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	reference	39	⊢
2	instantiation	234, 230, 7	⊢
	: , : , :
3	instantiation	8, 182, 9	⊢
	: , :
4	reference	228	⊢
5	instantiation	10, 182, 40, 208, 41, 11*	⊢
	: , : , :
6	instantiation	170, 236	⊢
	:
7	instantiation	234, 232, 12	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
9	instantiation	13, 14, 15	⊢
	:
10	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
11	instantiation	49, 16, 17, 175	⊢
	: , : , : , :
12	instantiation	234, 235, 18	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
14	instantiation	19, 20, 21	⊢
	: , :
15	instantiation	22, 23	⊢
	: , :
16	instantiation	24, 224, 171	⊢
	: , :
17	instantiation	25, 207, 26, 27, 28	⊢
	: , : , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
19	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
20	instantiation	234, 29, 123	⊢
	: , : , :
21	instantiation	234, 30, 31	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
23	instantiation	72, 76, 182, 32, 33, 34*, 35*	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.exponentiation.exp_nat_pos_expansion
25	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
26	instantiation	36, 207	⊢
	: , :
27	instantiation	183	⊢
	: , :
28	instantiation	37	⊢
	:
29	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
30	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
31	instantiation	38, 179	⊢
	:
32	instantiation	96, 40, 182	⊢
	: , :
33	instantiation	39, 182, 40, 41, 155	⊢
	: , : , :
34	instantiation	158, 42, 43	⊢
	: , : , :
35	instantiation	158, 44, 45	⊢
	: , : , :
36	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
37	theorem		⊢
	proveit.numbers.numerals.decimals.reduce_2_repeats
38	theorem		⊢
	proveit.numbers.negation.int_neg_closure
39	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
40	instantiation	96, 98, 142	⊢
	: , :
41	instantiation	56, 46, 47	⊢
	: , : , :
42	instantiation	114, 236, 207, 115, 62, 116, 171, 120, 63	⊢
	: , : , : , : , : , :
43	instantiation	119, 171, 120, 81	⊢
	: , : , :
44	instantiation	128, 48	⊢
	: , : , :
45	instantiation	49, 50, 51, 52	⊢
	: , : , : , :
46	instantiation	53, 233, 70, 54, 55*	⊢
	: , :
47	instantiation	56, 57, 58	⊢
	: , : , :
48	instantiation	114, 115, 207, 236, 116, 80, 83, 118, 171	⊢
	: , : , : , : , : , :
49	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
50	instantiation	114, 115, 60, 236, 116, 61, 83, 118, 171, 59	⊢
	: , : , : , : , : , :
51	instantiation	114, 60, 207, 115, 61, 62, 116, 83, 118, 171, 120, 63	⊢
	: , : , : , : , : , :
52	instantiation	158, 64, 65	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.rounding.ceil_of_real_above_int
54	instantiation	66, 216, 92, 67, 208, 68*	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
56	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
57	instantiation	69, 70, 189, 71	⊢
	: , :
58	instantiation	72, 142, 73, 98, 74, 75*	⊢
	: , : , :
59	instantiation	234, 193, 76	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
61	instantiation	77	⊢
	: , : , :
62	instantiation	183	⊢
	: , :
63	instantiation	78, 171	⊢
	:
64	instantiation	79, 207, 236, 115, 80, 116, 83, 118, 171, 120, 81	⊢
	: , : , : , : , : , : , : , :
65	instantiation	82, 120, 83, 122	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less
67	instantiation	84, 182, 85, 86, 87, 88*, 89*	⊢
	: , : , :
68	instantiation	90, 216	⊢
	:
69	theorem		⊢
	proveit.numbers.rounding.ceil_increasing_less_eq
70	instantiation	194, 216, 92, 196	⊢
	: , :
71	instantiation	91, 216, 92, 195, 93, 208	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
73	instantiation	96, 163, 143	⊢
	: , :
74	axiom		⊢
	proveit.physics.quantum.QPE._t_req
75	instantiation	158, 94, 95	⊢
	: , : , :
76	instantiation	96, 163, 97	⊢
	: , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
78	theorem		⊢
	proveit.numbers.negation.complex_closure
79	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
80	instantiation	183	⊢
	: , :
81	instantiation	144	⊢
	:
82	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
83	instantiation	234, 193, 98	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
85	instantiation	99, 165, 227	⊢
	: , :
86	instantiation	234, 230, 100	⊢
	: , : , :
87	instantiation	101, 165, 227, 228, 102, 103	⊢
	: , : , :
88	instantiation	158, 104, 105	⊢
	: , : , :
89	instantiation	158, 106, 107	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.logarithms.log_eq_1
91	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less_eq
92	instantiation	203, 108, 216, 133	⊢
	: , :
93	instantiation	109, 182, 110, 111, 112, 113*	⊢
	: , : , :
94	instantiation	114, 115, 207, 236, 116, 117, 120, 121, 118	⊢
	: , : , : , : , : , :
95	instantiation	119, 120, 121, 122	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
97	instantiation	162, 182	⊢
	:
98	instantiation	177, 178, 123	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
100	instantiation	124, 181, 231	⊢
	: , :
101	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
102	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
103	instantiation	125, 191	⊢
	:
104	instantiation	128, 126	⊢
	: , : , :
105	instantiation	127, 171	⊢
	:
106	instantiation	128, 129	⊢
	: , : , :
107	instantiation	138, 233, 198, 139*, 130*, 156*	⊢
	: , : , : , :
108	instantiation	234, 218, 131	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
110	instantiation	132, 228, 182, 133	⊢
	: , :
111	instantiation	234, 134, 200	⊢
	: , : , :
112	instantiation	135, 136, 214, 216, 137	⊢
	: , : , :
113	instantiation	138, 198, 233, 139*, 140*, 141*	⊢
	: , : , : , :
114	theorem		⊢
	proveit.numbers.addition.disassociation
115	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
116	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
117	instantiation	183	⊢
	: , :
118	instantiation	234, 193, 142	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
120	instantiation	234, 193, 163	⊢
