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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  ⊢  
  : , : , :
1reference40  ⊢  
2theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
3instantiation40, 4, 5  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
5instantiation40, 6, 7  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
7instantiation40, 8, 9  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
9instantiation10, 11, 12  ⊢  
  :
10theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
11instantiation40, 13, 21  ⊢  
  : , : , :
12instantiation14, 15, 16  ⊢  
  : , : , :
13instantiation17, 19, 20  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
15theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
16instantiation18, 19, 20, 21  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
18theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
19instantiation40, 32, 22  ⊢  
  : , : , :
20instantiation34, 23, 24  ⊢  
  : , :
21theorem  ⊢  
 proveit.physics.quantum.QPE._e_value_in_e_domain
22theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
23instantiation25, 28, 26  ⊢  
  : , :
24instantiation27, 28  ⊢  
  :
25theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
26instantiation29, 30, 31  ⊢  
  :
27theorem  ⊢  
 proveit.numbers.negation.int_closure
28instantiation40, 32, 33  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
30instantiation34, 35, 36  ⊢  
  : , :
31instantiation37, 38  ⊢  
  : , :
32theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
33theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
34theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
35instantiation40, 39, 44  ⊢  
  : , : , :
36instantiation40, 41, 42  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.addition.subtraction.nonneg_difference
38instantiation43, 44  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
40theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
42instantiation45, 46  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
44axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
45theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
46theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1