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.exponentiation.exp_monotonicity_large_base_less_eq
2	reference	124	⊢
3	reference	34	⊢
4	instantiation	19, 16, 14	⊢
	: , :
5	reference	97	⊢
6	instantiation	8, 9, 10	⊢
	: , : , :
7	instantiation	11, 127, 42, 72	⊢
	: , :
8	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less_eq
9	instantiation	12, 34	⊢
	:
10	instantiation	13, 14, 15, 16, 17, 18*	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.exponentiation.exponent_log_with_same_base
12	theorem		⊢
	proveit.numbers.rounding.ceil_x_ge_x
13	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
14	instantiation	129, 50	⊢
	:
15	instantiation	19, 50, 20	⊢
	: , :
16	instantiation	53, 54, 21	⊢
	: , : , :
17	axiom		⊢
	proveit.physics.quantum.QPE._t_req
18	instantiation	22, 23, 24, 25	⊢
	: , : , : , :
19	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
20	instantiation	152, 142, 26	⊢
	: , : , :
21	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
22	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
23	instantiation	77, 27, 28	⊢
	: , : , :
24	instantiation	47	⊢
	:
25	instantiation	29, 35	⊢
	: , :
26	instantiation	152, 149, 30	⊢
	: , : , :
27	instantiation	75, 31	⊢
	: , : , :
28	instantiation	77, 32, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.logic.equality.equals_reversal
30	instantiation	63, 34	⊢
	:
31	instantiation	75, 35	⊢
	: , : , :
32	instantiation	36, 89, 151, 154, 90, 37, 45, 40, 38	⊢
	: , : , : , : , : , :
33	instantiation	39, 45, 40, 41	⊢
	: , : , :
34	instantiation	70, 127, 42, 72	⊢
	: , :
35	instantiation	75, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.disassociation
37	instantiation	103	⊢
	: , :
38	instantiation	44, 45	⊢
	:
39	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
40	instantiation	152, 123, 46	⊢
	: , : , :
41	instantiation	47	⊢
	:
42	instantiation	80, 127, 48	⊢
	: , :
43	instantiation	75, 49	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.negation.complex_closure
45	instantiation	152, 123, 50	⊢
	: , : , :
46	instantiation	152, 142, 51	⊢
	: , : , :
47	axiom		⊢
	proveit.logic.equality.equals_reflexivity
48	instantiation	125, 126, 74, 59	⊢
	: , :
49	instantiation	75, 52	⊢
	: , : , :
50	instantiation	53, 54, 55	⊢
	: , : , :
51	instantiation	152, 149, 56	⊢
	: , : , :
52	instantiation	57, 87, 58, 59, 60*	⊢
	: , :
53	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
54	instantiation	61, 62	⊢
	: , :
55	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
56	instantiation	63, 64	⊢
	:
57	theorem		⊢
	proveit.numbers.division.div_as_mult
58	instantiation	152, 123, 65	⊢
	: , : , :
59	instantiation	66, 67	⊢
	:
60	instantiation	77, 68, 69	⊢
	: , : , :
61	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
63	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
64	instantiation	70, 127, 71, 72	⊢
	: , :
65	instantiation	152, 115, 74	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
67	instantiation	152, 73, 74	⊢
	: , : , :
68	instantiation	75, 76	⊢
	: , : , :
69	instantiation	77, 78, 79	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
71	instantiation	80, 127, 81	⊢
	: , :
72	instantiation	98, 82	⊢
	: , :
73	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
74	instantiation	94, 127, 109	⊢
	: , :
75	axiom		⊢
	proveit.logic.equality.substitution
76	instantiation	83, 114, 106, 117, 128, 84, 85*	⊢
	: , : , :
77	axiom		⊢
	proveit.logic.equality.equals_transitivity
78	instantiation	86, 154, 151, 89, 91, 90, 87, 92, 93	⊢
	: , : , : , : , : , :
79	instantiation	88, 89, 151, 90, 91, 92, 93	⊢
	: , : , : , :
80	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
81	instantiation	94, 116, 95	⊢
	: , :
82	instantiation	96, 154, 151, 97	⊢
	: , :
83	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
84	instantiation	98, 99	⊢
	: , :
85	instantiation	100, 101, 146, 102*	⊢
	: , :
86	theorem		⊢
	proveit.numbers.multiplication.disassociation
87	instantiation	152, 123, 133	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
89	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
90	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
91	instantiation	103	⊢
	: , :
92	instantiation	152, 123, 104	⊢
	: , : , :
93	instantiation	105, 106, 107	⊢
	: , :
94	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
95	instantiation	108, 109, 117	⊢
	: , :
96	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
97	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
98	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
99	instantiation	110, 132, 119, 120	⊢
	: , :
100	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
101	instantiation	152, 111, 112	⊢
	: , : , :
102	instantiation	113, 114	⊢
	:
103	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
104	instantiation	152, 115, 116	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
106	instantiation	152, 123, 119	⊢
	: , : , :
107	instantiation	152, 123, 117	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
109	instantiation	118, 119, 120	⊢
	:
110	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
111	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
112	instantiation	152, 121, 122	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
114	instantiation	152, 123, 124	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
116	instantiation	125, 126, 127, 128	⊢
	: , :
117	instantiation	129, 133	⊢
	:
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
119	instantiation	130, 132, 133, 134	⊢
	: , : , :
120	instantiation	131, 132, 133, 134	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
122	instantiation	152, 135, 136	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
124	instantiation	152, 142, 137	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
126	instantiation	152, 139, 138	⊢
	: , : , :
127	instantiation	152, 139, 140	⊢
	: , : , :
128	instantiation	141, 148	⊢
	:
129	theorem		⊢
	proveit.numbers.negation.real_closure
130	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
132	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
133	instantiation	152, 142, 143	⊢
	: , : , :
134	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
135	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
136	instantiation	152, 144, 148	⊢
	: , : , :
137	instantiation	152, 149, 145	⊢
	: , : , :
138	instantiation	152, 147, 146	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
140	instantiation	152, 147, 148	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
142	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
143	instantiation	152, 149, 150	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
145	instantiation	152, 153, 151	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
147	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
148	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
149	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
150	instantiation	152, 153, 154	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
152	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
153	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
154	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements