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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, 5, 6,  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.multiplication.mult_real_pos_closure
2theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
3instantiation7  ⊢  
  : , : , :
4instantiation59, 9, 8  ⊢  
  : , : , :
5instantiation59, 9, 10  ⊢  
  : , : , :
6instantiation11, 12,  ⊢  
  :
7theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
8instantiation59, 14, 13  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
10instantiation59, 14, 15  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.absolute_value.abs_nonzero_closure
12instantiation16, 17, 18,  ⊢  
  :
13theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat4
14theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
15theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
16theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
17instantiation59, 19, 20  ⊢  
  : , : , :
18instantiation21, 22,  ⊢  
  : , :
19theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
20instantiation23, 24, 31, 25  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
22instantiation26, 27, 28, 29,  ⊢  
  : , :
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
24instantiation30, 31  ⊢  
  :
25instantiation32, 37  ⊢  
  :
26theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt
27instantiation33, 34, 56, 35  ⊢  
  : , : , : , : , :
28instantiation59, 36, 37  ⊢  
  : , : , :
29assumption  ⊢  
30theorem  ⊢  
 proveit.numbers.negation.real_closure
31instantiation38, 39, 40, 41  ⊢  
  : , :
32theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
33theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
34axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
35theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36instantiation42, 43, 55  ⊢  
  : , :
37assumption  ⊢  
38theorem  ⊢  
 proveit.numbers.division.div_real_closure
39instantiation59, 45, 44  ⊢  
  : , : , :
40instantiation59, 45, 46  ⊢  
  : , : , :
41instantiation47, 48  ⊢  
  :
42theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
43instantiation49, 50, 51  ⊢  
  : , :
44instantiation59, 52, 51  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
46instantiation59, 52, 53  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
48theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
49theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
50instantiation54, 55  ⊢  
  :
51instantiation59, 57, 56  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
53instantiation59, 57, 58  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.negation.int_closure
55instantiation59, 60, 61  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
59theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
61theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos