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	⊢
	: , :
1	theorem		⊢
	proveit.logic.equality.equals_reversal
2	instantiation	3, 125, 135, 78, 4, 79, 5, 6, 7	⊢
	: , : , : , : , : , :
3	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
4	instantiation	8	⊢
	: , :
5	instantiation	133, 48, 9	⊢
	: , : , :
6	modus ponens	10, 11	⊢
7	modus ponens	12, 13	⊢
8	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
9	instantiation	26, 27, 14, 15	⊢
	: , :
10	instantiation	17	⊢
	: , : , :
11	generalization	16	⊢
12	instantiation	17	⊢
	: , : , :
13	generalization	18	⊢
14	instantiation	133, 62, 19	⊢
	: , : , :
15	instantiation	80, 20	⊢
	:
16	instantiation	133, 48, 21	,  ⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.summation.summation_complex_closure
18	instantiation	133, 48, 22	,  ⊢
	: , : , :
19	instantiation	133, 73, 23	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
21	instantiation	26, 27, 24, 25	,  ⊢
	: , :
22	instantiation	26, 27, 28, 29	,  ⊢
	: , :
23	instantiation	133, 134, 30	⊢
	: , : , :
24	instantiation	33, 46, 135	,  ⊢
	: , :
25	instantiation	34, 31	,  ⊢
	:
26	theorem		⊢
	proveit.numbers.division.div_real_closure
27	instantiation	133, 62, 32	⊢
	: , : , :
28	instantiation	33, 49, 135	,  ⊢
	: , :
29	instantiation	34, 35	,  ⊢
	:
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
31	instantiation	37, 36, 39	,  ⊢
	: , :
32	instantiation	133, 73, 122	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
35	instantiation	37, 38, 39	,  ⊢
	: , :
36	instantiation	42, 40, 41	,  ⊢
	:
37	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
38	instantiation	42, 43, 44	,  ⊢
	:
39	instantiation	133, 48, 45	⊢
	: , : , :
40	instantiation	133, 48, 46	,  ⊢
	: , : , :
41	instantiation	50, 47	,  ⊢
	: , :
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
43	instantiation	133, 48, 49	,  ⊢
	: , : , :
44	instantiation	50, 51	,  ⊢
	: , :
45	instantiation	133, 62, 52	⊢
	: , : , :
46	instantiation	55, 53, 57	,  ⊢
	: , :
47	instantiation	58, 54	,  ⊢
	: , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	instantiation	55, 56, 57	,  ⊢
	: , :
50	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
51	instantiation	58, 59	,  ⊢
	: , :
52	instantiation	133, 73, 132	⊢
	: , : , :
53	instantiation	133, 62, 60	,  ⊢
	: , : , :
54	instantiation	66, 67, 70, 61	,  ⊢
	: , :
55	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
56	instantiation	133, 62, 63	,  ⊢
	: , : , :
57	instantiation	64, 65	⊢
	:
58	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
59	instantiation	66, 67, 91, 68	,  ⊢
	: , :
60	instantiation	133, 73, 70	,  ⊢
	: , : , :
61	instantiation	69, 70, 71, 72	,  ⊢
	: , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
63	instantiation	133, 73, 91	,  ⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.negation.real_closure
65	instantiation	74, 75, 76	⊢
	: , :
66	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
67	instantiation	77, 78, 125, 79	⊢
	: , : , : , : , :
68	instantiation	80, 81	,  ⊢
	:
69	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
70	instantiation	133, 82, 96	,  ⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
72	instantiation	83, 84, 85	,  ⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
74	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
75	instantiation	86, 87, 88	⊢
	: , : , :
76	instantiation	89, 90	⊢
	:
77	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
78	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
79	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
80	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
81	instantiation	113, 91, 92	,  ⊢
	:
82	instantiation	120, 94, 95	⊢
	: , :
83	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
84	instantiation	93, 94, 95, 96	,  ⊢
	: , : , :
85	instantiation	97, 98	⊢
	:
86	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
87	instantiation	99, 100	⊢
	: , :
88	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
89	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
90	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
91	instantiation	133, 101, 109	,  ⊢
	: , : , :
92	instantiation	117, 102, 103	,  ⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
94	instantiation	126, 104, 122	⊢
	: , :
95	instantiation	131, 108	⊢
	:
96	assumption		⊢
97	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
98	instantiation	105, 107	⊢
	:
99	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
100	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
101	instantiation	120, 108, 127	⊢
	: , :
102	instantiation	106, 107	⊢
	:
103	instantiation	121, 108, 127, 109	,  ⊢
	: , : , :
104	instantiation	131, 127	⊢
	:
105	theorem		⊢
	proveit.numbers.negation.int_neg_closure
106	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
107	instantiation	110, 111, 112	⊢
	: , :
108	instantiation	126, 114, 122	⊢
	: , :
109	assumption		⊢
110	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
111	instantiation	113, 114, 115	⊢
	:
112	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
113	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
114	instantiation	133, 116, 124	⊢
	: , : , :
115	instantiation	117, 118, 119	⊢
	: , : , :
116	instantiation	120, 122, 123	⊢
	: , :
117	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
118	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
119	instantiation	121, 122, 123, 124	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
121	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
122	instantiation	133, 134, 125	⊢
	: , : , :
123	instantiation	126, 127, 128	⊢
	: , :
124	assumption		⊢
125	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
126	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
127	instantiation	133, 129, 130	⊢
	: , : , :
128	instantiation	131, 132	⊢
	:
129	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
130	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
131	theorem		⊢
	proveit.numbers.negation.int_closure
132	instantiation	133, 134, 135	⊢
	: , : , :
133	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
134	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
135	theorem		⊢
	proveit.numbers.numerals.decimals.nat2