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, 85, 6	⊢
	: , :
3	instantiation	7, 44, 8, 9, 10, 11*	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.rounding.ceil_increasing_less_eq
5	instantiation	88, 109, 13, 90	⊢
	: , :
6	instantiation	12, 109, 13, 89, 14, 101	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
8	instantiation	15, 62, 45	⊢
	: , :
9	instantiation	74, 75, 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	127, 111, 19	⊢
	: , : , :
14	instantiation	20, 78, 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, 100, 129, 27, 28, 31, 32, 29	⊢
	: , : , : , : , : , :
18	instantiation	30, 31, 32, 33	⊢
	: , : , :
19	instantiation	64, 34, 112	⊢
	: , :
20	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
21	instantiation	127, 123, 35	⊢
	: , : , :
22	instantiation	127, 36, 93	⊢
	: , : , :
23	instantiation	37, 38, 107, 109, 39	⊢
	: , : , :
24	instantiation	40, 91, 126, 41*, 42*, 43*	⊢
	: , : , : , :
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	79	⊢
	: , :
29	instantiation	127, 87, 44	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
31	instantiation	127, 87, 62	⊢
	: , : , :
32	instantiation	127, 87, 45	⊢
	: , : , :
33	instantiation	46	⊢
	:
34	instantiation	127, 116, 47	⊢
	: , : , :
35	instantiation	127, 48, 49	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
37	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
38	instantiation	127, 50, 51	⊢
	: , : , :
39	instantiation	52, 78, 114, 121, 53, 54, 55*	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
41	instantiation	56, 68	⊢
	:
42	instantiation	57, 58, 59	⊢
	: , : , :
43	instantiation	60, 68	⊢
	:
44	instantiation	61, 62	⊢
	:
45	instantiation	127, 123, 63	⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.equals_reflexivity
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
49	instantiation	64, 102, 112	⊢
	: , :
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
51	instantiation	127, 65, 129	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
53	instantiation	66, 120, 121, 122	⊢
	: , : , :
54	instantiation	67, 100	⊢
	:
55	instantiation	80, 68	⊢
	:
56	theorem		⊢
	proveit.numbers.division.frac_one_denom
57	axiom		⊢
	proveit.logic.equality.equals_transitivity
58	instantiation	69, 100, 70, 71, 72, 73	⊢
	: , : , : , :
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	74, 75, 76	⊢
	: , : , :
63	instantiation	127, 125, 77	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
67	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
68	instantiation	127, 87, 78	⊢
	: , : , :
69	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
70	instantiation	79	⊢
	: , :
71	instantiation	79	⊢
	: , :
72	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
73	instantiation	80, 81	⊢
	:
74	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
75	instantiation	82, 83	⊢
	: , :
76	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
77	instantiation	84, 85	⊢
	:
78	instantiation	127, 123, 86	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
80	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
81	instantiation	127, 87, 121	⊢
	: , : , :
82	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
84	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
85	instantiation	88, 109, 89, 90	⊢
	: , :
86	instantiation	127, 125, 91	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
88	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
89	instantiation	92, 109, 93	⊢
	: , :
90	instantiation	94, 95	⊢
	: , :
91	instantiation	127, 128, 100	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
93	instantiation	96, 97, 107, 98	⊢
	: , :
94	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
95	instantiation	99, 129, 100, 101	⊢
	: , :
96	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
97	instantiation	127, 111, 102	⊢
	: , : , :
98	instantiation	103, 104	⊢
	:
99	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
100	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
101	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
102	instantiation	127, 116, 105	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
104	instantiation	127, 106, 107	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
107	instantiation	108, 109, 110	⊢
	: , :
108	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
109	instantiation	127, 111, 112	⊢
	: , : , :
110	instantiation	113, 114, 115	⊢
	:
111	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
112	instantiation	127, 116, 117	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
114	instantiation	118, 120, 121, 122	⊢
	: , : , :
115	instantiation	119, 120, 121, 122	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
117	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
120	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
121	instantiation	127, 123, 124	⊢
	: , : , :
122	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
124	instantiation	127, 125, 126	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
126	instantiation	127, 128, 129	⊢
	: , : , :
127	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
128	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
129	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements