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.numbers.ordering.transitivity_less_eq_less_eq
2	instantiation	4, 5, 84, 6	⊢
	: , :
3	instantiation	7, 45, 8, 9, 10, 11*	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.rounding.ceil_increasing_less_eq
5	instantiation	87, 108, 13, 89	⊢
	: , :
6	instantiation	12, 108, 13, 88, 14, 100	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
8	instantiation	15, 62, 46	⊢
	: , :
9	instantiation	73, 74, 16	⊢
	: , : , :
10	axiom		⊢
	proveit.physics.quantum.QPE._t_req
11	instantiation	57, 17, 18	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less_eq
13	instantiation	95, 19, 108, 36	⊢
	: , :
14	instantiation	20, 77, 21, 22, 23, 24*	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
16	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
17	instantiation	25, 26, 99, 128, 27, 28, 31, 32, 29	⊢
	: , : , : , : , : , :
18	instantiation	30, 31, 32, 33	⊢
	: , : , :
19	instantiation	126, 110, 34	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
21	instantiation	35, 120, 77, 36	⊢
	: , :
22	instantiation	126, 37, 92	⊢
	: , : , :
23	instantiation	38, 39, 106, 108, 40	⊢
	: , : , :
24	instantiation	41, 90, 125, 42*, 43*, 44*	⊢
	: , : , : , :
25	theorem		⊢
	proveit.numbers.addition.disassociation
26	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
27	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28	instantiation	78	⊢
	: , :
29	instantiation	126, 86, 45	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
31	instantiation	126, 86, 62	⊢
	: , : , :
32	instantiation	126, 86, 46	⊢
	: , : , :
33	instantiation	47	⊢
	:
34	instantiation	126, 115, 48	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.division.div_real_closure
36	instantiation	49, 116	⊢
	:
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
38	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
39	instantiation	126, 50, 51	⊢
	: , : , :
40	instantiation	52, 77, 113, 120, 53, 54, 55*	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
42	instantiation	56, 67	⊢
	:
43	instantiation	57, 58, 59	⊢
	: , : , :
44	instantiation	60, 67	⊢
	:
45	instantiation	61, 62	⊢
	:
46	instantiation	126, 122, 63	⊢
	: , : , :
47	axiom		⊢
	proveit.logic.equality.equals_reflexivity
48	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
49	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
51	instantiation	126, 64, 128	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
53	instantiation	65, 119, 120, 121	⊢
	: , : , :
54	instantiation	66, 99	⊢
	:
55	instantiation	79, 67	⊢
	:
56	theorem		⊢
	proveit.numbers.division.frac_one_denom
57	axiom		⊢
	proveit.logic.equality.equals_transitivity
58	instantiation	68, 99, 69, 70, 71, 72	⊢
	: , : , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
60	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
61	theorem		⊢
	proveit.numbers.negation.real_closure
62	instantiation	73, 74, 75	⊢
	: , : , :
63	instantiation	126, 124, 76	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
66	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
67	instantiation	126, 86, 77	⊢
	: , : , :
68	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
69	instantiation	78	⊢
	: , :
70	instantiation	78	⊢
	: , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
72	instantiation	79, 80	⊢
	:
73	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
74	instantiation	81, 82	⊢
	: , :
75	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
76	instantiation	83, 84	⊢
	:
77	instantiation	126, 122, 85	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
79	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
80	instantiation	126, 86, 120	⊢
	: , : , :
81	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
83	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
84	instantiation	87, 108, 88, 89	⊢
	: , :
85	instantiation	126, 124, 90	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
87	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
88	instantiation	91, 108, 92	⊢
	: , :
89	instantiation	93, 94	⊢
	: , :
90	instantiation	126, 127, 99	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
92	instantiation	95, 96, 106, 97	⊢
	: , :
93	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
94	instantiation	98, 128, 99, 100	⊢
	: , :
95	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
96	instantiation	126, 110, 101	⊢
	: , : , :
97	instantiation	102, 103	⊢
	:
98	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
100	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
101	instantiation	126, 115, 104	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
103	instantiation	126, 105, 106	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
106	instantiation	107, 108, 109	⊢
	: , :
107	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
108	instantiation	126, 110, 111	⊢
	: , : , :
109	instantiation	112, 113, 114	⊢
	:
110	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
111	instantiation	126, 115, 116	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
113	instantiation	117, 119, 120, 121	⊢
	: , : , :
114	instantiation	118, 119, 120, 121	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
116	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
117	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
120	instantiation	126, 122, 123	⊢
	: , : , :
121	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
123	instantiation	126, 124, 125	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
125	instantiation	126, 127, 128	⊢
	: , : , :
126	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
127	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
128	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements