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.rhs_via_equality
2	literal generalization	4	⊢
3	instantiation	21, 5, 6*, 7*	⊢
	: , : , :
4	instantiation	8, 15, 9*, 10*	⊢
	:
5	modus ponens	11, 12	⊢
6	instantiation	13, 160	⊢
	: , :
7	instantiation	13, 160	⊢
	: , :
8	theorem		⊢
	proveit.physics.quantum.QPE._outcome_prob
9	modus ponens	14, 15	⊢
10	instantiation	92, 16, 17	⊢
	: , : , :
11	instantiation	18, 19	⊢
	: , : , : , : , : , : , :
12	generalization	20	⊢
13	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
14	theorem		⊢
	proveit.physics.quantum.QPE._alpha_ideal_case
15	assumption		⊢
16	instantiation	21, 22	⊢
	: , : , :
17	instantiation	23, 24	⊢
	:
18	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
19	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
20	instantiation	25, 26	⊢
	: , : , :
21	axiom		⊢
	proveit.logic.equality.substitution
22	instantiation	27, 28	⊢
	:
23	theorem		⊢
	proveit.numbers.exponentiation.exponentiated_one
24	instantiation	158, 128, 29	⊢
	: , : , :
25	axiom		⊢
	proveit.core_expr_types.conditionals.condition_replacement
26	instantiation	30, 31, 32	⊢
	: , :
27	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
28	instantiation	33, 151	⊢
	:
29	instantiation	158, 141, 34	⊢
	: , : , :
30	theorem		⊢
	proveit.logic.booleans.implication.iff_intro
31	deduction	35	⊢
32	deduction	36	⊢
33	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
34	instantiation	158, 149, 154	⊢
	: , : , :
35	instantiation	41, 46, 37, 38, 39, 40	⊢
	: , :
36	instantiation	41, 42, 43, 118, 112, 44, 45	,  ⊢
	: , :
37	instantiation	54	⊢
	: , : , :
38	instantiation	130, 131, 46, 132, 47, 49	⊢
	: , : , : , : , :
39	instantiation	130, 151, 157, 48, 49	⊢
	: , : , : , : , :
40	instantiation	130, 157, 151, 51, 49	⊢
	: , : , : , : , :
41	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
43	instantiation	50	⊢
	: , : , : , :
44	instantiation	130, 157, 131, 51, 132, 134	⊢
	: , : , : , : , :
45	instantiation	52, 82, 99, 118, 53	,  ⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
47	instantiation	54	⊢
	: , : , :
48	instantiation	143	⊢
	: , :
49	assumption		⊢
50	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
51	instantiation	143	⊢
	: , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalCO
53	instantiation	55, 56, 57	,  ⊢
	: , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
55	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
56	instantiation	72, 129, 82, 73, 58, 76, 59*, 77*	,  ⊢
	: , : , :
57	instantiation	60, 61, 62	,  ⊢
	: , : , :
58	instantiation	63, 123, 124, 112	,  ⊢
	: , : , :
59	instantiation	64, 117, 96	⊢
	:
60	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
61	instantiation	65, 66, 67	,  ⊢
	: , : , :
62	instantiation	68, 99, 69, 82, 70, 71*	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
64	theorem		⊢
	proveit.numbers.division.frac_zero_numer
65	theorem		⊢
	proveit.logic.equality.sub_right_side_into
66	instantiation	72, 129, 73, 74, 75, 76, 77*	,  ⊢
	: , : , :
67	instantiation	78, 117, 87, 96, 79*	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
69	instantiation	80, 83	⊢
	:
70	instantiation	81, 82, 83, 84, 85*	⊢
	: , :
71	instantiation	86, 87	⊢
	:
72	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
73	instantiation	158, 141, 88	,  ⊢
	: , : , :
74	instantiation	158, 141, 89	⊢
	: , : , :
75	instantiation	90, 123, 124, 112	,  ⊢
	: , : , :
76	instantiation	91, 146	⊢
	:
77	instantiation	92, 93, 94	,  ⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.division.distribute_frac_through_subtract
79	instantiation	95, 117, 96	⊢
	:
80	theorem		⊢
	proveit.numbers.negation.real_closure
81	theorem		⊢
	proveit.numbers.negation.negated_strong_bound
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
83	instantiation	158, 141, 97	⊢
	: , : , :
84	instantiation	98, 109	⊢
	:
85	theorem		⊢
	proveit.numbers.negation.negated_zero
86	theorem		⊢
	proveit.numbers.addition.elim_zero_right
87	instantiation	158, 128, 99	⊢
	: , : , :
88	instantiation	158, 149, 100	,  ⊢
	: , : , :
89	instantiation	158, 149, 124	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
91	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
92	axiom		⊢
	proveit.logic.equality.equals_transitivity
93	instantiation	101, 102, 103, 106, 104*	,  ⊢
	: , : , :
94	instantiation	105, 106	⊢
	:
95	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
96	instantiation	107, 146	⊢
	:
97	instantiation	158, 108, 109	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
99	instantiation	158, 141, 110	⊢
	: , : , :
100	instantiation	158, 111, 112	,  ⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.division.frac_cancel_left
102	instantiation	158, 114, 113	⊢
	: , : , :
103	instantiation	158, 114, 115	⊢
	: , : , :
104	instantiation	116, 117	⊢
	:
105	theorem		⊢
	proveit.numbers.division.frac_one_denom
106	instantiation	158, 128, 118	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
108	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
109	instantiation	119, 120, 121	⊢
	: , :
110	instantiation	158, 149, 145	⊢
	: , : , :
111	instantiation	122, 123, 124	⊢
	: , :
112	instantiation	130, 151, 134	⊢
	: , : , : , : , :
113	instantiation	158, 126, 125	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
115	instantiation	158, 126, 127	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
117	instantiation	158, 128, 129	⊢
	: , : , :
118	instantiation	130, 131, 157, 132, 133, 134	⊢
	: , : , : , : , :
119	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
120	instantiation	158, 135, 148	⊢
	: , : , :
121	instantiation	158, 135, 146	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
123	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
124	instantiation	136, 150, 137	⊢
	: , :
125	instantiation	158, 139, 138	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
127	instantiation	158, 139, 140	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
129	instantiation	158, 141, 142	⊢
	: , : , :
130	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
131	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
132	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
133	instantiation	143	⊢
	: , :
134	assumption		⊢
135	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
136	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
137	instantiation	144, 145	⊢
	:
138	instantiation	158, 147, 146	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
140	instantiation	158, 147, 148	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
142	instantiation	158, 149, 150	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
144	theorem		⊢
	proveit.numbers.negation.int_closure
145	instantiation	158, 156, 151	⊢
	: , : , :
146	instantiation	152, 157, 155	⊢
	: , :
147	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
148	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
149	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
150	instantiation	153, 154, 155	⊢
	: , :
151	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
152	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
153	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
154	instantiation	158, 156, 157	⊢
	: , : , :
155	instantiation	158, 159, 160	⊢
	: , : , :
156	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
157	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
158	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
159	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
160	assumption		⊢
*equality replacement requirements