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, 4*	,  ⊢
	: , : , :
1	theorem		⊢
	proveit.logic.equality.sub_right_side_into
2	instantiation	5, 6, 7	,  ⊢
	: , : , :
3	instantiation	8, 158, 9, 10, 96, 37, 85, 11*	⊢
	: , : , :
4	instantiation	112, 12, 13	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
6	instantiation	14, 18, 15, 72, 16	,  ⊢
	: , : , :
7	instantiation	17, 72, 18, 19, 20	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.division.distribute_frac_through_sum
9	instantiation	143	⊢
	: , :
10	instantiation	171, 149, 21	⊢
	: , : , :
11	instantiation	22, 36, 37, 85, 23*	⊢
	: , :
12	instantiation	98, 24	⊢
	: , : , :
13	instantiation	112, 25, 26	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
15	instantiation	27, 57, 72, 29	⊢
	: , : , :
16	instantiation	28, 57, 72, 29	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
18	instantiation	155, 32	⊢
	:
19	instantiation	155, 31	⊢
	:
20	instantiation	30, 31, 32, 33	⊢
	: , :
21	instantiation	171, 163, 34	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
23	instantiation	35, 36, 37, 85, 38*	⊢
	: , :
24	instantiation	39, 40, 61, 41*	⊢
	: , :
25	instantiation	126, 173, 170, 127, 42, 128, 59, 45	⊢
	: , : , : , : , : , :
26	instantiation	43, 127, 170, 173, 128, 44, 59, 45, 46*	⊢
	: , : , : , : , : , :
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
29	instantiation	47, 48	⊢
	:
30	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
31	instantiation	83, 50, 84, 85	⊢
	: , :
32	instantiation	83, 51, 84, 85	⊢
	: , :
33	instantiation	49, 84, 50, 51, 52, 53	⊢
	: , : , :
34	instantiation	171, 168, 125	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.division.div_as_mult
36	instantiation	171, 149, 54	⊢
	: , : , :
37	instantiation	171, 149, 84	⊢
	: , : , :
38	instantiation	112, 55, 56	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
40	instantiation	171, 149, 57	⊢
	: , : , :
41	instantiation	58, 59	⊢
	:
42	instantiation	143	⊢
	: , :
43	theorem		⊢
	proveit.numbers.addition.association
44	instantiation	143	⊢
	: , :
45	instantiation	60, 61	⊢
	:
46	instantiation	62, 169, 165, 63*	⊢
	: , : , : , :
47	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_in_interval
48	assumption		⊢
49	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
50	instantiation	171, 163, 64	⊢
	: , : , :
51	instantiation	171, 163, 65	⊢
	: , : , :
52	instantiation	66, 111, 142, 94	⊢
	: , : , :
53	instantiation	67, 104	⊢
	:
54	instantiation	160, 161, 153	⊢
	: , : , :
55	instantiation	98, 68	⊢
	: , : , :
56	instantiation	69, 139, 70, 144, 82, 71*	⊢
	: , : , :
57	instantiation	155, 72	⊢
	:
58	theorem		⊢
	proveit.numbers.negation.double_negation
59	instantiation	171, 149, 72	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.negation.complex_closure
61	instantiation	171, 149, 73	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
63	instantiation	112, 74, 75	⊢
	: , : , :
64	instantiation	171, 168, 111	⊢
	: , : , :
65	instantiation	171, 168, 76	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
67	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
68	instantiation	77, 139, 154, 145, 82, 78*	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
70	instantiation	79, 154, 145	⊢
	: , :
71	instantiation	112, 80, 81	⊢
	: , : , :
72	instantiation	83, 156, 150, 82	⊢
	: , :
73	instantiation	83, 156, 84, 85	⊢
	: , :
74	instantiation	118, 170, 86, 87, 88, 89	⊢
	: , : , : , :
75	instantiation	90, 91, 92	⊢
	:
76	instantiation	171, 93, 94	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
78	instantiation	95, 132, 96, 97*	⊢
	: , :
79	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
80	instantiation	98, 99	⊢
	: , : , :
81	instantiation	100, 101, 102, 103*	⊢
	: , :
82	instantiation	108, 158	⊢
	:
83	theorem		⊢
	proveit.numbers.division.div_real_closure
84	instantiation	160, 161, 104	⊢
	: , : , :
85	instantiation	108, 104	⊢
	:
86	instantiation	143	⊢
	: , :
87	instantiation	143	⊢
	: , :
88	instantiation	112, 105, 106	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
90	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
91	instantiation	171, 149, 107	⊢
	: , : , :
92	instantiation	108, 109	⊢
	:
93	instantiation	110, 111, 142	⊢
	: , :
94	assumption		⊢
95	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
96	instantiation	171, 149, 156	⊢
	: , : , :
97	instantiation	138, 132	⊢
	:
98	axiom		⊢
	proveit.logic.equality.substitution
99	instantiation	112, 113, 114	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
101	instantiation	171, 115, 116	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
103	instantiation	117, 139	⊢
	:
104	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
105	instantiation	118, 170, 119, 120, 121, 122	⊢
	: , : , : , :
106	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
107	instantiation	171, 163, 123	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
109	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
110	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
111	instantiation	124, 125, 169	⊢
	: , :
112	axiom		⊢
	proveit.logic.equality.equals_transitivity
113	instantiation	126, 127, 170, 173, 128, 129, 132, 133, 130	⊢
	: , : , : , : , : , :
114	instantiation	131, 132, 133, 134	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
116	instantiation	171, 135, 136	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
118	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
119	instantiation	143	⊢
	: , :
120	instantiation	143	⊢
	: , :
121	instantiation	137, 139	⊢
	:
122	instantiation	138, 139	⊢
	:
123	instantiation	171, 168, 140	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
125	instantiation	141, 142	⊢
	:
126	theorem		⊢
	proveit.numbers.addition.disassociation
127	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
128	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
129	instantiation	143	⊢
	: , :
130	instantiation	171, 149, 144	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
132	instantiation	171, 149, 154	⊢
	: , : , :
133	instantiation	171, 149, 145	⊢
	: , : , :
134	instantiation	146	⊢
	:
135	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
136	instantiation	171, 147, 148	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
138	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
139	instantiation	171, 149, 150	⊢
	: , : , :
140	instantiation	171, 172, 151	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.negation.int_closure
142	instantiation	171, 152, 153	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
144	instantiation	155, 154	⊢
	:
145	instantiation	155, 156	⊢
	:
146	axiom		⊢
	proveit.logic.equality.equals_reflexivity
147	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
148	instantiation	171, 157, 158	⊢
	: , : , :
149	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
150	instantiation	171, 163, 159	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
152	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
153	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
154	instantiation	160, 161, 162	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.negation.real_closure
156	instantiation	171, 163, 164	⊢
	: , : , :
157	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
158	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
159	instantiation	171, 168, 165	⊢
	: , : , :
160	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
161	instantiation	166, 167	⊢
	: , :
162	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
163	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
164	instantiation	171, 168, 169	⊢
	: , : , :
165	instantiation	171, 172, 170	⊢
	: , : , :
166	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
167	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
168	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
169	instantiation	171, 172, 173	⊢
	: , : , :
170	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
171	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
172	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
173	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements