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