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.equality.sub_left_side_into
2	instantiation	4, 5, 6, 111, 7, 8*, 9*	⊢
	: , : , :
3	instantiation	71, 10, 11	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
5	instantiation	12, 99	⊢
	:
6	instantiation	13, 15, 111, 16	⊢
	: , : , :
7	instantiation	14, 15, 111, 16	⊢
	: , : , :
8	instantiation	103, 17, 18	⊢
	: , : , :
9	instantiation	19, 132, 20, 134, 85*, 21*, 22*	⊢
	: , : , : , :
10	instantiation	71, 23, 24	⊢
	: , : , :
11	instantiation	71, 25, 26	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.negation.real_closure
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
14	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
16	instantiation	27, 89, 28*	⊢
	:
17	instantiation	44, 45, 29, 137, 46, 30, 48, 51, 49, 31	⊢
	: , : , : , : , : , :
18	instantiation	32, 137, 45, 46, 48, 51, 49, 33	⊢
	: , : , : , : , : , : , : , :
19	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
20	instantiation	34, 132	⊢
	:
21	instantiation	35, 95, 68, 113	⊢
	: , :
22	instantiation	103, 36, 37	⊢
	: , : , :
23	instantiation	117, 38	⊢
	: , : , :
24	instantiation	39, 137, 45, 46, 130, 40, 41, 42*	⊢
	: , : , : , : , : , :
25	axiom		⊢
	proveit.physics.quantum.QPE._best_round_def
26	instantiation	43, 98	⊢
	:
27	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
28	instantiation	44, 45, 140, 137, 46, 47, 48, 51, 49	⊢
	: , : , : , : , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
30	instantiation	50	⊢
	: , : , :
31	instantiation	65, 51	⊢
	:
32	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
33	instantiation	52	⊢
	:
34	theorem		⊢
	proveit.numbers.negation.int_closure
35	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
36	instantiation	53, 140, 54, 55, 56, 57	⊢
	: , : , : , :
37	instantiation	58, 95, 68, 59	⊢
	: , : , :
38	instantiation	60, 131	⊢
	:
39	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
40	instantiation	138, 135, 109	⊢
	: , : , :
41	instantiation	61, 96, 130, 62	⊢
	: , :
42	instantiation	71, 63, 64	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.rounding.round_in_terms_of_floor
44	theorem		⊢
	proveit.numbers.addition.disassociation
45	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
46	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
47	instantiation	67	⊢
	: , :
48	instantiation	138, 135, 98	⊢
	: , : , :
49	instantiation	65, 66	⊢
	:
50	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
51	instantiation	138, 135, 99	⊢
	: , : , :
52	axiom		⊢
	proveit.logic.equality.equals_reflexivity
53	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
54	instantiation	67	⊢
	: , :
55	instantiation	67	⊢
	: , :
56	instantiation	129, 68	⊢
	:
57	instantiation	69, 95, 70*	⊢
	: , :
58	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
59	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
60	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
61	theorem		⊢
	proveit.numbers.division.div_complex_closure
62	instantiation	125, 143	⊢
	:
63	instantiation	71, 72, 73	⊢
	: , : , :
64	instantiation	74, 75, 76, 77	⊢
	: , : , : , :
65	theorem		⊢
	proveit.numbers.negation.complex_closure
66	instantiation	141, 78, 79	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
68	instantiation	138, 135, 112	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
70	instantiation	120, 95	⊢
	:
71	theorem		⊢
	proveit.logic.equality.sub_right_side_into
72	instantiation	80, 95, 96, 81, 82	⊢
	: , : , : , : , :
73	instantiation	103, 83, 84	⊢
	: , : , :
74	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
75	instantiation	117, 85	⊢
	: , : , :
76	instantiation	117, 86	⊢
	: , : , :
77	instantiation	129, 96	⊢
	:
78	instantiation	144, 87	⊢
	: , :
79	instantiation	88, 89	⊢
	:
80	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
81	instantiation	138, 91, 90	⊢
	: , : , :
82	instantiation	138, 91, 92	⊢
	: , : , :
83	instantiation	117, 93	⊢
	: , : , :
84	instantiation	117, 94	⊢
	: , : , :
85	instantiation	119, 95	⊢
	:
86	instantiation	119, 96	⊢
	:
87	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.int_within_complex
88	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
89	instantiation	97, 98, 99	⊢
	: , :
90	instantiation	138, 101, 100	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
92	instantiation	138, 101, 102	⊢
	: , : , :
93	instantiation	103, 104, 105	⊢
	: , : , :
94	instantiation	117, 106	⊢
	: , : , :
95	instantiation	138, 135, 111	⊢
	: , : , :
96	instantiation	138, 135, 107	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
98	instantiation	108, 136, 109	⊢
	: , :
99	instantiation	110, 111, 112, 113	⊢
	: , :
100	instantiation	138, 115, 114	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
102	instantiation	138, 115, 116	⊢
	: , : , :
103	axiom		⊢
	proveit.logic.equality.equals_transitivity
104	instantiation	117, 118	⊢
	: , : , :
105	instantiation	119, 130	⊢
	:
106	instantiation	120, 130	⊢
	:
107	instantiation	138, 123, 121	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
109	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
110	theorem		⊢
	proveit.numbers.division.div_real_closure
111	instantiation	138, 123, 122	⊢
	: , : , :
112	instantiation	138, 123, 124	⊢
	: , : , :
113	instantiation	125, 126	⊢
	:
114	instantiation	138, 127, 143	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
116	instantiation	138, 127, 128	⊢
	: , : , :
117	axiom		⊢
	proveit.logic.equality.substitution
118	instantiation	129, 130	⊢
	:
119	theorem		⊢
	proveit.numbers.division.frac_one_denom
120	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
121	instantiation	138, 133, 131	⊢
	: , : , :
122	instantiation	138, 133, 132	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
124	instantiation	138, 133, 134	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
126	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
127	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
128	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
129	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
130	instantiation	138, 135, 136	⊢
	: , : , :
131	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
132	instantiation	138, 139, 137	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
134	instantiation	138, 139, 140	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
136	instantiation	141, 142, 143	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
138	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
139	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
140	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
141	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
142	instantiation	144, 145	⊢
	: , :
143	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
144	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
145	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements