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