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*, 7*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	instantiation	8, 87, 9	⊢
	: , :
3	reference	22	⊢
4	instantiation	220, 208, 10	⊢
	: , : , :
5	instantiation	11, 22, 12, 13, 14, 15	⊢
	: , : , :
6	instantiation	148, 16, 17	⊢
	: , : , :
7	instantiation	18, 19, 20, 21	⊢
	: , : , : , :
8	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
9	instantiation	190, 22	⊢
	:
10	instantiation	23, 24, 26	⊢
	: , :
11	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
12	instantiation	25, 28	⊢
	: , :
13	instantiation	220, 208, 26	⊢
	: , : , :
14	instantiation	27, 28, 29, 30, 31	⊢
	: , : , :
15	instantiation	66, 40	⊢
	:
16	instantiation	148, 32, 33	⊢
	: , : , :
17	instantiation	148, 34, 35	⊢
	: , : , :
18	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
19	instantiation	148, 36, 37	⊢
	: , : , :
20	instantiation	89	⊢
	:
21	instantiation	102, 38	⊢
	: , :
22	instantiation	220, 208, 39	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.addition.add_rational_closure_bin
24	instantiation	55, 56	⊢
	: , :
25	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
26	instantiation	220, 77, 40	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
28	instantiation	220, 208, 56	⊢
	: , : , :
29	instantiation	220, 208, 57	⊢
	: , : , :
30	instantiation	41, 42, 43, 44, 45	⊢
	: , : , :
31	instantiation	46, 47	⊢
	: , :
32	instantiation	165, 101	⊢
	: , : , :
33	instantiation	165, 68	⊢
	: , : , :
34	instantiation	69, 222, 219, 140, 70, 141, 88, 71, 73	⊢
	: , : , : , : , : , :
35	instantiation	48, 88, 71, 49	⊢
	: , : , :
36	instantiation	148, 50, 51	⊢
	: , : , :
37	instantiation	148, 52, 53	⊢
	: , : , :
38	instantiation	165, 54	⊢
	: , : , :
39	instantiation	55, 56, 57	⊢
	: , :
40	instantiation	94, 95, 58	⊢
	: , :
41	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
42	instantiation	220, 59, 60	⊢
	: , : , :
43	instantiation	220, 61, 96	⊢
	: , : , :
44	instantiation	220, 61, 62	⊢
	: , : , :
45	instantiation	63, 195, 201, 211, 64, 65, 156*	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.ordering.relax_less
47	instantiation	66, 78	⊢
	:
48	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
49	instantiation	89	⊢
	:
50	instantiation	165, 67	⊢
	: , : , :
51	instantiation	165, 68	⊢
	: , : , :
52	instantiation	69, 222, 219, 140, 70, 141, 143, 71, 73	⊢
	: , : , : , : , : , :
53	instantiation	72, 143, 73, 74	⊢
	: , : , :
54	instantiation	148, 75, 76	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
56	instantiation	220, 77, 78	⊢
	: , : , :
57	instantiation	79, 209, 80, 136	⊢
	: , :
58	instantiation	220, 110, 81	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
60	instantiation	220, 82, 222	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
62	instantiation	220, 110, 168	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
64	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
65	instantiation	83, 218	⊢
	:
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
67	instantiation	148, 84, 85	⊢
	: , : , :
68	instantiation	165, 86	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.addition.disassociation
70	instantiation	173	⊢
	: , :
71	instantiation	220, 210, 87	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
73	instantiation	196, 88	⊢
	:
74	instantiation	89	⊢
	:
75	instantiation	165, 90	⊢
	: , : , :
76	instantiation	131, 193, 91, 92, 93*	⊢
	: , :
77	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
78	instantiation	94, 95, 96	⊢
	: , :
79	theorem		⊢
	proveit.numbers.division.div_rational_closure
80	instantiation	220, 214, 97	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
82	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
83	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
84	instantiation	165, 98	⊢
	: , : , :
85	instantiation	99, 215, 207, 100*	⊢
	: , : , : , :
86	instantiation	165, 101	⊢
	: , : , :
87	instantiation	190, 157	⊢
	:
88	instantiation	104, 143, 167	⊢
	: , :
89	axiom		⊢
	proveit.logic.equality.equals_reflexivity
90	instantiation	102, 103	⊢
	: , :
91	instantiation	104, 183, 135	⊢
	: , :
92	instantiation	105, 219, 106, 154, 107	⊢
	: , :
93	instantiation	148, 108, 109	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
95	instantiation	220, 110, 155	⊢
	: , : , :
96	instantiation	220, 110, 206	⊢
	: , : , :
97	instantiation	220, 111, 168	⊢
	: , : , :
98	instantiation	112, 193, 154, 113*, 114*	⊢
	: , : , : , :
99	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
100	instantiation	148, 115, 116	⊢
	: , : , :
101	instantiation	165, 117	⊢
	: , : , :
102	theorem		⊢
	proveit.logic.equality.equals_reversal
103	instantiation	118, 183, 155, 218, 156*	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
105	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
106	instantiation	173	⊢
	: , :
107	instantiation	220, 169, 119	⊢
	: , : , :
108	instantiation	165, 120	⊢
	: , : , :
109	instantiation	148, 121, 122	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
111	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
112	theorem		⊢
	proveit.numbers.division.prod_of_fracs
113	instantiation	202, 193	⊢
	:
114	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
115	instantiation	158, 219, 123, 124, 125, 126	⊢
	: , : , : , :
116	instantiation	127, 128, 154, 193, 129*, 130*	⊢
	: , : , :
117	instantiation	131, 193, 135, 136, 132*	⊢
	: , :
118	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
119	instantiation	220, 185, 133	⊢
	: , : , :
120	instantiation	134, 183, 135, 179, 180, 136, 137*, 166*	⊢
	: , : , :
121	instantiation	138, 222, 219, 140, 142, 141, 193, 143, 167	⊢
	: , : , : , : , : , :
122	instantiation	139, 140, 219, 141, 142, 143, 167	⊢
	: , : , : , :
123	instantiation	173	⊢
	: , :
124	instantiation	173	⊢
	: , :
125	instantiation	148, 144, 145	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_4
127	theorem		⊢
	proveit.numbers.division.frac_cancel_left
128	instantiation	220, 169, 146	⊢
	: , : , :
129	instantiation	202, 147	⊢
	:
130	theorem		⊢
	proveit.numbers.numerals.decimals.mult_8_2
131	theorem		⊢
	proveit.numbers.division.div_as_mult
132	instantiation	148, 149, 150	⊢
	: , : , :
133	instantiation	220, 197, 151	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
135	instantiation	220, 210, 152	⊢
	: , : , :
136	instantiation	191, 168	⊢
	:
137	instantiation	153, 154, 155, 156*	⊢
	: , :
138	theorem		⊢
	proveit.numbers.multiplication.disassociation
139	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
140	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
141	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
142	instantiation	173	⊢
	: , :
143	instantiation	220, 210, 157	⊢
	: , : , :
144	instantiation	158, 219, 159, 160, 161, 162	⊢
	: , : , : , :
145	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_4
146	instantiation	220, 185, 163	⊢
	: , : , :
147	instantiation	220, 210, 164	⊢
	: , : , :
148	axiom		⊢
	proveit.logic.equality.equals_transitivity
149	instantiation	165, 166	⊢
	: , : , :
150	instantiation	174, 167	⊢
	:
151	instantiation	220, 205, 168	⊢
	: , : , :
152	instantiation	216, 217, 168	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
154	instantiation	220, 169, 170	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
156	instantiation	171, 183	⊢
	:
157	instantiation	172, 201, 195, 180	⊢
	: , :
158	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
159	instantiation	173	⊢
	: , :
160	instantiation	173	⊢
	: , :
161	instantiation	174, 175	⊢
	:
162	instantiation	202, 175	⊢
	:
163	instantiation	220, 197, 176	⊢
	: , : , :
164	instantiation	220, 208, 177	⊢
	: , : , :
165	axiom		⊢
	proveit.logic.equality.substitution
166	instantiation	178, 183, 211, 179, 180, 181*	⊢
	: , : , :
167	instantiation	182, 183, 184	⊢
	: , :
168	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
169	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
170	instantiation	220, 185, 186	⊢
	: , : , :
171	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
172	theorem		⊢
	proveit.numbers.division.div_real_closure
173	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
174	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
175	instantiation	220, 210, 187	⊢
	: , : , :
176	instantiation	220, 205, 188	⊢
	: , : , :
177	instantiation	220, 214, 189	⊢
	: , : , :
178	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
179	instantiation	190, 201	⊢
	:
180	instantiation	191, 206	⊢
	:
181	instantiation	192, 203, 193, 194*	⊢
	: , :
182	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
183	instantiation	220, 210, 195	⊢
	: , : , :
184	instantiation	196, 203	⊢
	:
185	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
186	instantiation	220, 197, 198	⊢
	: , : , :
187	instantiation	220, 208, 199	⊢
	: , : , :
188	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
189	instantiation	220, 221, 200	⊢
	: , : , :
190	theorem		⊢
	proveit.numbers.negation.real_closure
191	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
192	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
193	instantiation	220, 210, 201	⊢
	: , : , :
194	instantiation	202, 203	⊢
	:
195	instantiation	220, 208, 204	⊢
	: , : , :
196	theorem		⊢
	proveit.numbers.negation.complex_closure
197	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
198	instantiation	220, 205, 206	⊢
	: , : , :
199	instantiation	220, 214, 207	⊢
	: , : , :
200	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
201	instantiation	220, 208, 209	⊢
	: , : , :
202	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
203	instantiation	220, 210, 211	⊢
	: , : , :
204	instantiation	220, 214, 212	⊢
	: , : , :
205	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
206	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
207	instantiation	220, 221, 213	⊢
	: , : , :
208	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
209	instantiation	220, 214, 215	⊢
	: , : , :
210	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
211	instantiation	216, 217, 218	⊢
	: , : , :
212	instantiation	220, 221, 219	⊢
	: , : , :
213	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
214	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
215	instantiation	220, 221, 222	⊢
	: , : , :
216	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
217	instantiation	223, 224	⊢
	: , :
218	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
219	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
220	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
221	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
222	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
223	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
224	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements