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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.sqrd_pos_closure
2reference5,  ⊢  
3instantiation4, 5, 23, 6,  ⊢  
  : , :
4theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq
5instantiation7, 8, 9,  ⊢  
  : , :
6instantiation10, 11,  ⊢  
  : , :
7theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
8instantiation63, 31, 12,  ⊢  
  : , : , :
9instantiation13, 14  ⊢  
  :
10theorem  ⊢  
 proveit.numbers.addition.subtraction.neg_difference
11instantiation47, 15, 16,  ⊢  
  : , : , :
12instantiation63, 37, 17,  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.negation.real_closure
14instantiation18, 23, 24, 25  ⊢  
  : , : , :
15instantiation19, 20, 21,  ⊢  
  : , : , :
16instantiation22, 23, 24, 25  ⊢  
  : , : , :
17instantiation63, 26, 28,  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
19theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_eq_less
20instantiation27, 33, 34, 28,  ⊢  
  : , : , :
21instantiation29, 30  ⊢  
  :
22theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
24instantiation63, 31, 32  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
26instantiation50, 33, 34  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
28assumption  ⊢  
29theorem  ⊢  
 proveit.numbers.number_sets.integers.negative_if_in_neg_int
30instantiation35, 36  ⊢  
  :
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
32instantiation63, 37, 52  ⊢  
  : , : , :
33instantiation56, 38, 52  ⊢  
  : , :
34instantiation61, 39  ⊢  
  :
35theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
36instantiation40, 41, 42  ⊢  
  : , :
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
38instantiation61, 57  ⊢  
  :
39instantiation56, 44, 52  ⊢  
  : , :
40theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
41instantiation43, 44, 45  ⊢  
  :
42theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
43theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
44instantiation63, 46, 54  ⊢  
  : , : , :
45instantiation47, 48, 49  ⊢  
  : , : , :
46instantiation50, 52, 53  ⊢  
  : , :
47theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
48theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
49instantiation51, 52, 53, 54  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
51theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
52instantiation63, 64, 55  ⊢  
  : , : , :
53instantiation56, 57, 58  ⊢  
  : , :
54assumption  ⊢  
55theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
56theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
57instantiation63, 59, 60  ⊢  
  : , : , :
58instantiation61, 62  ⊢  
  :
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
60theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
61theorem  ⊢  
 proveit.numbers.negation.int_closure
62instantiation63, 64, 65  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
65theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2