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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  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.negation.negated_weak_bound
2instantiation5, 9, 8, 6  ⊢  
  : , :
3instantiation5, 10, 8, 6  ⊢  
  : , :
4instantiation7, 8, 9, 10, 11, 12  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.numbers.division.div_real_closure
6instantiation13, 20  ⊢  
  :
7theorem  ⊢  
 proveit.numbers.division.weak_div_from_numer_bound__pos_denom
8instantiation16, 17, 20  ⊢  
  : , : , :
9instantiation36, 14, 15  ⊢  
  : , : , :
10instantiation16, 17, 38  ⊢  
  : , : , :
11instantiation18, 28, 33, 26  ⊢  
  : , : , :
12instantiation19, 20  ⊢  
  :
13theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
14theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
15instantiation36, 21, 22  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
17instantiation23, 24  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
19theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
20theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
21theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
22instantiation36, 25, 26  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
25instantiation27, 28, 33  ⊢  
  : , :
26assumption  ⊢  
27theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
28instantiation29, 30, 31  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
30instantiation32, 33  ⊢  
  :
31instantiation36, 34, 35  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.negation.int_closure
33instantiation36, 37, 38  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
35theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
36theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
37theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
38theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos