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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,  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_nonzero_closure
2instantiation4, 5, 6,  ⊢  
  :
3instantiation80, 8, 7  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
5instantiation80, 8, 9,  ⊢  
  : , : , :
6instantiation10, 11,  ⊢  
  : , :
7instantiation80, 18, 12  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
9instantiation13, 14, 15,  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
11instantiation16, 17,  ⊢  
  : , :
12instantiation80, 25, 79  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
14instantiation80, 18, 19,  ⊢  
  : , : , :
15instantiation20, 21  ⊢  
  :
16theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
17instantiation22, 23, 33, 24,  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
19instantiation80, 25, 33,  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.negation.real_closure
21instantiation26, 27, 28  ⊢  
  : , :
22theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
23instantiation29, 30, 72, 31  ⊢  
  : , : , : , : , :
24instantiation32, 33, 34, 35,  ⊢  
  : , :
25theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
26theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
27instantiation36, 37, 38  ⊢  
  : , : , :
28instantiation39, 40  ⊢  
  :
29theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
30axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
31theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_int
33instantiation80, 41, 50,  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
35instantiation42, 43, 44,  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
37instantiation45, 46  ⊢  
  : , :
38theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
39theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
40theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
41instantiation67, 48, 49  ⊢  
  : , :
42theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_eq_less
43instantiation47, 48, 49, 50,  ⊢  
  : , : , :
44instantiation51, 52  ⊢  
  :
45theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
47theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
48instantiation73, 53, 69  ⊢  
  : , :
49instantiation78, 54  ⊢  
  :
50assumption  ⊢  
51theorem  ⊢  
 proveit.numbers.number_sets.integers.negative_if_in_neg_int
52instantiation55, 56  ⊢  
  :
53instantiation78, 74  ⊢  
  :
54instantiation73, 61, 69  ⊢  
  : , :
55theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
56instantiation57, 58, 59  ⊢  
  : , :
57theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
58instantiation60, 61, 62  ⊢  
  :
59theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
60theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
61instantiation80, 63, 71  ⊢  
  : , : , :
62instantiation64, 65, 66  ⊢  
  : , : , :
63instantiation67, 69, 70  ⊢  
  : , :
64theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
65theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
66instantiation68, 69, 70, 71  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
68theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
69instantiation80, 81, 72  ⊢  
  : , : , :
70instantiation73, 74, 75  ⊢  
  : , :
71assumption  ⊢  
72theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
73theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
74instantiation80, 76, 77  ⊢  
  : , : , :
75instantiation78, 79  ⊢  
  :
76theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
77theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
78theorem  ⊢  
 proveit.numbers.negation.int_closure
79instantiation80, 81, 82  ⊢  
  : , : , :
80theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
81theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
82theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2