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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.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
2instantiation68, 4, 5,  ⊢  
  : , : , :
3instantiation6, 7,  ⊢  
  : , :
4theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
5instantiation8, 9, 10,  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
7instantiation11, 12,  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
9instantiation68, 13, 14,  ⊢  
  : , : , :
10instantiation15, 16  ⊢  
  :
11theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
12instantiation17, 18, 34, 19,  ⊢  
  : , :
13theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
14instantiation68, 20, 34,  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.negation.real_closure
16instantiation21, 22, 23  ⊢  
  : , :
17theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
18instantiation24, 25, 60, 26  ⊢  
  : , : , : , : , :
19instantiation27, 28,  ⊢  
  :
20theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
21theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
22instantiation29, 30, 31  ⊢  
  : , : , :
23instantiation32, 33  ⊢  
  :
24theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
25axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
26theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28instantiation48, 34, 35,  ⊢  
  :
29theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
30instantiation36, 37  ⊢  
  : , :
31theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
32theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
33theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
34instantiation68, 38, 44,  ⊢  
  : , : , :
35instantiation52, 39, 40,  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
38instantiation55, 43, 62  ⊢  
  : , :
39instantiation41, 42  ⊢  
  :
40instantiation56, 43, 62, 44,  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
42instantiation45, 46, 47  ⊢  
  : , :
43instantiation61, 49, 57  ⊢  
  : , :
44assumption  ⊢  
45theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
46instantiation48, 49, 50  ⊢  
  :
47theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
48theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
49instantiation68, 51, 59  ⊢  
  : , : , :
50instantiation52, 53, 54  ⊢  
  : , : , :
51instantiation55, 57, 58  ⊢  
  : , :
52theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
53theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
54instantiation56, 57, 58, 59  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
56theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
57instantiation68, 69, 60  ⊢  
  : , : , :
58instantiation61, 62, 63  ⊢  
  : , :
59assumption  ⊢  
60theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
61theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
62instantiation68, 64, 65  ⊢  
  : , : , :
63instantiation66, 67  ⊢  
  :
64theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
65theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
66theorem  ⊢  
 proveit.numbers.negation.int_closure
67instantiation68, 69, 70  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
70theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2