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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,  ⊢  
  :
3instantiation73, 8, 7  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
5instantiation73, 8, 9,  ⊢  
  : , : , :
6instantiation10, 11,  ⊢  
  : , :
7instantiation73, 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,  ⊢  
  : , :
12instantiation73, 25, 72  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
14instantiation73, 18, 19,  ⊢  
  : , : , :
15instantiation20, 21  ⊢  
  :
16theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
17instantiation22, 23, 39, 24,  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
19instantiation73, 25, 39,  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.negation.real_closure
21instantiation26, 27, 28  ⊢  
  : , :
22theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
23instantiation29, 30, 65, 31  ⊢  
  : , : , : , : , :
24instantiation32, 33,  ⊢  
  :
25theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
26theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
27instantiation34, 35, 36  ⊢  
  : , : , :
28instantiation37, 38  ⊢  
  :
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.number_sets.natural_numbers.nonzero_if_is_nat_pos
33instantiation53, 39, 40,  ⊢  
  :
34theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
35instantiation41, 42  ⊢  
  : , :
36theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
37theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
38theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
39instantiation73, 43, 49,  ⊢  
  : , : , :
40instantiation57, 44, 45,  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
43instantiation60, 48, 67  ⊢  
  : , :
44instantiation46, 47  ⊢  
  :
45instantiation61, 48, 67, 49,  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
47instantiation50, 51, 52  ⊢  
  : , :
48instantiation66, 54, 62  ⊢  
  : , :
49assumption  ⊢  
50theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
51instantiation53, 54, 55  ⊢  
  :
52theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
53theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
54instantiation73, 56, 64  ⊢  
  : , : , :
55instantiation57, 58, 59  ⊢  
  : , : , :
56instantiation60, 62, 63  ⊢  
  : , :
57theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
58theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
59instantiation61, 62, 63, 64  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
61theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
62instantiation73, 74, 65  ⊢  
  : , : , :
63instantiation66, 67, 68  ⊢  
  : , :
64assumption  ⊢  
65theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
66theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
67instantiation73, 69, 70  ⊢  
  : , : , :
68instantiation71, 72  ⊢  
  :
69theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
70theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
71theorem  ⊢  
 proveit.numbers.negation.int_closure
72instantiation73, 74, 75  ⊢  
  : , : , :
73theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
75theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2