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.booleans.conjunction.and_if_both
2	instantiation	4, 114, 27, 82, 5, 6, 7*	⊢
	: , : , :
3	instantiation	8, 9, 119, 35, 10, 11	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
5	instantiation	12, 27, 91, 28	⊢
	: , : , :
6	instantiation	13, 19	⊢
	: , :
7	instantiation	14, 107	⊢
	:
8	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
9	instantiation	15, 117, 16	⊢
	: , : , :
10	instantiation	17, 114, 82, 91, 18, 19, 90*	⊢
	: , : , :
11	instantiation	20, 21, 22	⊢
	: , :
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
13	theorem		⊢
	proveit.numbers.ordering.relax_less
14	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
15	theorem		⊢
	proveit.logic.equality.sub_left_side_into
16	instantiation	23, 114, 82, 93, 24, 25*	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
18	instantiation	26, 27, 91, 28	⊢
	: , : , :
19	instantiation	29, 125	⊢
	:
20	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
21	instantiation	123, 102, 30	⊢
	: , : , :
22	instantiation	83	⊢
	:
23	theorem		⊢
	proveit.numbers.multiplication.left_mult_eq_real
24	instantiation	31, 32	⊢
	: , :
25	instantiation	59, 33, 34	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
28	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
29	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
30	instantiation	123, 118, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.logic.equality.equals_reversal
32	instantiation	36, 103, 47, 37, 48, 38*, 39*	⊢
	: , : , :
33	instantiation	59, 40, 41	⊢
	: , : , :
34	instantiation	42, 43, 44, 45	⊢
	: , : , : , :
35	instantiation	46, 108	⊢
	:
36	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
37	instantiation	59, 47, 48	⊢
	: , : , :
38	instantiation	49, 81	⊢
	:
39	instantiation	87, 50, 51	⊢
	: , : , :
40	instantiation	52, 76, 77, 53, 54	⊢
	: , : , : , : , :
41	instantiation	87, 55, 56	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
43	instantiation	97, 57	⊢
	: , : , :
44	instantiation	97, 58	⊢
	: , : , :
45	instantiation	106, 77	⊢
	:
46	theorem		⊢
	proveit.numbers.negation.int_closure
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
48	instantiation	59, 60, 61	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.addition.elim_zero_left
50	instantiation	62, 63, 64, 116, 65, 66, 69, 67, 81	⊢
	: , : , : , : , : , :
51	instantiation	68, 81, 69, 70	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
53	instantiation	123, 72, 71	⊢
	: , : , :
54	instantiation	123, 72, 73	⊢
	: , : , :
55	instantiation	97, 74	⊢
	: , : , :
56	instantiation	97, 75	⊢
	: , : , :
57	instantiation	99, 76	⊢
	:
58	instantiation	99, 77	⊢
	:
59	theorem		⊢
	proveit.logic.equality.sub_right_side_into
60	instantiation	78, 117	⊢
	:
61	assumption		⊢
62	theorem		⊢
	proveit.numbers.addition.disassociation
63	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
65	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
66	instantiation	79	⊢
	: , :
67	instantiation	80, 81	⊢
	:
68	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
69	instantiation	123, 113, 82	⊢
	: , : , :
70	instantiation	83	⊢
	:
71	instantiation	123, 85, 84	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
73	instantiation	123, 85, 86	⊢
	: , : , :
74	instantiation	87, 88, 89	⊢
	: , : , :
75	instantiation	97, 90	⊢
	: , : , :
76	instantiation	123, 113, 91	⊢
	: , : , :
77	instantiation	123, 113, 92	⊢
	: , : , :
78	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
79	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
80	theorem		⊢
	proveit.numbers.negation.complex_closure
81	instantiation	123, 113, 93	⊢
	: , : , :
82	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
83	axiom		⊢
	proveit.logic.equality.equals_reflexivity
84	instantiation	123, 95, 94	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
86	instantiation	123, 95, 96	⊢
	: , : , :
87	axiom		⊢
	proveit.logic.equality.equals_transitivity
88	instantiation	97, 98	⊢
	: , : , :
89	instantiation	99, 107	⊢
	:
90	instantiation	100, 107	⊢
	:
91	instantiation	123, 102, 101	⊢
	: , : , :
92	instantiation	123, 102, 110	⊢
	: , : , :
93	instantiation	123, 102, 103	⊢
	: , : , :
94	instantiation	123, 104, 125	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
96	instantiation	123, 104, 105	⊢
	: , : , :
97	axiom		⊢
	proveit.logic.equality.substitution
98	instantiation	106, 107	⊢
	:
99	theorem		⊢
	proveit.numbers.division.frac_one_denom
100	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
101	instantiation	123, 118, 108	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
103	instantiation	109, 110, 111, 112	⊢
	: , :
104	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
105	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
106	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
107	instantiation	123, 113, 114	⊢
	: , : , :
108	instantiation	123, 115, 116	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.division.div_rational_closure
110	instantiation	123, 118, 117	⊢
	: , : , :
111	instantiation	123, 118, 119	⊢
	: , : , :
112	instantiation	120, 125	⊢
	:
113	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
114	instantiation	121, 122, 125	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
116	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
117	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
118	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
119	instantiation	123, 124, 125	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
121	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
122	instantiation	126, 127	⊢
	: , :
123	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
124	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
125	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
126	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
127	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements