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, 5, 6	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
2	instantiation	203, 191, 7	⊢
	: , : , :
3	instantiation	100, 9, 10	⊢
	: , :
4	instantiation	100, 9, 11	⊢
	: , :
5	instantiation	8, 9, 10, 11, 12	⊢
	: , : , :
6	instantiation	105, 13	⊢
	: , :
7	instantiation	203, 14, 24	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
9	modus ponens	15, 16	⊢
10	modus ponens	17, 18	⊢
11	modus ponens	19, 20	⊢
12	modus ponens	21, 22	⊢
13	instantiation	23, 24	⊢
	:
14	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
15	instantiation	27	⊢
	: , : , :
16	generalization	25	⊢
17	instantiation	27	⊢
	: , : , :
18	generalization	26	⊢
19	instantiation	27	⊢
	: , : , :
20	generalization	28	⊢
21	instantiation	29	⊢
	: , : , :
22	generalization	30	⊢
23	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
24	instantiation	31, 54, 32	⊢
	: , :
25	instantiation	37, 186, 33, 34	,  ⊢
	: , :
26	instantiation	37, 186, 35, 36	,  ⊢
	: , :
27	theorem		⊢
	proveit.numbers.summation.summation_real_closure
28	instantiation	37, 186, 38, 39	,  ⊢
	: , :
29	theorem		⊢
	proveit.numbers.summation.weak_summation_from_summands_bound
30	instantiation	105, 40	,  ⊢
	: , :
31	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
32	instantiation	203, 65, 41	⊢
	: , : , :
33	instantiation	45, 61, 205	,  ⊢
	: , :
34	instantiation	43, 42	,  ⊢
	:
35	instantiation	45, 86, 205	,  ⊢
	: , :
36	instantiation	43, 44	,  ⊢
	:
37	theorem		⊢
	proveit.numbers.division.div_real_closure
38	instantiation	45, 58, 205	,  ⊢
	: , :
39	instantiation	46, 66	,  ⊢
	:
40	instantiation	47, 48, 49, 53, 50	,  ⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
42	instantiation	203, 52, 51	,  ⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
44	instantiation	203, 52, 53	,  ⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
46	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
47	theorem		⊢
	proveit.numbers.division.strong_div_from_denom_bound__all_pos
48	instantiation	203, 55, 54	⊢
	: , : , :
49	instantiation	203, 55, 56	,  ⊢
	: , : , :
50	instantiation	57, 169, 58, 86, 59, 60	,  ⊢
	: , : , :
51	instantiation	63, 61, 62	,  ⊢
	:
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
53	instantiation	63, 86, 64	,  ⊢
	:
54	instantiation	203, 65, 138	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
56	instantiation	203, 65, 66	,  ⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.exponentiation.exp_pos_less
58	instantiation	100, 101, 92	,  ⊢
	: , :
59	instantiation	67, 90, 68	,  ⊢
	: , :
60	instantiation	69, 70	⊢
	:
61	instantiation	203, 191, 71	,  ⊢
	: , : , :
62	instantiation	72, 81, 73, 74	,  ⊢
	: , :
63	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
64	instantiation	75, 76	,  ⊢
	: , :
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
66	instantiation	77, 78, 205	,  ⊢
	: , :
67	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
68	instantiation	79, 101, 92, 102, 80	,  ⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
71	instantiation	203, 196, 81	,  ⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
73	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
74	instantiation	82, 83, 84	,  ⊢
	: , : , :
75	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
76	instantiation	85, 151, 86, 87	,  ⊢
	: , :
77	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
78	instantiation	88, 89, 90	,  ⊢
	:
79	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
80	instantiation	91, 92, 118, 186, 120, 93, 94*, 95*	⊢
	: , : , :
81	instantiation	203, 96, 98	,  ⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
83	instantiation	97, 113, 114, 98	,  ⊢
	: , : , :
84	instantiation	107, 99	⊢
	:
85	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
86	instantiation	100, 101, 102	,  ⊢
	: , :
87	instantiation	123, 103	,  ⊢
	: , :
88	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
89	instantiation	193, 133, 104	,  ⊢
	: , :
90	instantiation	105, 106	,  ⊢
	: , :
91	theorem		⊢
	proveit.numbers.multiplication.reversed_strong_bound_via_right_factor_bound
92	instantiation	117, 186	⊢
	:
93	instantiation	107, 122	⊢
	:
94	instantiation	108, 177, 109*	⊢
	: , :
95	instantiation	110, 111, 112	⊢
	: , : , :
96	instantiation	189, 113, 114	⊢
	: , :
97	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
98	assumption		⊢
99	instantiation	137, 115	⊢
	:
100	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
101	instantiation	203, 191, 116	,  ⊢
	: , : , :
102	instantiation	117, 118	⊢
	:
103	instantiation	119, 120, 124	,  ⊢
	: , : , :
104	instantiation	203, 121, 122	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.ordering.relax_less
106	instantiation	123, 124	,  ⊢
	: , :
107	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
108	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
109	instantiation	125, 177	⊢
	:
110	axiom		⊢
	proveit.logic.equality.equals_transitivity
111	instantiation	126, 202, 205, 143, 145, 144, 127, 146, 147	⊢
	: , : , : , : , : , :
112	instantiation	128, 143, 205, 144, 145, 177, 146, 147, 129*	⊢
	: , : , : , : , :
113	instantiation	193, 130, 197	⊢
	: , :
114	instantiation	200, 161	⊢
	:
115	instantiation	131, 132, 138	⊢
	: , :
116	instantiation	203, 196, 133	,  ⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.negation.real_closure
118	instantiation	134, 151, 186, 136	⊢
	: , : , :
119	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
120	instantiation	135, 151, 186, 136	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
122	instantiation	137, 138	⊢
	:
123	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
124	instantiation	163, 139, 140	,  ⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
126	theorem		⊢
	proveit.numbers.multiplication.disassociation
127	instantiation	141, 177	⊢
	:
128	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
129	instantiation	142, 143, 205, 144, 145, 146, 147	⊢
	: , : , : , :
130	instantiation	200, 194	⊢
	:
131	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
132	instantiation	148, 173, 153	⊢
	:
133	instantiation	203, 149, 155	,  ⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
135	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
136	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
137	theorem		⊢
	proveit.numbers.negation.int_neg_closure
138	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
139	instantiation	150, 186, 151, 152, 153, 154*	⊢
	: , : , :
140	instantiation	174, 161, 194, 155	,  ⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.negation.complex_closure
142	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
143	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
144	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
145	instantiation	156	⊢
	: , :
146	instantiation	157, 158, 159	⊢
	: , :
147	instantiation	203, 185, 160	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
149	instantiation	189, 161, 194	⊢
	: , :
150	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
151	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
152	instantiation	203, 191, 162	⊢
	: , : , :
153	instantiation	163, 164, 165	⊢
	: , : , :
154	instantiation	166, 167, 168	⊢
	: , : , :
155	assumption		⊢
156	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
157	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
158	instantiation	203, 185, 169	⊢
	: , : , :
159	instantiation	203, 185, 170	⊢
	: , : , :
160	instantiation	171, 172	⊢
	:
161	instantiation	193, 173, 197	⊢
	: , :
162	instantiation	203, 196, 173	⊢
	: , : , :
163	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
164	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
165	instantiation	174, 197, 190, 184	⊢
	: , : , :
166	theorem		⊢
	proveit.logic.equality.sub_right_side_into
167	instantiation	175, 177	⊢
	:
168	instantiation	176, 177, 178	⊢
	: , :
169	instantiation	203, 191, 179	⊢
	: , : , :
170	instantiation	180, 181, 182	⊢
	: , : , :
171	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
172	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
173	instantiation	203, 183, 184	⊢
	: , : , :
174	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
175	theorem		⊢
	proveit.numbers.addition.elim_zero_right
176	theorem		⊢
	proveit.numbers.addition.commutation
177	instantiation	203, 185, 186	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
179	instantiation	203, 196, 201	⊢
	: , : , :
180	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
181	instantiation	187, 188	⊢
	: , :
182	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
183	instantiation	189, 197, 190	⊢
	: , :
184	assumption		⊢
185	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
186	instantiation	203, 191, 192	⊢
	: , : , :
187	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
188	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
189	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
190	instantiation	193, 194, 195	⊢
	: , :
191	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
192	instantiation	203, 196, 197	⊢
	: , : , :
193	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
194	instantiation	203, 198, 199	⊢
	: , : , :
195	instantiation	200, 201	⊢
	:
196	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
197	instantiation	203, 204, 202	⊢
	: , : , :
198	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
199	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
200	theorem		⊢
	proveit.numbers.negation.int_closure
201	instantiation	203, 204, 205	⊢
	: , : , :
202	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
203	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
204	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
205	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements