantiation	115, 87, 88	⊢
	: , : , :
79	axiom		⊢
	proveit.logic.equality.equals_transitivity
80	instantiation	89, 90	⊢
	: , : , :
81	instantiation	91, 99	⊢
	:
82	instantiation	92, 99	⊢
	:
83	instantiation	115, 94, 93	⊢
	: , : , :
84	instantiation	115, 94, 102	⊢
	: , : , :
85	instantiation	115, 94, 95	⊢
	: , : , :
86	instantiation	115, 96, 117	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
88	instantiation	115, 96, 97	⊢
	: , : , :
89	axiom		⊢
	proveit.logic.equality.substitution
90	instantiation	98, 99	⊢
	:
91	theorem		⊢
	proveit.numbers.division.frac_one_denom
92	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
93	instantiation	115, 110, 100	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
95	instantiation	101, 102, 103, 104	⊢
	: , :
96	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
97	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
98	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
99	instantiation	115, 105, 106	⊢
	: , : , :
100	instantiation	115, 107, 108	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.division.div_rational_closure
102	instantiation	115, 110, 109	⊢
	: , : , :
103	instantiation	115, 110, 111	⊢
	: , : , :
104	instantiation	112, 117	⊢
	:
105	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
106	instantiation	113, 114, 117	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
109	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
110	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
111	instantiation	115, 116, 117	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
113	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
114	instantiation	118, 119	⊢
	: , :
115	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
116	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
117	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
118	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements