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.logic.equality.sub_right_side_into
2	instantiation	4, 72, 5, 127, 6, 7, 8*	⊢
	: , : , :
3	instantiation	9, 10, 76, 54, 17, 11*	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.division.strong_div_from_numer_bound__pos_denom
5	instantiation	67, 22, 25	⊢
	: , :
6	instantiation	12, 13, 14	⊢
	: , : , :
7	instantiation	15, 103	⊢
	:
8	instantiation	16, 110, 54, 17, 18*	⊢
	: , :
9	theorem		⊢
	proveit.numbers.division.distribute_frac_through_subtract
10	instantiation	169, 130, 22	⊢
	: , : , :
11	instantiation	96, 19, 20	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
13	instantiation	21, 25, 22, 108, 23	⊢
	: , : , :
14	instantiation	24, 108, 25, 26, 27, 28*	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
16	theorem		⊢
	proveit.numbers.division.div_as_mult
17	instantiation	79, 103	⊢
	:
18	instantiation	96, 29, 30	⊢
	: , : , :
19	instantiation	31, 32, 33, 36, 34*	⊢
	: , : , :
20	instantiation	35, 36	⊢
	:
21	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
22	instantiation	37, 39, 108, 40	⊢
	: , : , :
23	instantiation	38, 39, 108, 40	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
25	instantiation	140, 88	⊢
	:
26	instantiation	67, 127, 131	⊢
	: , :
27	instantiation	41, 131, 124, 88, 42, 43, 44*, 45*	⊢
	: , : , :
28	instantiation	96, 46, 47	⊢
	: , : , :
29	instantiation	89, 48	⊢
	: , : , :
30	instantiation	49, 102, 50, 129, 65, 51*	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.division.frac_cancel_left
32	instantiation	169, 99, 52	⊢
	: , : , :
33	instantiation	169, 99, 53	⊢
	: , : , :
34	instantiation	95, 54	⊢
	:
35	theorem		⊢
	proveit.numbers.division.frac_one_denom
36	instantiation	169, 130, 55	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
40	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
41	theorem		⊢
	proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound
42	instantiation	56, 149, 164, 137	⊢
	: , : , :
43	instantiation	57, 58	⊢
	: , :
44	instantiation	60, 93, 76, 59*	⊢
	: , :
45	instantiation	60, 93, 106, 61*	⊢
	: , :
46	instantiation	111, 166, 155, 112, 62, 113, 93, 110, 118	⊢
	: , : , : , : , : , :
47	instantiation	116, 93, 110, 63	⊢
	: , : , :
48	instantiation	64, 102, 141, 131, 65, 66*	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
50	instantiation	67, 141, 131	⊢
	: , :
51	instantiation	96, 68, 69	⊢
	: , : , :
52	instantiation	169, 120, 70	⊢
	: , : , :
53	instantiation	169, 120, 71	⊢
	: , : , :
54	instantiation	169, 130, 72	⊢
	: , : , :
55	instantiation	73, 74	⊢
	:
56	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
57	theorem		⊢
	proveit.numbers.ordering.relax_less
58	instantiation	75, 162	⊢
	:
59	instantiation	105, 76	⊢
	:
60	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
61	instantiation	96, 77, 78	⊢
	: , : , :
62	instantiation	128	⊢
	: , :
63	instantiation	132	⊢
	:
64	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
65	instantiation	79, 145	⊢
	:
66	instantiation	80, 117, 93, 81*	⊢
	: , :
67	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
68	instantiation	89, 82	⊢
	: , : , :
69	instantiation	83, 84, 168, 85*	⊢
	: , :
70	instantiation	169, 133, 86	⊢
	: , : , :
71	instantiation	169, 133, 87	⊢
	: , : , :
72	instantiation	150, 151, 103	⊢
	: , : , :
73	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
74	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
75	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
76	instantiation	169, 130, 88	⊢
	: , : , :
77	instantiation	89, 90	⊢
	: , : , :
78	instantiation	91, 92, 93, 94*	⊢
	: , :
79	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
80	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
81	instantiation	95, 117	⊢
	:
82	instantiation	96, 97, 98	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
84	instantiation	169, 99, 100	⊢
	: , : , :
85	instantiation	101, 102	⊢
	:
86	instantiation	169, 144, 103	⊢
	: , : , :
87	instantiation	169, 144, 168	⊢
	: , : , :
88	instantiation	169, 138, 104	⊢
	: , : , :
89	axiom		⊢
	proveit.logic.equality.substitution
90	instantiation	105, 106	⊢
	:
91	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
92	instantiation	169, 130, 107	⊢
	: , : , :
93	instantiation	169, 130, 108	⊢
	: , : , :
94	instantiation	109, 110	⊢
	:
95	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
96	axiom		⊢
	proveit.logic.equality.equals_transitivity
97	instantiation	111, 112, 155, 166, 113, 114, 117, 118, 115	⊢
	: , : , : , : , : , :
98	instantiation	116, 117, 118, 119	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
100	instantiation	169, 120, 121	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
102	instantiation	169, 130, 122	⊢
	: , : , :
103	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
104	instantiation	169, 148, 123	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
106	instantiation	169, 130, 124	⊢
	: , : , :
107	instantiation	169, 138, 125	⊢
	: , : , :
108	instantiation	169, 138, 126	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.negation.double_negation
110	instantiation	169, 130, 127	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.addition.disassociation
112	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
113	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
114	instantiation	128	⊢
	: , :
115	instantiation	169, 130, 129	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
117	instantiation	169, 130, 141	⊢
	: , : , :
118	instantiation	169, 130, 131	⊢
	: , : , :
119	instantiation	132	⊢
	:
120	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
121	instantiation	169, 133, 134	⊢
	: , : , :
122	instantiation	169, 138, 135	⊢
	: , : , :
123	instantiation	169, 136, 137	⊢
	: , : , :
124	instantiation	169, 138, 139	⊢
	: , : , :
125	instantiation	169, 148, 157	⊢
	: , : , :
126	instantiation	169, 148, 158	⊢
	: , : , :
127	instantiation	150, 151, 171	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
129	instantiation	140, 141	⊢
	:
130	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
131	instantiation	169, 142, 143	⊢
	: , : , :
132	axiom		⊢
	proveit.logic.equality.equals_reflexivity
133	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
134	instantiation	169, 144, 145	⊢
	: , : , :
135	instantiation	169, 148, 146	⊢
	: , : , :
136	instantiation	147, 149, 164	⊢
	: , :
137	assumption		⊢
138	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
139	instantiation	169, 148, 149	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.negation.real_closure
141	instantiation	150, 151, 152	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
143	instantiation	169, 153, 154	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
145	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
146	instantiation	169, 165, 155	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
148	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
149	instantiation	156, 157, 158	⊢
	: , :
150	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
151	instantiation	159, 160	⊢
	: , :
152	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
153	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
154	instantiation	169, 161, 162	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
156	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
157	instantiation	163, 164	⊢
	:
158	instantiation	169, 165, 166	⊢
	: , : , :
159	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
160	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
161	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
162	instantiation	167, 168	⊢
	:
163	theorem		⊢
	proveit.numbers.negation.int_closure
164	instantiation	169, 170, 171	⊢
	: , : , :
165	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
166	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
167	theorem		⊢
	proveit.numbers.negation.int_neg_closure
168	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
169	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
170	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
171	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements