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.numbers.exponentiation.exp_pos_lesseq
2	reference	170	⊢
3	instantiation	59, 179, 65	⊢
	: , :
4	instantiation	198, 188, 7	⊢
	: , : , :
5	instantiation	8, 9, 10	⊢
	: , :
6	instantiation	11, 194	⊢
	:
7	instantiation	12, 23, 13	⊢
	: , :
8	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
9	instantiation	14, 15	⊢
	:
10	instantiation	45, 163, 16, 17, 18, 19*	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
12	theorem		⊢
	proveit.numbers.addition.add_rational_closure_bin
13	instantiation	198, 195, 20	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg
15	instantiation	198, 21, 22	⊢
	: , : , :
16	instantiation	198, 161, 88	⊢
	: , : , :
17	instantiation	198, 188, 23	⊢
	: , : , :
18	instantiation	24, 170, 80, 25, 143, 26, 27*	⊢
	: , : , :
19	instantiation	123, 28, 29	⊢
	: , : , :
20	instantiation	198, 30, 31	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg
22	instantiation	126, 172, 94	⊢
	: , :
23	instantiation	198, 32, 33	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
25	instantiation	59, 48, 46	⊢
	: , :
26	instantiation	34, 35, 36	⊢
	: , : , :
27	instantiation	37, 173, 88, 118	⊢
	: , :
28	instantiation	82, 135, 197, 200, 136, 38, 160, 54, 153	⊢
	: , : , : , : , : , :
29	instantiation	123, 39, 40	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
31	instantiation	41, 192	⊢
	:
32	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
33	instantiation	42, 168, 43	⊢
	: , :
34	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
35	instantiation	44, 80	⊢
	:
36	instantiation	45, 46, 47, 48, 49, 50*	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.exponentiation.exponent_log_with_same_base
38	instantiation	149	⊢
	: , :
39	instantiation	51, 200, 135, 136, 160, 54, 153	⊢
	: , : , : , : , : , : , :
40	instantiation	52, 135, 197, 200, 136, 53, 160, 153, 54, 55*	⊢
	: , : , : , : , : , :
41	theorem		⊢
	proveit.numbers.negation.int_neg_closure
42	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
43	instantiation	56, 57, 58	⊢
	: , :
44	theorem		⊢
	proveit.numbers.rounding.ceil_x_ge_x
45	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
46	instantiation	175, 96	⊢
	:
47	instantiation	59, 96, 60	⊢
	: , :
48	instantiation	99, 100, 68	⊢
	: , : , :
49	axiom		⊢
	proveit.physics.quantum.QPE._t_req
50	instantiation	61, 62, 63, 64	⊢
	: , : , : , :
51	theorem		⊢
	proveit.numbers.addition.leftward_commutation
52	theorem		⊢
	proveit.numbers.addition.association
53	instantiation	149	⊢
	: , :
54	instantiation	198, 169, 65	⊢
	: , : , :
55	instantiation	66, 133, 160, 67	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
57	instantiation	198, 75, 68	⊢
	: , : , :
58	instantiation	69, 70	⊢
	:
59	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
60	instantiation	198, 188, 71	⊢
	: , : , :
61	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
62	instantiation	123, 72, 73	⊢
	: , : , :
63	instantiation	93	⊢
	:
64	instantiation	74, 81	⊢
	: , :
65	instantiation	198, 161, 94	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
67	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
68	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
69	theorem		⊢
	proveit.numbers.negation.int_closure
70	instantiation	198, 75, 101	⊢
	: , : , :
71	instantiation	198, 195, 76	⊢
	: , : , :
72	instantiation	121, 77	⊢
	: , : , :
73	instantiation	123, 78, 79	⊢
	: , : , :
74	theorem		⊢
	proveit.logic.equality.equals_reversal
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
76	instantiation	109, 80	⊢
	:
77	instantiation	121, 81	⊢
	: , : , :
78	instantiation	82, 135, 197, 200, 136, 83, 91, 86, 84	⊢
	: , : , : , : , : , :
79	instantiation	85, 91, 86, 87	⊢
	: , : , :
80	instantiation	116, 173, 88, 118	⊢
	: , :
81	instantiation	121, 89	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.addition.disassociation
83	instantiation	149	⊢
	: , :
84	instantiation	90, 91	⊢
	:
85	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
86	instantiation	198, 169, 92	⊢
	: , : , :
87	instantiation	93	⊢
	:
88	instantiation	126, 173, 94	⊢
	: , :
89	instantiation	121, 95	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.negation.complex_closure
91	instantiation	198, 169, 96	⊢
	: , : , :
92	instantiation	198, 188, 97	⊢
	: , : , :
93	axiom		⊢
	proveit.logic.equality.equals_reflexivity
94	instantiation	171, 172, 120, 105	⊢
	: , :
95	instantiation	121, 98	⊢
	: , : , :
96	instantiation	99, 100, 101	⊢
	: , : , :
97	instantiation	198, 195, 102	⊢
	: , : , :
98	instantiation	103, 133, 104, 105, 106*	⊢
	: , :
99	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
100	instantiation	107, 108	⊢
	: , :
101	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
102	instantiation	109, 110	⊢
	:
103	theorem		⊢
	proveit.numbers.division.div_as_mult
104	instantiation	198, 169, 111	⊢
