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	reference	21	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	reference	9	⊢
4	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
5	instantiation	7, 8, 9	⊢
	: , : , :
6	instantiation	10, 55, 11, 102, 12, 13, 14*, 15*	⊢
	: , : , :
7	theorem		⊢
	proveit.logic.equality.sub_left_side_into
8	instantiation	16, 134, 78, 80, 17, 18*	⊢
	: , : , : , : , : , :
9	instantiation	57, 19	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
11	instantiation	20, 96, 56	⊢
	: , :
12	instantiation	21, 22, 23	⊢
	: , : , :
13	instantiation	87, 24	⊢
	: , :
14	instantiation	25, 134, 137, 71, 26, 72, 35, 76, 36	⊢
	: , : , : , : , : , :
15	instantiation	27, 35, 28	⊢
	: , :
16	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_factor_bound
17	instantiation	29, 95, 114, 30, 31, 32*, 33*	⊢
	: , : , :
18	instantiation	34, 134, 35, 36	⊢
	: , : , : , :
19	instantiation	52, 37, 38	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
21	theorem		⊢
	proveit.logic.equality.sub_right_side_into
22	instantiation	39, 40, 41	⊢
	: , :
23	instantiation	42, 127, 43, 76, 110, 44*	⊢
	: , :
24	instantiation	45, 78	⊢
	:
25	theorem		⊢
	proveit.numbers.multiplication.disassociation
26	instantiation	94	⊢
	: , :
27	theorem		⊢
	proveit.numbers.multiplication.commutation
28	instantiation	135, 121, 102	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
30	instantiation	135, 124, 46	⊢
	: , : , :
31	instantiation	47, 114, 96, 113, 48, 49	⊢
	: , : , :
32	instantiation	50, 82, 93, 51	⊢
	: , : , :
33	instantiation	52, 53, 54	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
35	instantiation	135, 121, 55	⊢
	: , : , :
36	instantiation	135, 121, 56	⊢
	: , : , :
37	instantiation	57, 58	⊢
	: , : , :
38	instantiation	59, 110	⊢
	:
39	theorem		⊢
	proveit.numbers.absolute_value.weak_upper_bound
40	instantiation	60, 85, 102, 86	⊢
	: , : , :
41	instantiation	87, 61	⊢
	: , :
42	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
43	instantiation	94	⊢
	: , :
44	instantiation	62, 63	⊢
	:
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
46	instantiation	135, 132, 64	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
48	instantiation	65, 114, 113, 66, 67, 68, 69*	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
50	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
51	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
52	axiom		⊢
	proveit.logic.equality.equals_transitivity
53	instantiation	70, 71, 137, 134, 72, 73, 76, 82, 74	⊢
	: , : , : , : , : , :
54	instantiation	75, 82, 76, 77	⊢
	: , : , :
55	instantiation	135, 79, 78	⊢
	: , : , :
56	instantiation	135, 79, 80	⊢
	: , : , :
57	axiom		⊢
	proveit.logic.equality.substitution
58	instantiation	81, 82, 110, 83*	⊢
	: , :
59	theorem		⊢
	proveit.numbers.absolute_value.abs_even
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
61	instantiation	84, 85, 102, 86	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
63	instantiation	87, 88	⊢
	: , :
64	instantiation	135, 136, 89	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
66	instantiation	107, 108, 91	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
68	instantiation	90, 91	⊢
	:
69	instantiation	92, 93	⊢
	:
70	theorem		⊢
	proveit.numbers.addition.disassociation
71	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
72	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
73	instantiation	94	⊢
	: , :
74	instantiation	135, 121, 95	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
76	instantiation	135, 121, 96	⊢
	: , : , :
77	instantiation	97	⊢
	:
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
79	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
80	instantiation	98, 99	⊢
	:
81	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
82	instantiation	135, 121, 113	⊢
	: , : , :
83	instantiation	100, 110	⊢
	:
84	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
85	instantiation	101, 102	⊢
	:
86	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_round_in_interval
87	theorem		⊢
	proveit.numbers.ordering.relax_less
88	instantiation	103, 117	⊢
	:
89	instantiation	104, 105, 134	⊢
	: , :
90	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
91	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
92	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
93	instantiation	135, 121, 114	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
95	instantiation	135, 124, 106	⊢
	: , : , :
96	instantiation	107, 108, 117	⊢
	: , : , :
97	axiom		⊢
	proveit.logic.equality.equals_reflexivity
98	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
99	instantiation	109, 110, 111	⊢
	:
100	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
101	theorem		⊢
	proveit.numbers.negation.real_closure
102	instantiation	112, 113, 114, 115	⊢
	: , :
103	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
104	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
105	instantiation	135, 116, 117	⊢
	: , : , :
106	instantiation	135, 132, 118	⊢
	: , : , :
107	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
108	instantiation	119, 120	⊢
	: , :
109	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
110	instantiation	135, 121, 122	⊢
	: , : , :
111	assumption		⊢
112	theorem		⊢
	proveit.numbers.division.div_real_closure
113	instantiation	135, 124, 123	⊢
	: , : , :
114	instantiation	135, 124, 125	⊢
	: , : , :
115	instantiation	126, 127	⊢
	:
116	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
117	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
118	instantiation	128, 131	⊢
	:
119	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
120	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
121	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
122	instantiation	129, 130	⊢
	:
123	instantiation	135, 132, 131	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
125	instantiation	135, 132, 133	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
127	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
128	theorem		⊢
	proveit.numbers.negation.int_closure
129	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
130	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
131	instantiation	135, 136, 134	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
133	instantiation	135, 136, 137	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
135	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
136	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
137	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements