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_left_side_into
2	instantiation	4, 5, 6	,  ⊢
	: , : , :
3	instantiation	7, 118	⊢
	:
4	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
5	instantiation	8, 9, 10, 11*	,  ⊢
	: , : , :
6	instantiation	12, 149, 195, 13, 150, 14, 178	⊢
	: , : , : , : , :
7	theorem		⊢
	proveit.numbers.addition.elim_zero_left
8	theorem		⊢
	proveit.logic.equality.sub_right_side_into
9	instantiation	15, 16, 17	,  ⊢
	: , : , :
10	instantiation	18, 180, 19, 20, 118, 55, 107, 21*	⊢
	: , : , :
11	instantiation	134, 22, 23	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.term_as_strong_upper_bound
13	instantiation	89, 24	⊢
	:
14	instantiation	25, 26	⊢
	:
15	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
16	instantiation	27, 31, 28, 94, 29	,  ⊢
	: , : , :
17	instantiation	30, 94, 31, 32, 33	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.division.distribute_frac_through_sum
19	instantiation	165	⊢
	: , :
20	instantiation	193, 171, 34	⊢
	: , : , :
21	instantiation	35, 54, 55, 107, 36*	⊢
	: , :
22	instantiation	120, 37	⊢
	: , : , :
23	instantiation	134, 38, 39	⊢
	: , : , :
24	instantiation	40, 195, 149, 150, 41	⊢
	: , : , : , : , :
25	theorem		⊢
	proveit.numbers.negation.real_neg_closure
26	instantiation	42, 43, 44, 107	⊢
	: , :
27	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
28	instantiation	45, 78, 94, 47	⊢
	: , : , :
29	instantiation	46, 78, 94, 47	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
31	instantiation	177, 50	⊢
	:
32	instantiation	177, 49	⊢
	:
33	instantiation	48, 49, 50, 51	⊢
	: , :
34	instantiation	193, 185, 52	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
36	instantiation	53, 54, 55, 107, 56*	⊢
	: , :
37	instantiation	57, 58, 82, 59*	⊢
	: , :
38	instantiation	148, 195, 192, 149, 60, 150, 80, 63	⊢
	: , : , : , : , : , :
39	instantiation	61, 149, 192, 195, 150, 62, 80, 63, 64*	⊢
	: , : , : , : , : , :
40	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
41	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
42	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
43	instantiation	193, 66, 65	⊢
	: , : , :
44	instantiation	193, 66, 67	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
47	instantiation	68, 69	⊢
	:
48	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
49	instantiation	105, 71, 106, 107	⊢
	: , :
50	instantiation	105, 72, 106, 107	⊢
	: , :
51	instantiation	70, 106, 71, 72, 73, 74	⊢
	: , : , :
52	instantiation	193, 190, 147	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.division.div_as_mult
54	instantiation	193, 171, 75	⊢
	: , : , :
55	instantiation	193, 171, 106	⊢
	: , : , :
56	instantiation	134, 76, 77	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
58	instantiation	193, 171, 78	⊢
	: , : , :
59	instantiation	79, 80	⊢
	:
60	instantiation	165	⊢
	: , :
61	theorem		⊢
	proveit.numbers.addition.association
62	instantiation	165	⊢
	: , :
63	instantiation	81, 82	⊢
	:
64	instantiation	83, 191, 187, 84*	⊢
	: , : , : , :
65	instantiation	193, 85, 124	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
67	instantiation	193, 85, 126	⊢
	: , : , :
68	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_in_interval
69	assumption		⊢
70	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
71	instantiation	193, 185, 86	⊢
	: , : , :
72	instantiation	193, 185, 87	⊢
	: , : , :
73	instantiation	88, 133, 164, 116	⊢
	: , : , :
74	instantiation	89, 126	⊢
	:
75	instantiation	182, 183, 175	⊢
	: , : , :
76	instantiation	120, 90	⊢
	: , : , :
77	instantiation	91, 161, 92, 166, 104, 93*	⊢
	: , : , :
78	instantiation	177, 94	⊢
	:
79	theorem		⊢
	proveit.numbers.negation.double_negation
80	instantiation	193, 171, 94	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.negation.complex_closure
82	instantiation	193, 171, 95	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
84	instantiation	134, 96, 97	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
86	instantiation	193, 190, 133	⊢
	: , : , :
87	instantiation	193, 190, 98	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
89	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
90	instantiation	99, 161, 176, 167, 104, 100*	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
92	instantiation	101, 176, 167	⊢
	: , :
93	instantiation	134, 102, 103	⊢
	: , : , :
94	instantiation	105, 178, 172, 104	⊢
	: , :
95	instantiation	105, 178, 106, 107	⊢
	: , :
96	instantiation	140, 192, 108, 109, 110, 111	⊢
	: , : , : , :
97	instantiation	112, 113, 114	⊢
	:
98	instantiation	193, 115, 116	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
100	instantiation	117, 154, 118, 119*	⊢
	: , :
101	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
102	instantiation	120, 121	⊢
	: , : , :
103	instantiation	122, 123, 124, 125*	⊢
	: , :
104	instantiation	130, 180	⊢
	:
105	theorem		⊢
	proveit.numbers.division.div_real_closure
106	instantiation	182, 183, 126	⊢
	: , : , :
107	instantiation	130, 126	⊢
	:
108	instantiation	165	⊢
	: , :
109	instantiation	165	⊢
	: , :
110	instantiation	134, 127, 128	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
112	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
113	instantiation	193, 171, 129	⊢
	: , : , :
114	instantiation	130, 131	⊢
	:
115	instantiation	132, 133, 164	⊢
	: , :
116	assumption		⊢
117	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
118	instantiation	193, 171, 178	⊢
	: , : , :
119	instantiation	160, 154	⊢
	:
120	axiom		⊢
	proveit.logic.equality.substitution
121	instantiation	134, 135, 136	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
123	instantiation	193, 137, 138	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
125	instantiation	139, 161	⊢
	:
126	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
127	instantiation	140, 192, 141, 142, 143, 144	⊢
	: , : , : , :
128	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
129	instantiation	193, 185, 145	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
131	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
132	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
133	instantiation	146, 147, 191	⊢
	: , :
134	axiom		⊢
	proveit.logic.equality.equals_transitivity
135	instantiation	148, 149, 192, 195, 150, 151, 154, 155, 152	⊢
	: , : , : , : , : , :
136	instantiation	153, 154, 155, 156	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
138	instantiation	193, 157, 158	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
140	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
141	instantiation	165	⊢
	: , :
142	instantiation	165	⊢
	: , :
143	instantiation	159, 161	⊢
	:
144	instantiation	160, 161	⊢
	:
145	instantiation	193, 190, 162	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
147	instantiation	163, 164	⊢
	:
148	theorem		⊢
	proveit.numbers.addition.disassociation
149	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
150	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
151	instantiation	165	⊢
	: , :
152	instantiation	193, 171, 166	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
154	instantiation	193, 171, 176	⊢
	: , : , :
155	instantiation	193, 171, 167	⊢
	: , : , :
156	instantiation	168	⊢
	:
157	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
158	instantiation	193, 169, 170	⊢
	: , : , :
159	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
160	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
161	instantiation	193, 171, 172	⊢
	: , : , :
162	instantiation	193, 194, 173	⊢
	: , : , :
163	theorem		⊢
	proveit.numbers.negation.int_closure
164	instantiation	193, 174, 175	⊢
	: , : , :
165	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
166	instantiation	177, 176	⊢
	:
167	instantiation	177, 178	⊢
	:
168	axiom		⊢
	proveit.logic.equality.equals_reflexivity
169	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
170	instantiation	193, 179, 180	⊢
	: , : , :
171	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
172	instantiation	193, 185, 181	⊢
	: , : , :
173	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
174	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
175	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
176	instantiation	182, 183, 184	⊢
	: , : , :
177	theorem		⊢
	proveit.numbers.negation.real_closure
178	instantiation	193, 185, 186	⊢
	: , : , :
179	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
180	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
181	instantiation	193, 190, 187	⊢
	: , : , :
182	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
183	instantiation	188, 189	⊢
	: , :
184	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
185	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
186	instantiation	193, 190, 191	⊢
	: , : , :
187	instantiation	193, 194, 192	⊢
	: , : , :
188	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
189	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
190	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
191	instantiation	193, 194, 195	⊢
	: , : , :
192	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
193	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
194	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
195	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements