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