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