	: , : , :
105	instantiation	112, 113	⊢
	:
106	instantiation	123, 114, 115	⊢
	: , : , :
107	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
109	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
110	instantiation	116, 173, 117, 118	⊢
	: , :
111	instantiation	198, 161, 120	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
113	instantiation	198, 119, 120	⊢
	: , : , :
114	instantiation	121, 122	⊢
	: , : , :
115	instantiation	123, 124, 125	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
117	instantiation	126, 173, 127	⊢
	: , :
118	instantiation	144, 128	⊢
	: , :
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
120	instantiation	140, 173, 155	⊢
	: , :
121	axiom		⊢
	proveit.logic.equality.substitution
122	instantiation	129, 160, 152, 163, 174, 130, 131*	⊢
	: , : , :
123	axiom		⊢
	proveit.logic.equality.equals_transitivity
124	instantiation	132, 200, 197, 135, 137, 136, 133, 138, 139	⊢
	: , : , : , : , : , :
125	instantiation	134, 135, 197, 136, 137, 138, 139	⊢
	: , : , : , :
126	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
127	instantiation	140, 162, 141	⊢
	: , :
128	instantiation	142, 200, 197, 143	⊢
	: , :
129	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
130	instantiation	144, 145	⊢
	: , :
131	instantiation	146, 147, 192, 148*	⊢
	: , :
132	theorem		⊢
	proveit.numbers.multiplication.disassociation
133	instantiation	198, 169, 179	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
135	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
136	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
137	instantiation	149	⊢
	: , :
138	instantiation	198, 169, 150	⊢
	: , : , :
139	instantiation	151, 152, 153	⊢
	: , :
140	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
141	instantiation	154, 155, 163	⊢
	: , :
142	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
143	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
144	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
145	instantiation	156, 178, 165, 166	⊢
	: , :
146	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
147	instantiation	198, 157, 158	⊢
	: , : , :
148	instantiation	159, 160	⊢
	:
149	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
150	instantiation	198, 161, 162	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
152	instantiation	198, 169, 165	⊢
	: , : , :
153	instantiation	198, 169, 163	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
155	instantiation	164, 165, 166	⊢
	:
156	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
157	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
158	instantiation	198, 167, 168	⊢
	: , : , :
159	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
160	instantiation	198, 169, 170	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
162	instantiation	171, 172, 173, 174	⊢
	: , :
163	instantiation	175, 179	⊢
	:
164	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
165	instantiation	176, 178, 179, 180	⊢
	: , : , :
166	instantiation	177, 178, 179, 180	⊢
	: , : , :
167	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
168	instantiation	198, 181, 182	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
170	instantiation	198, 188, 183	⊢
	: , : , :
171	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
172	instantiation	198, 185, 184	⊢
	: , : , :
173	instantiation	198, 185, 186	⊢
	: , : , :
174	instantiation	187, 194	⊢
	:
175	theorem		⊢
	proveit.numbers.negation.real_closure
176	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
177	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
178	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
179	instantiation	198, 188, 189	⊢
	: , : , :
180	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
181	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
182	instantiation	198, 190, 194	⊢
	: , : , :
183	instantiation	198, 195, 191	⊢
	: , : , :
184	instantiation	198, 193, 192	⊢
	: , : , :
185	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
186	instantiation	198, 193, 194	⊢
	: , : , :
187	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
188	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
189	instantiation	198, 195, 196	⊢
	: , : , :
190	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
191	instantiation	198, 199, 197	⊢
	: , : , :
192	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
193	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
194	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
195	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
196	instantiation	198, 199, 200	⊢
	: , : , :
197	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
198	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
199	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
200	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements