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	modus ponens	1, 2	⊢
1	instantiation	3	⊢
	: , : , :
2	generalization	4	⊢
3	theorem		⊢
	proveit.numbers.summation.weak_summation_from_summands_bound
4	instantiation	5, 6, 7	,  ⊢
	:
5	theorem		⊢
	proveit.physics.quantum.QPE._alpha_sqrd_upper_bound
6	instantiation	8, 9, 85, 15, 10	,  ⊢
	: , : , :
7	instantiation	105, 11	,  ⊢
	:
8	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
9	instantiation	84, 56, 124	⊢
	: , :
10	instantiation	12, 13, 14	,  ⊢
	: , :
11	instantiation	53, 15, 22	,  ⊢
	:
12	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
13	instantiation	16, 17	,  ⊢
	: , :
14	instantiation	18, 36, 85, 37	,  ⊢
	: , : , :
15	instantiation	128, 19, 37	,  ⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.ordering.relax_less
17	instantiation	20, 21, 22	,  ⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
19	instantiation	74, 36, 85	⊢
	: , :
20	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
21	instantiation	23, 38, 112, 24, 25, 26*, 27*	⊢
	: , : , :
22	instantiation	63, 28, 29	,  ⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
24	instantiation	108, 109, 98	⊢
	: , : , :
25	instantiation	30, 98	⊢
	:
26	instantiation	87, 102, 31	⊢
	: , :
27	instantiation	39, 32, 33	⊢
	: , : , :
28	instantiation	34, 35	⊢
	:
29	instantiation	75, 36, 85, 37	,  ⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
31	instantiation	128, 111, 38	⊢
	: , : , :
32	instantiation	39, 40, 41	⊢
	: , : , :
33	instantiation	42, 43, 44	⊢
	: , :
34	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
35	instantiation	45, 46, 96	⊢
	: , :
36	instantiation	84, 54, 124	⊢
	: , :
37	assumption		⊢
38	instantiation	128, 118, 47	⊢
	: , : , :
39	axiom		⊢
	proveit.logic.equality.equals_transitivity
40	instantiation	81, 57	⊢
	: , : , :
41	instantiation	81, 48	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
43	instantiation	49, 50, 51	⊢
	: , :
44	instantiation	52	⊢
	:
45	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
46	instantiation	53, 54, 55	⊢
	:
47	instantiation	128, 123, 56	⊢
	: , : , :
48	instantiation	81, 57	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
50	instantiation	58, 102, 59, 60	⊢
	: , :
51	instantiation	128, 111, 61	⊢
	: , : , :
52	axiom		⊢
	proveit.logic.equality.equals_reflexivity
53	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
54	instantiation	128, 62, 77	⊢
	: , : , :
55	instantiation	63, 64, 65	⊢
	: , : , :
56	instantiation	99, 85	⊢
	:
57	instantiation	66, 67, 68, 69	⊢
	: , : , : , :
58	theorem		⊢
	proveit.numbers.division.div_complex_closure
59	instantiation	70, 91, 102	⊢
	: , :
60	instantiation	71, 93, 72	⊢
	: , : , :
61	instantiation	108, 109, 73	⊢
	: , : , :
62	instantiation	74, 124, 76	⊢
	: , :
63	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
64	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
65	instantiation	75, 124, 76, 77	⊢
	: , : , :
66	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
67	instantiation	81, 78	⊢
	: , : , :
68	instantiation	79, 80	⊢
	: , :
69	instantiation	81, 82	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
71	theorem		⊢
	proveit.logic.equality.sub_left_side_into
72	instantiation	83, 91	⊢
	:
73	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
74	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
75	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
76	instantiation	84, 85, 86	⊢
	: , :
77	assumption		⊢
78	instantiation	87, 88, 89	⊢
	: , :
79	theorem		⊢
	proveit.logic.equality.equals_reversal
80	instantiation	90, 91, 92, 100, 93	⊢
	: , : , :
81	axiom		⊢
	proveit.logic.equality.substitution
82	instantiation	94, 95, 96	⊢
	: , :
83	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
84	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
85	instantiation	128, 97, 98	⊢
	: , : , :
86	instantiation	99, 120	⊢
	:
87	theorem		⊢
	proveit.numbers.addition.commutation
88	instantiation	128, 111, 100	⊢
	: , : , :
89	instantiation	101, 102	⊢
	:
90	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
91	instantiation	128, 111, 103	⊢
	: , : , :
92	instantiation	104, 112	⊢
	:
93	instantiation	105, 127	⊢
	:
94	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
95	instantiation	128, 106, 107	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
97	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
98	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
99	theorem		⊢
	proveit.numbers.negation.int_closure
100	instantiation	108, 109, 110	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.negation.complex_closure
102	instantiation	128, 111, 112	⊢
	: , : , :
103	instantiation	128, 118, 113	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.negation.real_closure
105	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
106	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
107	instantiation	128, 114, 115	⊢
	: , : , :
108	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
109	instantiation	116, 117	⊢
	: , :
110	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
111	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
112	instantiation	128, 118, 119	⊢
	: , : , :
113	instantiation	128, 123, 120	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
115	instantiation	128, 121, 122	⊢
	: , : , :
116	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
117	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
119	instantiation	128, 123, 124	⊢
	: , : , :
120	instantiation	128, 129, 125	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
122	instantiation	128, 126, 127	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
124	instantiation	128, 129, 130	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
126	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
127	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
128	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
129	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
130	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements