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.booleans.conjunction.and_if_both
2	instantiation	265, 4, 5	,  ⊢
	: , : , :
3	instantiation	6, 12	⊢
	: , :
4	instantiation	7, 271, 8, 9, 10	⊢
	: , : , :
5	instantiation	11, 12	⊢
	: , :
6	theorem		⊢
	proveit.logic.booleans.conjunction.right_from_and
7	theorem		⊢
	proveit.logic.sets.unification.union_inclusion
8	instantiation	219	⊢
	: , :
9	instantiation	15, 56, 13, 283, 14	⊢
	: , : , : , :
10	instantiation	15, 56, 17, 283, 16	⊢
	: , : , : , :
11	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
12	assumption		⊢
13	instantiation	289, 17	⊢
	:
14	instantiation	21, 215, 18, 19, 30, 20	⊢
	: , :
15	theorem		⊢
	proveit.numbers.number_sets.integers.interval_subset_eq
16	instantiation	21, 215, 22, 23, 24, 25	⊢
	: , :
17	instantiation	282, 258, 279	⊢
	: , :
18	instantiation	226	⊢
	: , : , :
19	instantiation	35, 26, 27	⊢
	: , :
20	instantiation	156, 28	⊢
	: , :
21	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
22	instantiation	226	⊢
	: , : , :
23	instantiation	29, 30, 31	⊢
	: , : , :
24	instantiation	91, 261, 240, 32, 33, 34*	⊢
	: , : , :
25	instantiation	35, 36, 37	⊢
	: , :
26	instantiation	291, 280, 38	⊢
	: , : , :
27	instantiation	206	⊢
	:
28	instantiation	39, 40, 41	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
30	instantiation	91, 42, 240, 51, 52, 43*, 44*	⊢
	: , : , :
31	instantiation	91, 123, 45, 46, 47, 48*, 49*	⊢
	: , : , :
32	instantiation	144, 51, 261	⊢
	: , :
33	instantiation	50, 240, 51, 261, 52, 53	⊢
	: , : , :
34	instantiation	210, 54, 193, 55	⊢
	: , : , : , :
35	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
36	instantiation	265, 266, 288	⊢
	: , : , :
37	instantiation	206	⊢
	:
38	instantiation	291, 286, 56	⊢
	: , : , :
39	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
40	instantiation	57, 58	⊢
	:
41	instantiation	115, 288	⊢
	:
42	instantiation	59, 215, 60, 61, 261, 145	⊢
	: , :
43	instantiation	210, 62, 63, 64	⊢
	: , : , : , :
44	instantiation	222, 65	⊢
	: , :
45	instantiation	162, 274, 92	⊢
	: , :
46	instantiation	144, 146, 274	⊢
	: , :
47	instantiation	66, 67, 68, 290, 69, 70	⊢
	: , : , :
48	instantiation	222, 71	⊢
	: , :
49	instantiation	210, 72, 73, 74	⊢
	: , : , : , :
50	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
51	instantiation	291, 280, 75	⊢
	: , : , :
52	instantiation	76, 279, 278, 269	⊢
	: , : , :
53	instantiation	116, 285	⊢
	:
54	instantiation	188, 77, 78	⊢
	: , : , :
55	instantiation	222, 200	⊢
	: , :
56	instantiation	282, 109, 279	⊢
	: , :
57	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
58	instantiation	79, 80	⊢
	:
59	theorem		⊢
	proveit.numbers.addition.add_real_closure
60	instantiation	226	⊢
	: , : , :
61	instantiation	291, 280, 81	⊢
	: , : , :
62	instantiation	188, 82, 83	⊢
	: , : , :
63	instantiation	206	⊢
	:
64	instantiation	222, 84	⊢
	: , :
65	instantiation	210, 96, 85, 86	⊢
	: , : , : , :
66	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
67	instantiation	291, 292, 87	⊢
	: , : , :
68	instantiation	291, 292, 88	⊢
	: , : , :
69	instantiation	89, 274, 92, 240, 157, 90	⊢
	: , : , :
70	instantiation	91, 233, 92, 141, 93, 94*, 95*	⊢
	: , : , :
71	instantiation	210, 96, 97, 98	⊢
	: , : , : , :
72	instantiation	202, 203, 293, 285, 205, 100, 126, 264, 99	⊢
	: , : , : , : , : , :
73	instantiation	202, 293, 203, 100, 181, 205, 126, 264, 218, 231	⊢
	: , : , : , : , : , :
74	instantiation	210, 101, 102, 103	⊢
	: , : , : , :
75	instantiation	291, 286, 278	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
77	instantiation	224, 104	⊢
	: , : , :
78	instantiation	188, 105, 106	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.negation.int_neg_closure
80	instantiation	107, 108, 236	⊢
	: , :
81	instantiation	291, 286, 109	⊢
	: , : , :
82	instantiation	224, 168	⊢
	: , : , :
83	instantiation	188, 110, 111	⊢
	: , : , :
84	instantiation	224, 187	⊢
	: , : , :
85	instantiation	230, 218, 231	⊢
	: , :
86	instantiation	222, 112	⊢
	: , :
87	instantiation	113, 293, 203	⊢
	: , :
88	instantiation	113, 293, 114	⊢
	: , :
89	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
90	instantiation	115, 271	⊢
	:
91	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
93	instantiation	116, 215	⊢
	:
94	instantiation	194, 117, 118	⊢
	: , : , :
95	instantiation	199, 264, 253, 119, 120	⊢
	: , : , :
96	instantiation	121, 228, 253	⊢
	: , :
97	instantiation	206	⊢
	:
98	instantiation	222, 122	⊢
	: , :
99	instantiation	291, 273, 123	⊢
	: , : , :
100	instantiation	219	⊢
	: , :
101	instantiation	124, 285, 126, 264, 218, 231	⊢
	: , : , : , : , : , : , :
102	instantiation	171, 203, 293, 205, 125, 184, 126, 218, 264, 231, 127*	⊢
	: , : , : , : , : , :
103	instantiation	171, 285, 293, 203, 184, 205, 228, 264, 231, 185*	⊢
	: , : , : , : , : , :
104	instantiation	188, 128, 129	⊢
	: , : , :
105	instantiation	202, 203, 293, 285, 205, 130, 227, 231, 253	⊢
	: , : , : , : , : , :
106	instantiation	131, 253, 227, 132	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
108	instantiation	133, 258, 157	⊢
	:
109	instantiation	289, 283	⊢
	:
110	instantiation	202, 285, 215, 203, 216, 205, 228, 217, 253, 218	⊢
	: , : , : , : , : , :
111	instantiation	191, 203, 293, 205, 134, 228, 217, 253, 135	⊢
	: , : , : , : , : , : , : , :
112	instantiation	188, 136, 137	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.multiplication.mult_nat_closure_bin
114	instantiation	138, 258, 139	⊢
	:
115	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
116	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
117	instantiation	140, 231	⊢
	:
118	instantiation	230, 231, 179	⊢
	: , :
119	instantiation	291, 273, 141	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
121	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
122	instantiation	188, 142, 143	⊢
	: , : , :
123	instantiation	144, 145, 233	⊢
	: , :
124	theorem		⊢
	proveit.numbers.addition.leftward_commutation
125	instantiation	219	⊢
	: , :
126	instantiation	291, 273, 146	⊢
	: , : , :
127	instantiation	188, 147, 148, 149*	⊢
	: , : , :
128	instantiation	224, 167	⊢
	: , : , :
129	instantiation	188, 150, 151	⊢
	: , : , :
130	instantiation	219	⊢
	: , :
131	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
132	instantiation	206	⊢
	:
133	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
134	instantiation	219	⊢
	: , :
135	instantiation	206	⊢
	:
136	instantiation	188, 152, 153	⊢
	: , : , :
137	instantiation	188, 154, 155	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
139	instantiation	156, 157	⊢
	: , :
140	theorem		⊢
	proveit.numbers.addition.elim_zero_right
141	instantiation	291, 280, 158	⊢
	: , : , :
142	instantiation	224, 159	⊢
	: , : , :
143	instantiation	188, 160, 161	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
145	instantiation	242, 240	⊢
	:
146	instantiation	162, 274, 240	⊢
	: , :
147	instantiation	224, 163	⊢
	: , : , :
148	instantiation	222, 164	⊢
	: , :
149	instantiation	188, 165, 166	⊢
	: , : , :
150	instantiation	202, 203, 293, 285, 205, 204, 227, 209, 253	⊢
	: , : , : , : , : , :
151	instantiation	171, 285, 293, 203, 172, 205, 227, 209, 253, 173*	⊢
	: , : , : , : , : , :
152	instantiation	224, 167	⊢
	: , : , :
153	instantiation	224, 168	⊢
	: , : , :
154	instantiation	188, 169, 170	⊢
	: , : , :
155	instantiation	171, 203, 293, 285, 205, 172, 209, 253, 218, 173*	⊢
	: , : , : , : , : , :
156	theorem		⊢
	proveit.numbers.ordering.relax_less
157	instantiation	174, 175, 176	⊢
	: , : , :
158	instantiation	291, 286, 177	⊢
	: , : , :
159	instantiation	178, 264	⊢
	:
160	instantiation	202, 285, 293, 203, 181, 205, 179, 218, 231	⊢
	: , : , : , : , : , :
161	instantiation	180, 203, 293, 205, 181, 218, 231	⊢
	: , : , : , :
162	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
163	instantiation	222, 182	⊢
	: , :
164	instantiation	183, 203, 293, 285, 205, 184, 264, 231, 228	⊢
	: , : , : , : , : , :
165	instantiation	224, 185	⊢
	: , : , :
166	instantiation	186, 228	⊢
	:
167	instantiation	224, 200	⊢
	: , : , :
168	instantiation	224, 187	⊢
	: , : , :
169	instantiation	188, 189, 190	⊢
	: , : , :
170	instantiation	191, 203, 285, 293, 205, 192, 227, 209, 253, 218, 193	⊢
	: , : , : , : , : , : , : , :
171	theorem		⊢
	proveit.numbers.addition.association
172	instantiation	219	⊢
	: , :
173	instantiation	194, 195, 196	⊢
	: , : , :
174	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
175	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
176	instantiation	197, 279, 278, 269	⊢
	: , : , :
177	instantiation	291, 292, 215	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
179	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
180	theorem		⊢
	proveit.numbers.addition.elim_zero_any
181	instantiation	219	⊢
	: , :
182	instantiation	198, 228	⊢
	:
183	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
184	instantiation	219	⊢
	: , :
185	instantiation	199, 253, 264, 208	⊢
	: , : , :
186	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
187	instantiation	224, 200	⊢
	: , : , :
188	axiom		⊢
	proveit.logic.equality.equals_transitivity
189	instantiation	202, 203, 293, 285, 205, 204, 227, 209, 201	⊢
	: , : , : , : , : , :
190	instantiation	202, 293, 215, 203, 204, 216, 205, 227, 209, 217, 253, 218	⊢
	: , : , : , : , : , :
191	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
192	instantiation	219	⊢
	: , :
193	instantiation	206	⊢
	:
194	theorem		⊢
	proveit.logic.equality.sub_right_side_into
195	instantiation	207, 253, 264, 208	⊢
	: , : , :
196	instantiation	230, 253, 209	⊢
	: , :
197	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
198	theorem		⊢
	proveit.numbers.negation.mult_neg_one_left
199	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
200	instantiation	210, 211, 212, 213	⊢
	: , : , : , :
201	instantiation	214, 215, 216, 217, 253, 218	⊢
	: , :
202	theorem		⊢
	proveit.numbers.addition.disassociation
203	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
204	instantiation	219	⊢
	: , :
205	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
206	axiom		⊢
	proveit.logic.equality.equals_reflexivity
207	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
208	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
209	instantiation	291, 273, 220	⊢
	: , : , :
210	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
211	instantiation	224, 221	⊢
	: , : , :
212	instantiation	222, 223	⊢
	: , :
213	instantiation	224, 225	⊢
	: , : , :
214	theorem		⊢
	proveit.numbers.addition.add_complex_closure
215	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
216	instantiation	226	⊢
	: , : , :
217	instantiation	241, 227	⊢
	:
218	instantiation	241, 228	⊢
	:
219	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
220	instantiation	291, 280, 229	⊢
	: , : , :
221	instantiation	230, 248, 231	⊢
	: , :
222	theorem		⊢
	proveit.logic.equality.equals_reversal
223	instantiation	232, 264, 233, 257, 255	⊢
	: , : , :
224	axiom		⊢
	proveit.logic.equality.substitution
225	instantiation	234, 235, 236	⊢
	: , :
226	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
227	instantiation	237, 238, 239	⊢
	: , :
228	instantiation	291, 273, 240	⊢
	: , : , :
229	instantiation	291, 286, 284	⊢
	: , : , :
230	theorem		⊢
	proveit.numbers.addition.commutation
231	instantiation	241, 253	⊢
	:
232	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
233	instantiation	242, 261	⊢
	:
234	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
235	instantiation	291, 243, 244	⊢
	: , : , :
236	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
237	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
238	instantiation	245, 253, 246, 247	⊢
	: , :
239	instantiation	252, 264, 248	⊢
	: , :
240	instantiation	291, 280, 249	⊢
	: , : , :
241	theorem		⊢
	proveit.numbers.negation.complex_closure
242	theorem		⊢
	proveit.numbers.negation.real_closure
243	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
244	instantiation	291, 250, 251	⊢
	: , : , :
245	theorem		⊢
	proveit.numbers.division.div_complex_closure
246	instantiation	252, 264, 253	⊢
	: , :
247	instantiation	254, 255, 256	⊢
	: , : , :
248	instantiation	291, 273, 257	⊢
	: , : , :
249	instantiation	291, 286, 258	⊢
	: , : , :
250	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
251	instantiation	291, 259, 260	⊢
	: , : , :
252	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
253	instantiation	291, 273, 261	⊢
	: , : , :
254	theorem		⊢
	proveit.logic.equality.sub_left_side_into
255	instantiation	262, 271	⊢
	:
256	instantiation	263, 264	⊢
	:
257	instantiation	265, 266, 267	⊢
	: , : , :
258	instantiation	291, 268, 269	⊢
	: , : , :
259	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
260	instantiation	291, 270, 271	⊢
	: , : , :
261	instantiation	291, 280, 272	⊢
	: , : , :
262	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
263	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
264	instantiation	291, 273, 274	⊢
	: , : , :
265	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
266	instantiation	275, 276	⊢
	: , :
267	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
268	instantiation	277, 279, 278	⊢
	: , :
269	assumption		⊢
270	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
271	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
272	instantiation	291, 286, 279	⊢
	: , : , :
273	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
274	instantiation	291, 280, 281	⊢
	: , : , :
275	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
276	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
277	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
278	instantiation	282, 283, 284	⊢
	: , :
279	instantiation	291, 292, 285	⊢
	: , : , :
280	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
281	instantiation	291, 286, 290	⊢
	: , : , :
282	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
283	instantiation	291, 287, 288	⊢
	: , : , :
284	instantiation	289, 290	⊢
	:
285	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
286	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
287	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
288	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
289	theorem		⊢
	proveit.numbers.negation.int_closure
290	instantiation	291, 292, 293	⊢
	: , : , :
291	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
292	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
293	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements