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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,  ⊢  
  :
1theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
2instantiation3, 4, 5,  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.multiplication.mult_real_pos_closure_bin
4instantiation54, 6, 7  ⊢  
  : , : , :
5instantiation8, 9,  ⊢  
  :
6theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
7instantiation54, 10, 43  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.absolute_value.abs_nonzero_closure
9instantiation11, 12, 13,  ⊢  
  :
10theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
11theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
12instantiation54, 14, 15  ⊢  
  : , : , :
13instantiation16, 17,  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
15instantiation18, 19, 26, 20  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
17instantiation21, 22, 23, 24,  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
19instantiation25, 26  ⊢  
  :
20instantiation27, 32  ⊢  
  :
21theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt
22instantiation28, 29, 51, 30  ⊢  
  : , : , : , : , :
23instantiation54, 31, 32  ⊢  
  : , : , :
24assumption  ⊢  
25theorem  ⊢  
 proveit.numbers.negation.real_closure
26instantiation33, 34, 35, 36  ⊢  
  : , :
27theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
28theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
29axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
30theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
31instantiation37, 38, 50  ⊢  
  : , :
32assumption  ⊢  
33theorem  ⊢  
 proveit.numbers.division.div_real_closure
34instantiation54, 40, 39  ⊢  
  : , : , :
35instantiation54, 40, 41  ⊢  
  : , : , :
36instantiation42, 43  ⊢  
  :
37theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
38instantiation44, 45, 46  ⊢  
  : , :
39instantiation54, 47, 46  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
41instantiation54, 47, 48  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
43theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
44theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
45instantiation49, 50  ⊢  
  :
46instantiation54, 52, 51  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
48instantiation54, 52, 53  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.negation.int_closure
50instantiation54, 55, 56  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
52theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
54theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
56theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos