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