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	5, 4, 7	⊢
	: , : , :
3	instantiation	5, 6, 7	⊢
	: , : , :
4	instantiation	8, 12, 25, 13, 9, 10*, 15*	⊢
	: , : , :
5	theorem		⊢
	proveit.logic.equality.sub_left_side_into
6	instantiation	11, 12, 13, 124, 14, 15*, 16*	⊢
	: , : , :
7	instantiation	84, 17, 18	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
9	instantiation	19, 25, 124, 26	⊢
	: , : , :
10	instantiation	84, 20, 21	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
12	instantiation	22, 112	⊢
	:
13	instantiation	23, 25, 124, 26	⊢
	: , : , :
14	instantiation	24, 25, 124, 26	⊢
	: , : , :
15	instantiation	116, 27, 28	⊢
	: , : , :
16	instantiation	29, 145, 30, 147, 98*, 31*, 32*	⊢
	: , : , : , :
17	instantiation	84, 33, 34	⊢
	: , : , :
18	instantiation	84, 35, 36	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
20	instantiation	37, 44	⊢
	:
21	instantiation	38, 44, 39	⊢
	: , :
22	theorem		⊢
	proveit.numbers.negation.real_closure
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
26	instantiation	40, 102, 41*	⊢
	:
27	instantiation	57, 58, 42, 150, 59, 43, 61, 64, 62, 44	⊢
	: , : , : , : , : , :
28	instantiation	45, 150, 58, 59, 61, 64, 62, 46	⊢
	: , : , : , : , : , : , : , :
29	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
30	instantiation	47, 145	⊢
	:
31	instantiation	48, 108, 81, 126	⊢
	: , :
32	instantiation	116, 49, 50	⊢
	: , : , :
33	instantiation	130, 51	⊢
	: , : , :
34	instantiation	52, 150, 58, 59, 143, 53, 54, 55*	⊢
	: , : , : , : , : , :
35	axiom		⊢
	proveit.physics.quantum.QPE._best_round_def
36	instantiation	56, 111	⊢
	:
37	theorem		⊢
	proveit.numbers.addition.elim_zero_right
38	theorem		⊢
	proveit.numbers.addition.commutation
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
40	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
41	instantiation	57, 58, 153, 150, 59, 60, 61, 64, 62	⊢
	: , : , : , : , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
43	instantiation	63	⊢
	: , : , :
44	instantiation	78, 64	⊢
	:
45	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
46	instantiation	65	⊢
	:
47	theorem		⊢
	proveit.numbers.negation.int_closure
48	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
49	instantiation	66, 153, 67, 68, 69, 70	⊢
	: , : , : , :
50	instantiation	71, 108, 81, 72	⊢
	: , : , :
51	instantiation	73, 144	⊢
	:
52	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
53	instantiation	151, 148, 122	⊢
	: , : , :
54	instantiation	74, 109, 143, 75	⊢
	: , :
55	instantiation	84, 76, 77	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.rounding.round_in_terms_of_floor
57	theorem		⊢
	proveit.numbers.addition.disassociation
58	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
59	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
60	instantiation	80	⊢
	: , :
61	instantiation	151, 148, 111	⊢
	: , : , :
62	instantiation	78, 79	⊢
	:
63	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
64	instantiation	151, 148, 112	⊢
	: , : , :
65	axiom		⊢
	proveit.logic.equality.equals_reflexivity
66	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
67	instantiation	80	⊢
	: , :
68	instantiation	80	⊢
	: , :
69	instantiation	142, 81	⊢
	:
70	instantiation	82, 108, 83*	⊢
	: , :
71	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
72	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
73	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
74	theorem		⊢
	proveit.numbers.division.div_complex_closure
75	instantiation	138, 156	⊢
	:
76	instantiation	84, 85, 86	⊢
	: , : , :
77	instantiation	87, 88, 89, 90	⊢
	: , : , : , :
78	theorem		⊢
	proveit.numbers.negation.complex_closure
79	instantiation	154, 91, 92	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
81	instantiation	151, 148, 125	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
83	instantiation	133, 108	⊢
	:
84	theorem		⊢
	proveit.logic.equality.sub_right_side_into
85	instantiation	93, 108, 109, 94, 95	⊢
	: , : , : , : , :
86	instantiation	116, 96, 97	⊢
	: , : , :
87	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
88	instantiation	130, 98	⊢
	: , : , :
89	instantiation	130, 99	⊢
	: , : , :
90	instantiation	142, 109	⊢
	:
91	instantiation	157, 100	⊢
	: , :
92	instantiation	101, 102	⊢
	:
93	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
94	instantiation	151, 104, 103	⊢
	: , : , :
95	instantiation	151, 104, 105	⊢
	: , : , :
96	instantiation	130, 106	⊢
	: , : , :
97	instantiation	130, 107	⊢
	: , : , :
98	instantiation	132, 108	⊢
	:
99	instantiation	132, 109	⊢
	:
100	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.int_within_complex
101	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
102	instantiation	110, 111, 112	⊢
	: , :
103	instantiation	151, 114, 113	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
105	instantiation	151, 114, 115	⊢
	: , : , :
106	instantiation	116, 117, 118	⊢
	: , : , :
107	instantiation	130, 119	⊢
	: , : , :
108	instantiation	151, 148, 124	⊢
	: , : , :
109	instantiation	151, 148, 120	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
111	instantiation	121, 149, 122	⊢
	: , :
112	instantiation	123, 124, 125, 126	⊢
	: , :
113	instantiation	151, 128, 127	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
115	instantiation	151, 128, 129	⊢
	: , : , :
116	axiom		⊢
	proveit.logic.equality.equals_transitivity
117	instantiation	130, 131	⊢
	: , : , :
118	instantiation	132, 143	⊢
	:
119	instantiation	133, 143	⊢
	:
120	instantiation	151, 136, 134	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
122	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
123	theorem		⊢
	proveit.numbers.division.div_real_closure
124	instantiation	151, 136, 135	⊢
	: , : , :
125	instantiation	151, 136, 137	⊢
	: , : , :
126	instantiation	138, 139	⊢
	:
127	instantiation	151, 140, 156	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
129	instantiation	151, 140, 141	⊢
	: , : , :
130	axiom		⊢
	proveit.logic.equality.substitution
131	instantiation	142, 143	⊢
	:
132	theorem		⊢
	proveit.numbers.division.frac_one_denom
133	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
134	instantiation	151, 146, 144	⊢
	: , : , :
135	instantiation	151, 146, 145	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
137	instantiation	151, 146, 147	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
139	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
140	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
141	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
142	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
143	instantiation	151, 148, 149	⊢
	: , : , :
144	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
145	instantiation	151, 152, 150	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
147	instantiation	151, 152, 153	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
149	instantiation	154, 155, 156	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
151	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
152	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
153	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
154	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
155	instantiation	157, 158	⊢
	: , :
156	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
157	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
158	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements