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