	: , : , :
121	instantiation	234, 193, 143	⊢
	: , : , :
122	instantiation	144	⊢
	:
123	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
124	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
125	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
126	instantiation	145, 146	⊢
	:
127	theorem		⊢
	proveit.numbers.addition.elim_zero_left
128	axiom		⊢
	proveit.logic.equality.substitution
129	instantiation	184, 146	⊢
	:
130	instantiation	158, 147, 148	⊢
	: , : , :
131	instantiation	234, 223, 149	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.division.div_real_closure
133	instantiation	150, 224	⊢
	:
134	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
135	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
136	instantiation	234, 151, 152	⊢
	: , : , :
137	instantiation	153, 182, 221, 228, 154, 155, 156*	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
139	instantiation	157, 171	⊢
	:
140	instantiation	158, 159, 160	⊢
	: , : , :
141	instantiation	161, 171	⊢
	:
142	instantiation	162, 163	⊢
	:
143	instantiation	234, 230, 164	⊢
	: , : , :
144	axiom		⊢
	proveit.logic.equality.equals_reflexivity
145	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
146	instantiation	234, 193, 165	⊢
	: , : , :
147	instantiation	172, 207, 166, 167, 176, 175	⊢
	: , : , : , :
148	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_4
149	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
150	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
151	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
152	instantiation	234, 168, 236	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
154	instantiation	169, 227, 228, 229	⊢
	: , : , :
155	instantiation	170, 207	⊢
	:
156	instantiation	184, 171	⊢
	:
157	theorem		⊢
	proveit.numbers.division.frac_one_denom
158	axiom		⊢
	proveit.logic.equality.equals_transitivity
159	instantiation	172, 207, 173, 174, 175, 176	⊢
	: , : , : , :
160	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
161	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
162	theorem		⊢
	proveit.numbers.negation.real_closure
163	instantiation	177, 178, 179	⊢
	: , : , :
164	instantiation	234, 232, 180	⊢
	: , : , :
165	instantiation	234, 230, 181	⊢
	: , : , :
166	instantiation	183	⊢
	: , :
167	instantiation	183	⊢
	: , :
168	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
169	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
170	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
171	instantiation	234, 193, 182	⊢
	: , : , :
172	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
173	instantiation	183	⊢
	: , :
174	instantiation	183	⊢
	: , :
175	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
176	instantiation	184, 185	⊢
	:
177	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
178	instantiation	186, 187	⊢
	: , :
179	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
180	instantiation	188, 189	⊢
	:
181	instantiation	234, 190, 191	⊢
	: , : , :
182	instantiation	234, 230, 192	⊢
	: , : , :
183	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
184	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
185	instantiation	234, 193, 228	⊢
	: , : , :
186	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
187	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
188	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
189	instantiation	194, 216, 195, 196	⊢
	: , :
190	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
191	instantiation	197, 209, 219	⊢
	: , :
192	instantiation	234, 232, 198	⊢
	: , : , :
193	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
194	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
195	instantiation	199, 216, 200	⊢
	: , :
196	instantiation	201, 202	⊢
	: , :
197	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
198	instantiation	234, 235, 207	⊢
	: , : , :
199	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
200	instantiation	203, 204, 214, 205	⊢
	: , :
201	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
202	instantiation	206, 236, 207, 208	⊢
	: , :
203	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
204	instantiation	234, 218, 209	⊢
	: , : , :
205	instantiation	210, 211	⊢
	:
206	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
207	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
208	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
209	instantiation	234, 223, 212	⊢
	: , : , :
210	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
211	instantiation	234, 213, 214	⊢
	: , : , :
212	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
213	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
214	instantiation	215, 216, 217	⊢
	: , :
215	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
216	instantiation	234, 218, 219	⊢
	: , : , :
217	instantiation	220, 221, 222	⊢
	:
218	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
219	instantiation	234, 223, 224	⊢
	: , : , :
220	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
221	instantiation	225, 227, 228, 229	⊢
	: , : , :
222	instantiation	226, 227, 228, 229	⊢
	: , : , :
223	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
224	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
225	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
226	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
227	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
228	instantiation	234, 230, 231	⊢
	: , : , :
229	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
230	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
231	instantiation	234, 232, 233	⊢
	: , : , :
232	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
233	instantiation	234, 235, 236	⊢
	: , : , :
234	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
235	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
236	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements