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	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
2	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
3	instantiation	6, 125, 41	⊢
	: , :
4	reference	15	⊢
5	instantiation	7, 8, 9	⊢
	: , :
6	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
7	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
8	instantiation	10, 120, 33, 88, 11, 12, 13*	⊢
	: , : , :
9	instantiation	14, 15, 125, 41, 16, 17	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
11	instantiation	18, 33, 97, 34	⊢
	: , : , :
12	instantiation	19, 25	⊢
	: , :
13	instantiation	20, 113	⊢
	:
14	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
15	instantiation	21, 123, 22	⊢
	: , : , :
16	instantiation	23, 120, 88, 97, 24, 25, 96*	⊢
	: , : , :
17	instantiation	26, 27, 28	⊢
	: , :
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
19	theorem		⊢
	proveit.numbers.ordering.relax_less
20	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
21	theorem		⊢
	proveit.logic.equality.sub_left_side_into
22	instantiation	29, 120, 88, 99, 30, 31*	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
24	instantiation	32, 33, 97, 34	⊢
	: , : , :
25	instantiation	35, 131	⊢
	:
26	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
27	instantiation	129, 108, 36	⊢
	: , : , :
28	instantiation	89	⊢
	:
29	theorem		⊢
	proveit.numbers.multiplication.left_mult_eq_real
30	instantiation	37, 38	⊢
	: , :
31	instantiation	65, 39, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
34	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
36	instantiation	129, 124, 41	⊢
	: , : , :
37	theorem		⊢
	proveit.logic.equality.equals_reversal
38	instantiation	42, 109, 53, 43, 54, 44*, 45*	⊢
	: , : , :
39	instantiation	65, 46, 47	⊢
	: , : , :
40	instantiation	48, 49, 50, 51	⊢
	: , : , : , :
41	instantiation	52, 114	⊢
	:
42	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
43	instantiation	65, 53, 54	⊢
	: , : , :
44	instantiation	55, 87	⊢
	:
45	instantiation	93, 56, 57	⊢
	: , : , :
46	instantiation	58, 82, 83, 59, 60	⊢
	: , : , : , : , :
47	instantiation	93, 61, 62	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
49	instantiation	103, 63	⊢
	: , : , :
50	instantiation	103, 64	⊢
	: , : , :
51	instantiation	112, 83	⊢
	:
52	theorem		⊢
	proveit.numbers.negation.int_closure
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
54	instantiation	65, 66, 67	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.addition.elim_zero_left
56	instantiation	68, 69, 70, 122, 71, 72, 75, 73, 87	⊢
	: , : , : , : , : , :
57	instantiation	74, 87, 75, 76	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
59	instantiation	129, 78, 77	⊢
	: , : , :
60	instantiation	129, 78, 79	⊢
	: , : , :
61	instantiation	103, 80	⊢
	: , : , :
62	instantiation	103, 81	⊢
	: , : , :
63	instantiation	105, 82	⊢
	:
64	instantiation	105, 83	⊢
	:
65	theorem		⊢
	proveit.logic.equality.sub_right_side_into
66	instantiation	84, 123	⊢
	:
67	assumption		⊢
68	theorem		⊢
	proveit.numbers.addition.disassociation
69	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
71	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
72	instantiation	85	⊢
	: , :
73	instantiation	86, 87	⊢
	:
74	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
75	instantiation	129, 119, 88	⊢
	: , : , :
76	instantiation	89	⊢
	:
77	instantiation	129, 91, 90	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
79	instantiation	129, 91, 92	⊢
	: , : , :
80	instantiation	93, 94, 95	⊢
	: , : , :
81	instantiation	103, 96	⊢
	: , : , :
82	instantiation	129, 119, 97	⊢
	: , : , :
83	instantiation	129, 119, 98	⊢
	: , : , :
84	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
85	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
86	theorem		⊢
	proveit.numbers.negation.complex_closure
87	instantiation	129, 119, 99	⊢
	: , : , :
88	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
89	axiom		⊢
	proveit.logic.equality.equals_reflexivity
90	instantiation	129, 101, 100	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
92	instantiation	129, 101, 102	⊢
	: , : , :
93	axiom		⊢
	proveit.logic.equality.equals_transitivity
94	instantiation	103, 104	⊢
	: , : , :
95	instantiation	105, 113	⊢
	:
96	instantiation	106, 113	⊢
	:
97	instantiation	129, 108, 107	⊢
	: , : , :
98	instantiation	129, 108, 116	⊢
	: , : , :
99	instantiation	129, 108, 109	⊢
	: , : , :
100	instantiation	129, 110, 131	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
102	instantiation	129, 110, 111	⊢
	: , : , :
103	axiom		⊢
	proveit.logic.equality.substitution
104	instantiation	112, 113	⊢
	:
105	theorem		⊢
	proveit.numbers.division.frac_one_denom
106	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
107	instantiation	129, 124, 114	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
109	instantiation	115, 116, 117, 118	⊢
	: , :
110	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
111	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
112	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
113	instantiation	129, 119, 120	⊢
	: , : , :
114	instantiation	129, 121, 122	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.division.div_rational_closure
116	instantiation	129, 124, 123	⊢
	: , : , :
117	instantiation	129, 124, 125	⊢
	: , : , :
118	instantiation	126, 131	⊢
	:
119	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
120	instantiation	127, 128, 131	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
122	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
123	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
124	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
125	instantiation	129, 130, 131	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
127	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
128	instantiation	132, 133	⊢
	: , :
129	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
130	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
131	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
132	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
133	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements