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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.nonzero_if_in_real_nonzero
2instantiation52, 3, 4,  ⊢  
  : , : , :
3theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
4instantiation5, 6, 7,  ⊢  
  :
5theorem  ⊢  
 proveit.numbers.exponentiation.sqrd_pos_closure
6instantiation52, 8, 9,  ⊢  
  : , : , :
7instantiation10, 14, 11, 12,  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
9instantiation52, 13, 14,  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_int
11theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
12instantiation15, 16, 17,  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
14instantiation52, 18, 20,  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_eq_less
16instantiation19, 23, 24, 20,  ⊢  
  : , : , :
17instantiation21, 22  ⊢  
  :
18instantiation39, 23, 24  ⊢  
  : , :
19theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
20assumption  ⊢  
21theorem  ⊢  
 proveit.numbers.number_sets.integers.negative_if_in_neg_int
22instantiation25, 26  ⊢  
  :
23instantiation45, 27, 41  ⊢  
  : , :
24instantiation50, 28  ⊢  
  :
25theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
26instantiation29, 30, 31  ⊢  
  : , :
27instantiation50, 46  ⊢  
  :
28instantiation45, 33, 41  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
30instantiation32, 33, 34  ⊢  
  :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
32theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
33instantiation52, 35, 43  ⊢  
  : , : , :
34instantiation36, 37, 38  ⊢  
  : , : , :
35instantiation39, 41, 42  ⊢  
  : , :
36theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
37theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
38instantiation40, 41, 42, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
40theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
41instantiation52, 53, 44  ⊢  
  : , : , :
42instantiation45, 46, 47  ⊢  
  : , :
43assumption  ⊢  
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
45theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
46instantiation52, 48, 49  ⊢  
  : , : , :
47instantiation50, 51  ⊢  
  :
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
49theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
50theorem  ⊢  
 proveit.numbers.negation.int_closure
51instantiation52, 53, 54  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2