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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.exp_rational_non_zero__not_zero
2instantiation47, 5, 4,  ⊢  
  : , : , :
3instantiation47, 5, 6  ⊢  
  : , : , :
4instantiation47, 8, 7,  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
6instantiation47, 8, 9  ⊢  
  : , : , :
7instantiation23, 10, 11,  ⊢  
  :
8theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
9theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
10instantiation47, 12, 19,  ⊢  
  : , : , :
11instantiation29, 13, 14,  ⊢  
  : , : , :
12instantiation34, 17, 18  ⊢  
  : , :
13instantiation15, 16  ⊢  
  :
14instantiation35, 17, 18, 19,  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
16instantiation20, 21, 33  ⊢  
  : , :
17instantiation40, 24, 36  ⊢  
  : , :
18instantiation40, 41, 22  ⊢  
  : , :
19assumption  ⊢  
20theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
21instantiation23, 24, 25  ⊢  
  :
22instantiation47, 26, 27  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
24instantiation47, 28, 38  ⊢  
  : , : , :
25instantiation29, 30, 31  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
27instantiation32, 33  ⊢  
  :
28instantiation34, 36, 37  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
30theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
31instantiation35, 36, 37, 38  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
33theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
34theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
35theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
36instantiation47, 48, 39  ⊢  
  : , : , :
37instantiation40, 41, 42  ⊢  
  : , :
38assumption  ⊢  
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
40theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
41instantiation47, 43, 44  ⊢  
  : , : , :
42instantiation45, 46  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
44theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
45theorem  ⊢  
 proveit.numbers.negation.int_closure
46instantiation47, 48, 49  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2