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Show the Proof

In [1]:
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
Out[1]:
 step typerequirementsstatement
0instantiation1, 2, 3, 4,  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.division.div_real_closure
2instantiation88, 26, 5  ⊢  
  : , : , :
3instantiation6, 17, 90,  ⊢  
  : , :
4instantiation7, 8,  ⊢  
  :
5instantiation88, 33, 77  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
7theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
8instantiation9, 10, 11,  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_nonzero_closure
10instantiation12, 13, 14,  ⊢  
  :
11instantiation88, 16, 15  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
13instantiation88, 16, 17,  ⊢  
  : , : , :
14instantiation18, 19,  ⊢  
  : , :
15instantiation88, 26, 20  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
17instantiation21, 22, 23,  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
19instantiation24, 25,  ⊢  
  : , :
20instantiation88, 33, 87  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
22instantiation88, 26, 27,  ⊢  
  : , : , :
23instantiation28, 29  ⊢  
  :
24theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
25instantiation30, 31, 41, 32,  ⊢  
  : , :
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
27instantiation88, 33, 41,  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.negation.real_closure
29instantiation34, 35, 36  ⊢  
  : , :
30theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
31instantiation37, 38, 80, 39  ⊢  
  : , : , : , : , :
32instantiation40, 41, 42, 43,  ⊢  
  : , :
33theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
34theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
35instantiation44, 45, 46  ⊢  
  : , : , :
36instantiation47, 48  ⊢  
  :
37theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
38axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
39theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
40theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_int
41instantiation88, 49, 58,  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
43instantiation50, 51, 52,  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
45instantiation53, 54  ⊢  
  : , :
46theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
47theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
48theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
49instantiation75, 56, 57  ⊢  
  : , :
50theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_eq_less
51instantiation55, 56, 57, 58,  ⊢  
  : , : , :
52instantiation59, 60  ⊢  
  :
53theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
55theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
56instantiation81, 61, 77  ⊢  
  : , :
57instantiation86, 62  ⊢  
  :
58assumption  ⊢  
59theorem  ⊢  
 proveit.numbers.number_sets.integers.negative_if_in_neg_int
60instantiation63, 64  ⊢  
  :
61instantiation86, 82  ⊢  
  :
62instantiation81, 69, 77  ⊢  
  : , :
63theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
64instantiation65, 66, 67  ⊢  
  : , :
65theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
66instantiation68, 69, 70  ⊢  
  :
67theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
68theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
69instantiation88, 71, 79  ⊢  
  : , : , :
70instantiation72, 73, 74  ⊢  
  : , : , :
71instantiation75, 77, 78  ⊢  
  : , :
72theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
73theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
74instantiation76, 77, 78, 79  ⊢  
  : , : , :
75theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
76theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
77instantiation88, 89, 80  ⊢  
  : , : , :
78instantiation81, 82, 83  ⊢  
  : , :
79assumption  ⊢  
80theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
81theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
82instantiation88, 84, 85  ⊢  
  : , : , :
83instantiation86, 87  ⊢  
  :
84theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
85theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
86theorem  ⊢  
 proveit.numbers.negation.int_closure
87instantiation88, 89, 90  ⊢  
  : , : , :
88theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
89theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
90theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2