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