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, 127, 43	⊢
	: , :
4	reference	125	⊢
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	67, 10, 24	⊢
	: , : , :
9	instantiation	67, 11, 24	⊢
	: , : , :
10	instantiation	12, 122, 35, 90, 13, 14, 15*	⊢
	: , : , :
11	instantiation	16, 17, 127, 43, 18, 19	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
13	instantiation	20, 35, 99, 36	⊢
	: , : , :
14	instantiation	21, 27	⊢
	: , :
15	instantiation	22, 115	⊢
	:
16	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
17	instantiation	23, 125, 24	⊢
	: , : , :
18	instantiation	25, 122, 90, 99, 26, 27, 98*	⊢
	: , : , :
19	instantiation	28, 29, 30	⊢
	: , :
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
21	theorem		⊢
	proveit.numbers.ordering.relax_less
22	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
23	theorem		⊢
	proveit.logic.equality.sub_left_side_into
24	instantiation	31, 122, 90, 101, 32, 33*	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
26	instantiation	34, 35, 99, 36	⊢
	: , : , :
27	instantiation	37, 133	⊢
	:
28	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
29	instantiation	131, 110, 38	⊢
	: , : , :
30	instantiation	91	⊢
	:
31	theorem		⊢
	proveit.numbers.multiplication.left_mult_eq_real
32	instantiation	39, 40	⊢
	: , :
33	instantiation	67, 41, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
36	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
38	instantiation	131, 126, 43	⊢
	: , : , :
39	theorem		⊢
	proveit.logic.equality.equals_reversal
40	instantiation	44, 111, 55, 45, 56, 46*, 47*	⊢
	: , : , :
41	instantiation	67, 48, 49	⊢
	: , : , :
42	instantiation	50, 51, 52, 53	⊢
	: , : , : , :
43	instantiation	54, 116	⊢
	:
44	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
45	instantiation	67, 55, 56	⊢
	: , : , :
46	instantiation	57, 89	⊢
	:
47	instantiation	95, 58, 59	⊢
	: , : , :
48	instantiation	60, 84, 85, 61, 62	⊢
	: , : , : , : , :
49	instantiation	95, 63, 64	⊢
	: , : , :
50	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
51	instantiation	105, 65	⊢
	: , : , :
52	instantiation	105, 66	⊢
	: , : , :
53	instantiation	114, 85	⊢
	:
54	theorem		⊢
	proveit.numbers.negation.int_closure
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
56	instantiation	67, 68, 69	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.addition.elim_zero_left
58	instantiation	70, 71, 72, 124, 73, 74, 77, 75, 89	⊢
	: , : , : , : , : , :
59	instantiation	76, 89, 77, 78	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
61	instantiation	131, 80, 79	⊢
	: , : , :
62	instantiation	131, 80, 81	⊢
	: , : , :
63	instantiation	105, 82	⊢
	: , : , :
64	instantiation	105, 83	⊢
	: , : , :
65	instantiation	107, 84	⊢
	:
66	instantiation	107, 85	⊢
	:
67	theorem		⊢
	proveit.logic.equality.sub_right_side_into
68	instantiation	86, 125	⊢
	:
69	assumption		⊢
70	theorem		⊢
	proveit.numbers.addition.disassociation
71	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
73	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
74	instantiation	87	⊢
	: , :
75	instantiation	88, 89	⊢
	:
76	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
77	instantiation	131, 121, 90	⊢
	: , : , :
78	instantiation	91	⊢
	:
79	instantiation	131, 93, 92	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
81	instantiation	131, 93, 94	⊢
	: , : , :
82	instantiation	95, 96, 97	⊢
	: , : , :
83	instantiation	105, 98	⊢
	: , : , :
84	instantiation	131, 121, 99	⊢
	: , : , :
85	instantiation	131, 121, 100	⊢
	: , : , :
86	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
87	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
88	theorem		⊢
	proveit.numbers.negation.complex_closure
89	instantiation	131, 121, 101	⊢
	: , : , :
90	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
91	axiom		⊢
	proveit.logic.equality.equals_reflexivity
92	instantiation	131, 103, 102	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
94	instantiation	131, 103, 104	⊢
	: , : , :
95	axiom		⊢
	proveit.logic.equality.equals_transitivity
96	instantiation	105, 106	⊢
	: , : , :
97	instantiation	107, 115	⊢
	:
98	instantiation	108, 115	⊢
	:
99	instantiation	131, 110, 109	⊢
	: , : , :
100	instantiation	131, 110, 118	⊢
	: , : , :
101	instantiation	131, 110, 111	⊢
	: , : , :
102	instantiation	131, 112, 133	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
104	instantiation	131, 112, 113	⊢
	: , : , :
105	axiom		⊢
	proveit.logic.equality.substitution
106	instantiation	114, 115	⊢
	:
107	theorem		⊢
	proveit.numbers.division.frac_one_denom
108	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
109	instantiation	131, 126, 116	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
111	instantiation	117, 118, 119, 120	⊢
	: , :
112	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
113	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
114	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
115	instantiation	131, 121, 122	⊢
	: , : , :
116	instantiation	131, 123, 124	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.division.div_rational_closure
118	instantiation	131, 126, 125	⊢
	: , : , :
119	instantiation	131, 126, 127	⊢
	: , : , :
120	instantiation	128, 133	⊢
	:
121	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
122	instantiation	129, 130, 133	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
124	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
125	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
126	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
127	instantiation	131, 132, 133	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
129	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
130	instantiation	134, 135	⊢
	: , :
131	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
132	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
133	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
134	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
135	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements