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.number_sets.integers.disjoint_intervals
2	instantiation	244, 68, 239	⊢
	: , :
3	instantiation	251, 7	⊢
	:
4	reference	7	⊢
5	reference	245	⊢
6	instantiation	8, 170, 9, 10, 11, 12	⊢
	: , :
7	instantiation	244, 217, 239	⊢
	: , :
8	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
9	instantiation	181	⊢
	: , : , :
10	instantiation	21, 13, 196, 41, 42, 14*, 15*	⊢
	: , : , :
11	instantiation	16, 139, 33, 17, 18, 19*, 20*	⊢
	: , : , :
12	instantiation	21, 223, 196, 22, 23, 24*	⊢
	: , : , :
13	instantiation	25, 170, 26, 27, 223, 153	⊢
	: , :
14	instantiation	165, 28, 29, 30	⊢
	: , : , : , :
15	instantiation	177, 31	⊢
	: , :
16	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
17	instantiation	152, 93, 234	⊢
	: , :
18	instantiation	32, 33, 93, 234, 34, 35	⊢
	: , : , :
19	instantiation	177, 36	⊢
	: , :
20	instantiation	165, 37, 38, 39	⊢
	: , : , : , :
21	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
22	instantiation	152, 41, 223	⊢
	: , :
23	instantiation	40, 196, 41, 223, 42, 43	⊢
	: , : , :
24	instantiation	165, 44, 146, 45	⊢
	: , : , : , :
25	theorem		⊢
	proveit.numbers.addition.add_real_closure
26	instantiation	181	⊢
	: , : , :
27	instantiation	253, 240, 46	⊢
	: , : , :
28	instantiation	141, 47, 48	⊢
	: , : , :
29	instantiation	160	⊢
	:
30	instantiation	177, 49	⊢
	: , :
31	instantiation	165, 56, 50, 51	⊢
	: , : , : , :
32	theorem		⊢
	proveit.numbers.ordering.less_add_right
33	instantiation	111, 234, 53	⊢
	: , :
34	instantiation	52, 234, 53, 196, 54, 55	⊢
	: , : , :
35	instantiation	65, 255	⊢
	:
36	instantiation	165, 56, 57, 58	⊢
	: , : , : , :
37	instantiation	156, 157, 255, 247, 159, 59, 81, 226, 120	⊢
	: , : , : , : , : , :
38	instantiation	156, 255, 157, 59, 136, 159, 81, 226, 173, 188	⊢
	: , : , : , : , : , :
39	instantiation	165, 60, 61, 62	⊢
	: , : , : , :
40	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
41	instantiation	253, 240, 63	⊢
	: , : , :
42	instantiation	64, 239, 238, 229	⊢
	: , : , :
43	instantiation	65, 247	⊢
	:
44	instantiation	141, 66, 67	⊢
	: , : , :
45	instantiation	177, 154	⊢
	: , :
46	instantiation	253, 248, 68	⊢
	: , : , :
47	instantiation	179, 122	⊢
	: , : , :
48	instantiation	141, 69, 70	⊢
	: , : , :
49	instantiation	179, 140	⊢
	: , : , :
50	instantiation	177, 71	⊢
	: , :
51	instantiation	177, 72	⊢
	: , :
52	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
54	instantiation	73, 74, 75	⊢
	: , : , :
55	instantiation	76, 231	⊢
	:
56	instantiation	77, 184, 212	⊢
	: , :
57	instantiation	160	⊢
	:
58	instantiation	177, 78	⊢
	: , :
59	instantiation	174	⊢
	: , :
60	instantiation	79, 247, 81, 226, 173, 188	⊢
	: , : , : , : , : , : , :
61	instantiation	133, 157, 255, 159, 80, 130, 81, 173, 226, 188, 82*	⊢
	: , : , : , : , : , :
62	instantiation	133, 247, 255, 157, 130, 159, 184, 226, 188, 131*	⊢
	: , : , : , : , : , :
63	instantiation	253, 248, 238	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
65	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
66	instantiation	179, 83	⊢
	: , : , :
67	instantiation	141, 84, 85	⊢
	: , : , :
68	instantiation	251, 245	⊢
	:
69	instantiation	156, 247, 170, 157, 171, 159, 184, 172, 212, 173	⊢
	: , : , : , : , : , :
70	instantiation	144, 157, 255, 159, 86, 184, 172, 212, 138	⊢
	: , : , : , : , : , : , : , :
71	instantiation	148, 120, 184, 188, 87	⊢
	: , : , :
72	instantiation	141, 88, 89	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
74	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
75	instantiation	90, 239, 238, 229	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
77	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
78	instantiation	141, 91, 92	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.addition.leftward_commutation
80	instantiation	174	⊢
	: , :
81	instantiation	253, 233, 93	⊢
	: , : , :
82	instantiation	141, 94, 95, 96*	⊢
	: , : , :
83	instantiation	141, 97, 98	⊢
	: , : , :
84	instantiation	156, 157, 255, 247, 159, 99, 182, 188, 212	⊢
	: , : , : , : , : , :
85	instantiation	100, 212, 182, 101	⊢
	: , : , :
86	instantiation	174	⊢
	: , :
87	instantiation	149, 102, 103	⊢
	: , : , :
88	instantiation	141, 104, 105	⊢
	: , : , :
89	instantiation	141, 106, 107	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
91	instantiation	179, 108	⊢
	: , : , :
92	instantiation	141, 109, 110	⊢
	: , : , :
93	instantiation	111, 234, 196	⊢
	: , :
94	instantiation	179, 112	⊢
	: , : , :
95	instantiation	177, 113	⊢
	: , :
96	instantiation	141, 114, 115	⊢
	: , : , :
97	instantiation	179, 121	⊢
	: , : , :
98	instantiation	141, 116, 117	⊢
	: , : , :
99	instantiation	174	⊢
	: , :
100	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
101	instantiation	160	⊢
	:
102	instantiation	141, 118, 119	⊢
	: , : , :
103	instantiation	186, 184, 120	⊢
	: , :
104	instantiation	179, 121	⊢
	: , : , :
105	instantiation	179, 122	⊢
	: , : , :
106	instantiation	141, 123, 124	⊢
	: , : , :
107	instantiation	133, 157, 255, 247, 159, 134, 163, 212, 173, 135*	⊢
	: , : , : , : , : , :
108	instantiation	125, 226	⊢
	:
109	instantiation	156, 247, 255, 157, 136, 159, 126, 173, 188	⊢
	: , : , : , : , : , :
110	instantiation	127, 157, 255, 159, 136, 173, 188	⊢
	: , : , : , :
111	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
112	instantiation	177, 128	⊢
	: , :
113	instantiation	129, 157, 255, 247, 159, 130, 226, 188, 184	⊢
	: , : , : , : , : , :
114	instantiation	179, 131	⊢
	: , : , :
115	instantiation	132, 184	⊢
	:
116	instantiation	156, 157, 255, 247, 159, 158, 182, 163, 212	⊢
	: , : , : , : , : , :
117	instantiation	133, 247, 255, 157, 134, 159, 182, 163, 212, 135*	⊢
	: , : , : , : , : , :
118	instantiation	156, 247, 255, 157, 136, 159, 184, 173, 188	⊢
	: , : , : , : , : , :
119	instantiation	137, 184, 188, 138	⊢
	: , : , :
120	instantiation	253, 233, 139	⊢
	: , : , :
121	instantiation	179, 154	⊢
	: , : , :
122	instantiation	179, 140	⊢
	: , : , :
123	instantiation	141, 142, 143	⊢
	: , : , :
124	instantiation	144, 157, 247, 255, 159, 145, 182, 163, 212, 173, 146	⊢
	: , : , : , : , : , : , : , :
125	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
126	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
127	theorem		⊢
	proveit.numbers.addition.elim_zero_any
128	instantiation	147, 184	⊢
	:
129	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
130	instantiation	174	⊢
	: , :
131	instantiation	148, 212, 226, 162	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
133	theorem		⊢
	proveit.numbers.addition.association
134	instantiation	174	⊢
	: , :
135	instantiation	149, 150, 151	⊢
	: , : , :
136	instantiation	174	⊢
	: , :
137	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
138	instantiation	160	⊢
	:
139	instantiation	152, 153, 198	⊢
	: , :
140	instantiation	179, 154	⊢
	: , : , :
141	axiom		⊢
	proveit.logic.equality.equals_transitivity
142	instantiation	156, 157, 255, 247, 159, 158, 182, 163, 155	⊢
	: , : , : , : , : , :
143	instantiation	156, 255, 170, 157, 158, 171, 159, 182, 163, 172, 212, 173	⊢
	: , : , : , : , : , :
144	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
145	instantiation	174	⊢
	: , :
146	instantiation	160	⊢
	:
147	theorem		⊢
	proveit.numbers.negation.mult_neg_one_left
148	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
149	theorem		⊢
	proveit.logic.equality.sub_right_side_into
150	instantiation	161, 212, 226, 162	⊢
	: , : , :
151	instantiation	186, 212, 163	⊢
	: , :
152	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
153	instantiation	164, 196	⊢
	:
154	instantiation	165, 166, 167, 168	⊢
	: , : , : , :
155	instantiation	169, 170, 171, 172, 212, 173	⊢
	: , :
156	theorem		⊢
	proveit.numbers.addition.disassociation
157	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
158	instantiation	174	⊢
	: , :
159	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
160	axiom		⊢
	proveit.logic.equality.equals_reflexivity
161	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
162	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
163	instantiation	253, 233, 175	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.negation.real_closure
165	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
166	instantiation	179, 176	⊢
	: , : , :
167	instantiation	177, 178	⊢
	: , :
168	instantiation	179, 180	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.addition.add_complex_closure
170	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
171	instantiation	181	⊢
	: , : , :
172	instantiation	183, 182	⊢
	:
173	instantiation	183, 184	⊢
	:
174	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
175	instantiation	253, 240, 185	⊢
	: , : , :
176	instantiation	186, 187, 188	⊢
	: , :
177	theorem		⊢
	proveit.logic.equality.equals_reversal
178	instantiation	189, 226, 198, 197, 214	⊢
	: , : , :
179	axiom		⊢
	proveit.logic.equality.substitution
180	instantiation	190, 191, 192	⊢
	: , :
181	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
182	instantiation	193, 194, 195	⊢
	: , :
183	theorem		⊢
	proveit.numbers.negation.complex_closure
184	instantiation	253, 233, 196	⊢
	: , : , :
185	instantiation	253, 248, 246	⊢
	: , : , :
186	theorem		⊢
	proveit.numbers.addition.commutation
187	instantiation	253, 233, 197	⊢
	: , : , :
188	instantiation	253, 233, 198	⊢
	: , : , :
189	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
190	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
191	instantiation	253, 199, 200	⊢
	: , : , :
192	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
193	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
194	instantiation	201, 212, 202, 203	⊢
	: , :
195	instantiation	253, 233, 204	⊢
	: , : , :
196	instantiation	253, 240, 205	⊢
	: , : , :
197	instantiation	206, 207, 243	⊢
	: , : , :
198	instantiation	253, 240, 208	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
200	instantiation	253, 209, 210	⊢
	: , : , :
201	theorem		⊢
	proveit.numbers.division.div_complex_closure
202	instantiation	211, 226, 212	⊢
	: , :
203	instantiation	213, 214, 215	⊢
	: , : , :
204	instantiation	253, 240, 216	⊢
	: , : , :
205	instantiation	253, 248, 217	⊢
	: , : , :
206	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
207	instantiation	218, 219	⊢
	: , :
208	instantiation	253, 248, 220	⊢
	: , : , :
209	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
210	instantiation	253, 221, 222	⊢
	: , : , :
211	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
212	instantiation	253, 233, 223	⊢
	: , : , :
213	theorem		⊢
	proveit.logic.equality.sub_left_side_into
214	instantiation	224, 231	⊢
	:
215	instantiation	225, 226	⊢
	:
216	instantiation	253, 248, 227	⊢
	: , : , :
217	instantiation	253, 228, 229	⊢
	: , : , :
218	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
219	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
220	instantiation	251, 239	⊢
	:
221	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
222	instantiation	253, 230, 231	⊢
	: , : , :
223	instantiation	253, 240, 232	⊢
	: , : , :
224	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
225	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
226	instantiation	253, 233, 234	⊢
	: , : , :
227	instantiation	235, 252, 236	⊢
	: , :
228	instantiation	237, 239, 238	⊢
	: , :
229	assumption		⊢
230	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
231	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
232	instantiation	253, 248, 239	⊢
	: , : , :
233	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
234	instantiation	253, 240, 241	⊢
	: , : , :
235	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
236	instantiation	253, 242, 243	⊢
	: , : , :
237	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
238	instantiation	244, 245, 246	⊢
	: , :
239	instantiation	253, 254, 247	⊢
	: , : , :
240	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
241	instantiation	253, 248, 252	⊢
	: , : , :
242	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
243	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
244	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
245	instantiation	253, 249, 250	⊢
	: , : , :
246	instantiation	251, 252	⊢
	:
247	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
248	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
249	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
250	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
251	theorem		⊢
	proveit.numbers.negation.int_closure
252	instantiation	253, 254, 255	⊢
	: , : , :
253	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
254	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
255	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements